{"id":6819,"date":"2024-07-27T13:01:03","date_gmt":"2024-07-27T05:01:03","guid":{"rendered":""},"modified":"2024-07-27T13:01:03","modified_gmt":"2024-07-27T05:01:03","slug":"autostore\u673a\u5668\u4eba\u7a0b\u5e8f_\u673a\u5668\u4eba\u5de5\u7a0b\u5e08\u662f\u505a\u4ec0\u4e48\u7684","status":"publish","type":"post","link":"https:\/\/mushiming.com\/6819.html","title":{"rendered":"autostore\u673a\u5668\u4eba\u7a0b\u5e8f_\u673a\u5668\u4eba\u5de5\u7a0b\u5e08\u662f\u505a\u4ec0\u4e48\u7684"},"content":{"rendered":"<p><svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" style=\"display: none;\"> \n <path stroke-linecap=\"round\" d=\"M5,0 0,2.5 5,5z\" id=\"raphael-marker-block\" style=\"-webkit-tap-highlight-color: rgba(0, 0, 0, 0);\"><\/path> \n<\/svg> <\/p>\n<h3>\u4e00\u3001\u5f15\u5165<\/h3>\n<p>GraphSLAM\u662f\u89e3\u51b3\u5b8c\u6574\u7684slam\u95ee\u9898\u7684slam\u7b97\u6cd5\u3002\u8fd9\u610f\u5473\u7740\u8be5\u7b97\u6cd5\u5c06\u6062\u590d\u6574\u4e2a\u8def\u5f84\u548c\u5730\u56fe\uff0c\u800c\u4e0d\u4ec5\u4ec5\u662f\u6700\u8fd1\u7684\u59ff\u52bf\u548c\u5730\u56fe\u3002\u8fd9\u79cd\u5dee\u5f02\u4f7f\u5b83\u53ef\u4ee5\u8003\u8651\u5f53\u524d\u59ff\u52bf\u4e0e\u5148\u524d\u59ff\u52bf\u4e4b\u95f4\u7684\u4f9d\u8d56\u6027\u3002\u9002\u7528\u4e8e\u6211\u4eec\u7684GraphSLAM\u7684\u4e00\u4e2a\u793a\u4f8b\u662f\u5730\u4e0b\u91c7\u77ff\u3002\u6bcf\u5929\u90fd\u7528\u5728\u94bb\u5b54\u673a\u4e0a\u7684\u5927\u578b\u673a\u5668\u5728\u5ca9\u58c1\u4e0a\u5207\u5272\u3002\u73af\u5883\u77ac\u606f\u4e07\u53d8\uff0c\u4fdd\u6301\u6b63\u786e\u7684\u5de5\u4f5c\u7a7a\u95f4\u56fe\u975e\u5e38\u91cd\u8981\u3002\u6620\u5c04\u6b64\u7a7a\u95f4\u7684\u4e00\u79cd\u65b9\u6cd5\u662f\u5728\u5468\u56f4\u73af\u5883\u4e2d\u9a7e\u9a76\u88c5\u6709\u6fc0\u5149\u96f7\u8fbe\u7684\u8f66\u8f86\u5e76\u6536\u96c6\u6709\u5173\u5468\u56f4\u73af\u5883\u7684\u6570\u636e\u3002<\/p>\n<p>GraphSLAM \u7b97\u6cd5\u89e3\u51b3\u4e86\u5168SLAM \u95ee\u9898\u3002\u8be5\u7b97\u6cd5\u65e8\u5728\u89e3\u51b3\u5b9a\u4e49\u5728\u6240\u6709\u4f4d\u59ff\u548c\u5730\u56fe\u4e2d\u6240\u6709\u7279\u5f81\u4e0a\u7684\u79bb\u7ebf\u95ee\u9898\u3002<\/p>\n<h3>\u4e8c\u3001GraphSLAM\u6a21\u578b<\/h3>\n<h4>1. \u6700\u5927\u4f3c\u7136\u4f30\u8ba1<\/h4>\n<p>GraphSLAM\u7684\u6838\u5fc3\u662f\u56fe\u5f62\u4f18\u5316-\u5c06\u56fe\u5f62\u4e2d\u6240\u6709\u7ea6\u675f\u4e2d\u5b58\u5728\u7684\u9519\u8bef\u6700\u5c0f\u5316\u7684\u8fc7\u7a0b\u3002\u8ba9\u6211\u4eec\u770b\u4e00\u4e0b\u8fd9\u4e9b\u7ea6\u675f\uff0c\u5e76\u5b66\u4e60\u5e94\u7528\u79f0\u4e3a\u6700\u5927\u4f3c\u7136\u4f30\u8ba1\uff08MLE\uff09\u7684\u539f\u7406\u6765\u6784\u9020\u548c\u89e3\u51b3\u56fe\u5f62\u7684\u4f18\u5316\u95ee\u9898\u3002<\/p>\n<h5>\uff081\uff09\u7279\u5f81\u91cf\u6d4b\u793a\u4f8b<\/h5>\n<p>\u8ba9\u6211\u4eec\u770b\u4e00\u4e2a\u975e\u5e38\u7b80\u5355\u7684\u793a\u4f8b-\u6211\u4eec\u7684\u673a\u5668\u4eba\u5728\u73af\u5883\u4e2d\u91cd\u590d\u6d4b\u91cf\u529f\u80fd\u7684\u4e00\u4e2a\u793a\u4f8b\u3002\u672c\u793a\u4f8b\u5c06\u5f15\u5bfc\u60a8\u5b8c\u6210\u89e3\u51b3\u8be5\u95ee\u9898\u6240\u9700\u7684\u6b65\u9aa4\uff0c\u7136\u540e\u53ef\u4ee5\u5c06\u5176\u5e94\u7528\u4e8e\u66f4\u590d\u6742\u7684\u95ee\u9898\u3002<\/p>\n<p>\u673a\u5668\u4eba\u7684\u521d\u59cb\u59ff\u6001\u7684\u65b9\u5dee\u4e3a0-\u4ec5\u4ec5\u662f\u56e0\u4e3a\u8fd9\u662f\u673a\u5668\u4eba\u7684\u8d77\u59cb\u4f4d\u7f6e\u3002\u56de\u60f3\u4e00\u4e0b\u5f00\u59cb\u4f4d\u7f6e\u53ef\u80fd\u5728\u54ea\u91cc-\u6211\u4eec\u5728\u76f8\u5bf9\u5730\u56fe\u4e2d\u5c06\u5176\u79f0\u4e3a\u4f4d\u7f6e0\u3002\u6b64\u540e\u7684\u6bcf\u4e2a\u52a8\u4f5c\u59ff\u52bf\u548c\u6d4b\u91cf\u90fd\u4e0d\u786e\u5b9a\u3002\u5728GraphSLAM\u4e2d\uff0c\u6211\u4eec\u5c06\u7ee7\u7eed\u5047\u8bbe\u8fd0\u52a8\u548c\u6d4b\u91cf\u6570\u636e\u5177\u6709\u9ad8\u65af\u566a\u58f0\u3002<\/p>\n<p>\u673a\u5668\u4eba\u6d4b\u91cf\u4e00\u4e2a\u7279\u5f81\uff0c<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> m 1 m_1 <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.58056em; vertical-align: -0.15em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">m<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.301108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\uff0c\u8fd4\u56de\u8ddd\u79bb\u4e3a1.8\u7c73\u3002<\/p>\n<p>\u5982\u679c\u6211\u4eec\u5c06\u8fd9\u4e2a\u7279\u5f81\u7c7b\u6bd4\u505a\u5f39\u7c27\u2014\u20141.8\u7c73\u662f\u5f39\u7c27\u7684\u9759\u6b62\u957f\u5ea6\u3002\u8fd9\u662f\u5f39\u7c27\u6700\u7406\u60f3\u7684\u957f\u5ea6\u3002\u7136\u800c\uff0c\u5f39\u7c27\u6709\u53ef\u80fd\u88ab\u538b\u7f29\u6216\u62c9\u957f\uff0c\u4ee5\u9002\u5e94\u4f5c\u7528\u4e8e\u7cfb\u7edf\u7684\u5176\u4ed6\u529b(\u7ea6\u675f)\u3002<\/p>\n<p>\u8fd9\u79cd\u6d4b\u91cf\u7684\u6982\u7387\u5206\u5e03\u53ef\u4ee5\u5b9a\u4e49\u4e3a\uff0c<br \/> <span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"> p ( x ) = 1 \u03c3 2 \u03c0 e \u2212 1 2 ( z 1 \u2212 ( x 0 + 1.8 ) ) 2 \u03c3 2 p(x)=\\frac{1}{\u03c3\\sqrt{2\u03c0}}e^{-\\frac{1}{2}\\frac{(z_1\u2212(x_0+1.8))^2}{\u03c3^2}} <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em; vertical-align: -0.25em;\"><\/span><span class=\"mord mathdefault\">p<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathdefault\">x<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 2.28391em; vertical-align: -0.93em;\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.32144em;\"><span class=\"\" style=\"top: -2.20278em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\" style=\"margin-right: 0.03588em;\">\u03c3<\/span><span class=\"mord sqrt\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.90722em;\"><span class=\"svg-align\" style=\"top: -3em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"mord\" style=\"padding-left: 0.833em;\"><span class=\"mord\">2<\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.03588em;\">\u03c0<\/span><\/span><\/span><span class=\"\" style=\"top: -2.86722em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"hide-tail\" style=\"min-width: 0.853em; height: 1.08em;\"><br \/>\n <svg width=\"400em\" height=\"1.08em\" viewbox=\"0 0 400000 1080\" preserveaspectratio=\"xMinYMin slice\"> \n <path d=\"M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,\n-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,\n-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,\n35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,\n-221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467\ns-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422\ns-65,47,-65,47z M834 80H400000v40H845z\"><\/path> \n <\/svg><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.13278em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em;\"><\/span><\/span><span class=\"\" style=\"top: -3.677em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"mord\"><span class=\"mord\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.93em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><span class=\"mord\"><span class=\"mord mathdefault\">e<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.35391em;\"><span class=\"\" style=\"top: -3.45342em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">\u2212<\/span><span class=\"mord mtight\"><span class=\"mopen nulldelimiter sizing reset-size3 size6\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.844314em;\"><span class=\"\" style=\"top: -2.656em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"sizing reset-size3 size1 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.2255em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"frac-line mtight\" style=\"border-bottom-width: 0.049em;\"><\/span><\/span><span class=\"\" style=\"top: -3.384em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"sizing reset-size3 size1 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.344em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter sizing reset-size3 size6\"><\/span><\/span><span class=\"mord mtight\"><span class=\"mopen nulldelimiter sizing reset-size3 size6\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.28641em;\"><span class=\"\" style=\"top: -2.50619em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"sizing reset-size3 size1 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.03588em;\">\u03c3<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.93844em;\"><span class=\"\" style=\"top: -2.93844em; margin-right: 0.1em;\"><span class=\"pstrut\" style=\"height: 2.64444em;\"><\/span><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.2255em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"frac-line mtight\" style=\"border-bottom-width: 0.049em;\"><\/span><\/span><span class=\"\" style=\"top: -3.53753em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"sizing reset-size3 size1 mtight\"><span class=\"mord mtight\"><span class=\"mopen mtight\">(<\/span><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.04398em;\">z<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3448em;\"><span class=\"\" style=\"top: -2.3448em; margin-left: -0.04398em; margin-right: 0.1em;\"><span class=\"pstrut\" style=\"height: 2.64444em;\"><\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.29964em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord mtight\">\u2212<\/span><span class=\"mopen mtight\">(<\/span><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3448em;\"><span class=\"\" style=\"top: -2.3448em; margin-left: 0em; margin-right: 0.1em;\"><span class=\"pstrut\" style=\"height: 2.64444em;\"><\/span><span class=\"mord mtight\">0<\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.29964em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mbin mtight\">+<\/span><span class=\"mord mtight\">1<\/span><span class=\"mord mtight\">.<\/span><span class=\"mord mtight\">8<\/span><span class=\"mclose mtight\">)<\/span><span class=\"mclose mtight\"><span class=\"mclose mtight\">)<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.04844em;\"><span class=\"\" style=\"top: -3.04844em; margin-right: 0.1em;\"><span class=\"pstrut\" style=\"height: 2.64444em;\"><\/span><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.493814em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter sizing reset-size3 size6\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p>\u7b80\u5355\u5730\u8bf4\uff0c\u5f53<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> z 1 z_1 <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.58056em; vertical-align: -0.15em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\" style=\"margin-right: 0.04398em;\">z<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.301108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: -0.04398em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u548c<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> x 0 x_0 <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.58056em; vertical-align: -0.15em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.301108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">0<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u76f8\u8ddd1.8\u7c73\u65f6\uff0c\u6982\u7387\u5206\u5e03\u6700\u9ad8\u3002<br \/> <img decoding=\"async\" src=\"https:\/\/img-blog.csdnimg.cn\/20200521001723942.png\" =\"\" =\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" alt=\"autostore\u673a\u5668\u4eba\u7a0b\u5e8f_\u673a\u5668\u4eba\u5de5\u7a0b\u5e08\u662f\u505a\u4ec0\u4e48\u7684 (https:\/\/mushiming.com\/) \u7b2c1\u5f20\" title=\"autostore\u673a\u5668\u4eba\u7a0b\u5e8f_\u673a\u5668\u4eba\u5de5\u7a0b\u5e08\u662f\u505a\u4ec0\u4e48\u7684 \u7b2c1\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" ><\/p>\n<p>\u7136\u800c\uff0c\u7531\u4e8e\u4f4d\u7f6e\u7684\u7b2c\u4e00\u4e2a\u59ff\u52bf\uff0c<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> x 0 x_0 <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.58056em; vertical-align: -0.15em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.301108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">0<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u8bbe\u4e3a0\uff0c\u8fd9\u4e00\u9879\u53ef\u4ee5\u7b80\u5355\u5730\u4ece\u65b9\u7a0b\u4e2d\u79fb\u9664\u3002<br \/> <span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"> p ( x ) = 1 \u03c3 2 \u03c0 e \u2212 1 2 ( z 1 \u2212 1.8 ) 2 \u03c3 2 p(x)=\\frac{1}{\u03c3\\sqrt{2\u03c0}}e^{-\\frac{1}{2}\\frac{(z_1\u22121.8)^2}{\u03c3^2}} <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em; vertical-align: -0.25em;\"><\/span><span class=\"mord mathdefault\">p<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathdefault\">x<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 2.28391em; vertical-align: -0.93em;\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.32144em;\"><span class=\"\" style=\"top: -2.20278em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\" style=\"margin-right: 0.03588em;\">\u03c3<\/span><span class=\"mord sqrt\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.90722em;\"><span class=\"svg-align\" style=\"top: -3em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"mord\" style=\"padding-left: 0.833em;\"><span class=\"mord\">2<\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.03588em;\">\u03c0<\/span><\/span><\/span><span class=\"\" style=\"top: -2.86722em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"hide-tail\" style=\"min-width: 0.853em; height: 1.08em;\"><br \/>\n <svg width=\"400em\" height=\"1.08em\" viewbox=\"0 0 400000 1080\" preserveaspectratio=\"xMinYMin slice\"> \n <path d=\"M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,\n-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,\n-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,\n35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,\n-221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467\ns-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422\ns-65,47,-65,47z M834 80H400000v40H845z\"><\/path> \n <\/svg><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.13278em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em;\"><\/span><\/span><span class=\"\" style=\"top: -3.677em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"mord\"><span class=\"mord\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.93em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><span class=\"mord\"><span class=\"mord mathdefault\">e<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.35391em;\"><span class=\"\" style=\"top: -3.45342em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">\u2212<\/span><span class=\"mord mtight\"><span class=\"mopen nulldelimiter sizing reset-size3 size6\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.844314em;\"><span class=\"\" style=\"top: -2.656em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"sizing reset-size3 size1 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.2255em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"frac-line mtight\" style=\"border-bottom-width: 0.049em;\"><\/span><\/span><span class=\"\" style=\"top: -3.384em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"sizing reset-size3 size1 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.344em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter sizing reset-size3 size6\"><\/span><\/span><span class=\"mord mtight\"><span class=\"mopen nulldelimiter sizing reset-size3 size6\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.28641em;\"><span class=\"\" style=\"top: -2.50619em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"sizing reset-size3 size1 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.03588em;\">\u03c3<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.93844em;\"><span class=\"\" style=\"top: -2.93844em; margin-right: 0.1em;\"><span class=\"pstrut\" style=\"height: 2.64444em;\"><\/span><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.2255em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"frac-line mtight\" style=\"border-bottom-width: 0.049em;\"><\/span><\/span><span class=\"\" style=\"top: -3.53753em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"sizing reset-size3 size1 mtight\"><span class=\"mord mtight\"><span class=\"mopen mtight\">(<\/span><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.04398em;\">z<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3448em;\"><span class=\"\" style=\"top: -2.3448em; margin-left: -0.04398em; margin-right: 0.1em;\"><span class=\"pstrut\" style=\"height: 2.64444em;\"><\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.29964em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord mtight\">\u2212<\/span><span class=\"mord mtight\">1<\/span><span class=\"mord mtight\">.<\/span><span class=\"mord mtight\">8<\/span><span class=\"mclose mtight\"><span class=\"mclose mtight\">)<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.04844em;\"><span class=\"\" style=\"top: -3.04844em; margin-right: 0.1em;\"><span class=\"pstrut\" style=\"height: 2.64444em;\"><\/span><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.493814em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter sizing reset-size3 size6\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><br \/> \u63a5\u4e0b\u6765\uff0c\u673a\u5668\u4eba\u5bf9\u73af\u5883\u4e2d\u7684\u76f8\u540c\u7279\u5f81\u8fdb\u884c\u53e6\u4e00\u6b21\u6d4b\u91cf\u3002\u8fd9\u6b21\uff0c\u6570\u636e\u8bfb\u53d6\u4e3a2.2m\u3002\u7531\u4e8e\u5b58\u5728\u4e24\u4e2a\u76f8\u4e92\u77db\u76fe\u7684\u6d4b\u91cf\u7ed3\u679c\uff0c\u56e0\u6b64\u8fd9\u662f\u4e00\u4e2a\u8d85\u5b9a\u7684\u7cfb\u7edf-\u56e0\u4e3a\u65b9\u7a0b\u5f0f\u591a\u4e8e\u672a\u77e5\u6570\u3002<\/p>\n<p>\u901a\u8fc7\u4e24\u6b21\u6d4b\u91cf\uff0c\u53ef\u4ee5\u901a\u8fc7\u4e24\u4e2a\u6982\u7387\u7684\u4e58\u79ef\u6765\u8868\u793a\u7279\u5f81\u7684\u6700\u53ef\u80fd\u4f4d\u7f6e\u3002<br \/> <span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"> p ( x ) = 1 \u03c3 2 \u03c0 e \u2212 1 2 ( z 1 \u2212 1.8 ) 2 \u03c3 2 \u00d7 1 \u03c3 2 \u03c0 e \u2212 1 2 ( z 1 \u2212 2.2 ) 2 \u03c3 2 p(x)=\\frac{1}{\u03c3\\sqrt{2\u03c0}}e^{-\\frac{1}{2}\\frac{(z_1\u22121.8)^2}{\u03c3^2}}\\times\\frac{1}{\u03c3\\sqrt{2\u03c0}}e^{-\\frac{1}{2}\\frac{(z_1\u22122.2)^2}{\u03c3^2}} <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em; vertical-align: -0.25em;\"><\/span><span class=\"mord mathdefault\">p<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathdefault\">x<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 2.28391em; vertical-align: -0.93em;\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.32144em;\"><span class=\"\" style=\"top: -2.20278em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\" style=\"margin-right: 0.03588em;\">\u03c3<\/span><span class=\"mord sqrt\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.90722em;\"><span class=\"svg-align\" style=\"top: -3em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"mord\" style=\"padding-left: 0.833em;\"><span class=\"mord\">2<\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.03588em;\">\u03c0<\/span><\/span><\/span><span class=\"\" style=\"top: -2.86722em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"hide-tail\" style=\"min-width: 0.853em; height: 1.08em;\"><br \/>\n <svg width=\"400em\" height=\"1.08em\" viewbox=\"0 0 400000 1080\" preserveaspectratio=\"xMinYMin slice\"> \n <path d=\"M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,\n-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,\n-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,\n35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,\n-221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467\ns-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422\ns-65,47,-65,47z M834 80H400000v40H845z\"><\/path> \n <\/svg><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.13278em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em;\"><\/span><\/span><span class=\"\" style=\"top: -3.677em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"mord\"><span class=\"mord\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.93em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><span class=\"mord\"><span class=\"mord mathdefault\">e<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.35391em;\"><span class=\"\" style=\"top: -3.45342em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">\u2212<\/span><span class=\"mord mtight\"><span class=\"mopen nulldelimiter sizing reset-size3 size6\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.844314em;\"><span class=\"\" style=\"top: -2.656em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"sizing reset-size3 size1 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.2255em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"frac-line mtight\" style=\"border-bottom-width: 0.049em;\"><\/span><\/span><span class=\"\" style=\"top: -3.384em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"sizing reset-size3 size1 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.344em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter sizing reset-size3 size6\"><\/span><\/span><span class=\"mord mtight\"><span class=\"mopen nulldelimiter sizing reset-size3 size6\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.28641em;\"><span class=\"\" style=\"top: -2.50619em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"sizing reset-size3 size1 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.03588em;\">\u03c3<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.93844em;\"><span class=\"\" style=\"top: -2.93844em; margin-right: 0.1em;\"><span class=\"pstrut\" style=\"height: 2.64444em;\"><\/span><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.2255em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"frac-line mtight\" style=\"border-bottom-width: 0.049em;\"><\/span><\/span><span class=\"\" style=\"top: -3.53753em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"sizing reset-size3 size1 mtight\"><span class=\"mord mtight\"><span class=\"mopen mtight\">(<\/span><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.04398em;\">z<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3448em;\"><span class=\"\" style=\"top: -2.3448em; margin-left: -0.04398em; margin-right: 0.1em;\"><span class=\"pstrut\" style=\"height: 2.64444em;\"><\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.29964em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord mtight\">\u2212<\/span><span class=\"mord mtight\">1<\/span><span class=\"mord mtight\">.<\/span><span class=\"mord mtight\">8<\/span><span class=\"mclose mtight\"><span class=\"mclose mtight\">)<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.04844em;\"><span class=\"\" style=\"top: -3.04844em; margin-right: 0.1em;\"><span class=\"pstrut\" style=\"height: 2.64444em;\"><\/span><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.493814em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter sizing reset-size3 size6\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><span class=\"mbin\">\u00d7<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 2.28391em; vertical-align: -0.93em;\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.32144em;\"><span class=\"\" style=\"top: -2.20278em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\" style=\"margin-right: 0.03588em;\">\u03c3<\/span><span class=\"mord sqrt\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.90722em;\"><span class=\"svg-align\" style=\"top: -3em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"mord\" style=\"padding-left: 0.833em;\"><span class=\"mord\">2<\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.03588em;\">\u03c0<\/span><\/span><\/span><span class=\"\" style=\"top: -2.86722em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"hide-tail\" style=\"min-width: 0.853em; height: 1.08em;\"><br \/>\n <svg width=\"400em\" height=\"1.08em\" viewbox=\"0 0 400000 1080\" preserveaspectratio=\"xMinYMin slice\"> \n <path d=\"M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,\n-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,\n-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,\n35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,\n-221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467\ns-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422\ns-65,47,-65,47z M834 80H400000v40H845z\"><\/path> \n <\/svg><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.13278em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em;\"><\/span><\/span><span class=\"\" style=\"top: -3.677em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"mord\"><span class=\"mord\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.93em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><span class=\"mord\"><span class=\"mord mathdefault\">e<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.35391em;\"><span class=\"\" style=\"top: -3.45342em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">\u2212<\/span><span class=\"mord mtight\"><span class=\"mopen nulldelimiter sizing reset-size3 size6\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.844314em;\"><span class=\"\" style=\"top: -2.656em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"sizing reset-size3 size1 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.2255em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"frac-line mtight\" style=\"border-bottom-width: 0.049em;\"><\/span><\/span><span class=\"\" style=\"top: -3.384em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"sizing reset-size3 size1 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.344em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter sizing reset-size3 size6\"><\/span><\/span><span class=\"mord mtight\"><span class=\"mopen nulldelimiter sizing reset-size3 size6\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.28641em;\"><span class=\"\" style=\"top: -2.50619em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"sizing reset-size3 size1 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.03588em;\">\u03c3<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.93844em;\"><span class=\"\" style=\"top: -2.93844em; margin-right: 0.1em;\"><span class=\"pstrut\" style=\"height: 2.64444em;\"><\/span><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.2255em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"frac-line mtight\" style=\"border-bottom-width: 0.049em;\"><\/span><\/span><span class=\"\" style=\"top: -3.53753em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"sizing reset-size3 size1 mtight\"><span class=\"mord mtight\"><span class=\"mopen mtight\">(<\/span><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.04398em;\">z<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3448em;\"><span class=\"\" style=\"top: -2.3448em; margin-left: -0.04398em; margin-right: 0.1em;\"><span class=\"pstrut\" style=\"height: 2.64444em;\"><\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.29964em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord mtight\">\u2212<\/span><span class=\"mord mtight\">2<\/span><span class=\"mord mtight\">.<\/span><span class=\"mord mtight\">2<\/span><span class=\"mclose mtight\"><span class=\"mclose mtight\">)<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.04844em;\"><span class=\"\" style=\"top: -3.04844em; margin-right: 0.1em;\"><span class=\"pstrut\" style=\"height: 2.64444em;\"><\/span><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.493814em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter sizing reset-size3 size6\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p>\u5728\u8fd9\u4e2a\u7b80\u5355\u7684\u793a\u4f8b\u4e2d\uff0c\u6240\u4ee5\u6211\u4eec\u53ef\u4ee5\u731c\u6d4b<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> z 1 z_1 <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.58056em; vertical-align: -0.15em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\" style=\"margin-right: 0.04398em;\">z<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.301108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: -0.04398em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u6700\u6709\u53ef\u80fd\u51fa\u73b0\u7684\u4f4d\u7f6e\u662f\u57282.0\u7c73\u5904\u3002\u7136\u800c\uff0c\u901a\u8fc7\u6700\u5927\u4f3c\u7136\u4f30\u8ba1\u8fc7\u7a0b\u6765\u7406\u89e3\u6240\u6d89\u53ca\u7684\u6b65\u9aa4\u662f\u6709\u4ef7\u503c\u7684\uff0c\u7136\u540e\u624d\u80fd\u5c06\u5176\u5e94\u7528\u4e8e\u66f4\u590d\u6742\u7684\u7cfb\u7edf\u3002<\/p>\n<p>\u8981\u89e3\u6790\u5730\u89e3\u51b3\u8fd9\u4e2a\u95ee\u9898\uff0c\u53ef\u4ee5\u91c7\u53d6\u51e0\u4e2a\u6b65\u9aa4\u628a\u65b9\u7a0b\u7b80\u5316\u6210\u66f4\u7b80\u5355\u7684\u5f62\u5f0f\u3002<\/p>\n<h6>\u5220\u9664\u6bd4\u4f8b\u7cfb\u6570<\/h6>\n<p>\u4f7f\u65b9\u7a0b\u5f0f\u6700\u5927\u5316\u7684m\u503c\u4e0d\u53d6\u51b3\u4e8e\u6bcf\u4e2a\u6307\u6570\u524d\u9762\u7684\u5e38\u6570\u3002\u8fd9\u4e9b\u662f\u6bd4\u4f8b\u7cfb\u6570\uff0c\u4f46\u662f\u5728SLAM\u4e2d\uff0c\u6211\u4eec\u901a\u5e38\u5bf9\u6982\u7387\u7684\u7edd\u5bf9\u503c\u4e0d\u611f\u5174\u8da3\uff0c\u800c\u662f\u627e\u5230\u6700\u5927\u4f3c\u7136\u4f30\u8ba1\u3002\u56e0\u6b64\uff0c\u53ef\u4ee5\u6211\u4eec\u53ef\u4ee5\u7b80\u5355\u5730\u6d88\u9664\u8fd9\u4e9b\u7cfb\u6570\u3002<br \/> <span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"> p ( x ) = e \u2212 1 2 ( z 1 \u2212 1.8 ) 2 \u03c3 2 \u00d7 e \u2212 1 2 ( z 1 \u2212 2.2 ) 2 \u03c3 2 p(x)=e^{-\\frac{1}{2}\\frac{(z_1\u22121.8)^2}{\u03c3^2}}\\times e^{-\\frac{1}{2}\\frac{(z_1\u22122.2)^2}{\u03c3^2}} <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em; vertical-align: -0.25em;\"><\/span><span class=\"mord mathdefault\">p<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathdefault\">x<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1.43724em; vertical-align: -0.08333em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">e<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.35391em;\"><span class=\"\" style=\"top: -3.45342em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">\u2212<\/span><span class=\"mord mtight\"><span class=\"mopen nulldelimiter sizing reset-size3 size6\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.844314em;\"><span class=\"\" style=\"top: -2.656em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"sizing reset-size3 size1 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.2255em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"frac-line mtight\" style=\"border-bottom-width: 0.049em;\"><\/span><\/span><span class=\"\" style=\"top: -3.384em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"sizing reset-size3 size1 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.344em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter sizing reset-size3 size6\"><\/span><\/span><span class=\"mord mtight\"><span class=\"mopen nulldelimiter sizing reset-size3 size6\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.28641em;\"><span class=\"\" style=\"top: -2.50619em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"sizing reset-size3 size1 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.03588em;\">\u03c3<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.93844em;\"><span class=\"\" style=\"top: -2.93844em; margin-right: 0.1em;\"><span class=\"pstrut\" style=\"height: 2.64444em;\"><\/span><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.2255em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"frac-line mtight\" style=\"border-bottom-width: 0.049em;\"><\/span><\/span><span class=\"\" style=\"top: -3.53753em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"sizing reset-size3 size1 mtight\"><span class=\"mord mtight\"><span class=\"mopen mtight\">(<\/span><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.04398em;\">z<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3448em;\"><span class=\"\" style=\"top: -2.3448em; margin-left: -0.04398em; margin-right: 0.1em;\"><span class=\"pstrut\" style=\"height: 2.64444em;\"><\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.29964em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord mtight\">\u2212<\/span><span class=\"mord mtight\">1<\/span><span class=\"mord mtight\">.<\/span><span class=\"mord mtight\">8<\/span><span class=\"mclose mtight\"><span class=\"mclose mtight\">)<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.04844em;\"><span class=\"\" style=\"top: -3.04844em; margin-right: 0.1em;\"><span class=\"pstrut\" style=\"height: 2.64444em;\"><\/span><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.493814em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter sizing reset-size3 size6\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><span class=\"mbin\">\u00d7<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1.35391em; vertical-align: 0em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">e<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.35391em;\"><span class=\"\" style=\"top: -3.45342em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">\u2212<\/span><span class=\"mord mtight\"><span class=\"mopen nulldelimiter sizing reset-size3 size6\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.844314em;\"><span class=\"\" style=\"top: -2.656em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"sizing reset-size3 size1 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.2255em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"frac-line mtight\" style=\"border-bottom-width: 0.049em;\"><\/span><\/span><span class=\"\" style=\"top: -3.384em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"sizing reset-size3 size1 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.344em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter sizing reset-size3 size6\"><\/span><\/span><span class=\"mord mtight\"><span class=\"mopen nulldelimiter sizing reset-size3 size6\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.28641em;\"><span class=\"\" style=\"top: -2.50619em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"sizing reset-size3 size1 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.03588em;\">\u03c3<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.93844em;\"><span class=\"\" style=\"top: -2.93844em; margin-right: 0.1em;\"><span class=\"pstrut\" style=\"height: 2.64444em;\"><\/span><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.2255em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"frac-line mtight\" style=\"border-bottom-width: 0.049em;\"><\/span><\/span><span class=\"\" style=\"top: -3.53753em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"sizing reset-size3 size1 mtight\"><span class=\"mord mtight\"><span class=\"mopen mtight\">(<\/span><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.04398em;\">z<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3448em;\"><span class=\"\" style=\"top: -2.3448em; margin-left: -0.04398em; margin-right: 0.1em;\"><span class=\"pstrut\" style=\"height: 2.64444em;\"><\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.29964em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord mtight\">\u2212<\/span><span class=\"mord mtight\">2<\/span><span class=\"mord mtight\">.<\/span><span class=\"mord mtight\">2<\/span><span class=\"mclose mtight\"><span class=\"mclose mtight\">)<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.04844em;\"><span class=\"\" style=\"top: -3.04844em; margin-right: 0.1em;\"><span class=\"pstrut\" style=\"height: 2.64444em;\"><\/span><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.493814em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter sizing reset-size3 size6\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<h6>\u5bf9\u6570\u4f3c\u7136\u51fd\u6570<\/h6>\n<p>\u6982\u7387\u7684\u4e58\u79ef\u5df2\u88ab\u7b80\u5316\uff0c\u4f46\u65b9\u7a0b\u4ecd\u7136\u76f8\u5f53\u590d\u6742\u2014\u2014\u5b58\u5728\u6307\u6570\u51fd\u6570\u3002\u8fd9\u91cc\u6709\u4e00\u4e2a\u6570\u5b66\u6027\u8d28\u53ef\u4ee5\u7528\u6765\u628a\u6307\u6570\u7684\u4e58\u79ef\u8f6c\u6362\u6210\u6307\u6570\u7684\u548c\u3002<br \/> \u9996\u5148\uff0c\u6211\u4eec\u5fc5\u987b\u4f7f\u7528\u4e0b\u9762\u7684\u6027\u8d28\uff0c<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> e a e b = e a + b e^ae^b=e^{a+b} <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.849108em; vertical-align: 0em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">e<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.664392em;\"><span class=\"\" style=\"top: -3.063em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">a<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\"><span class=\"mord mathdefault\">e<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.849108em;\"><span class=\"\" style=\"top: -3.063em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.849108em; vertical-align: 0em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">e<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.849108em;\"><span class=\"\" style=\"top: -3.063em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">a<\/span><span class=\"mbin mtight\">+<\/span><span class=\"mord mathdefault mtight\">b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\uff0c\u628a\u4e24\u4e2a\u6307\u6570\u5408\u5e76\u6210\u4e00\u4e2a\u3002<br \/> <span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"> e \u2212 1 2 ( z 1 \u2212 1.8 ) 2 \u03c3 2 \u00d7 e \u2212 1 2 ( z 1 \u2212 2.2 ) 2 \u03c3 2 = e \u2212 1 2 ( z 1 \u2212 1.8 ) 2 \u03c3 2 \u2212 1 2 ( z 1 \u2212 2.2 ) 2 \u03c3 2 e^{-\\frac{1}{2}\\frac{(z_1\u22121.8)^2}{\u03c3^2}}\\times e^{-\\frac{1}{2}\\frac{(z_1\u22122.2)^2}{\u03c3^2}} = e^{-\\frac{1}{2}\\frac{(z_1\u22121.8)^2}{\u03c3^2}-\\frac{1}{2}\\frac{(z_1\u22122.2)^2}{\u03c3^2}} <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.43724em; vertical-align: -0.08333em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">e<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.35391em;\"><span class=\"\" style=\"top: -3.45342em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">\u2212<\/span><span class=\"mord mtight\"><span class=\"mopen nulldelimiter sizing reset-size3 size6\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.844314em;\"><span class=\"\" style=\"top: -2.656em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"sizing reset-size3 size1 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.2255em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"frac-line mtight\" style=\"border-bottom-width: 0.049em;\"><\/span><\/span><span class=\"\" style=\"top: -3.384em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"sizing reset-size3 size1 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.344em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter sizing reset-size3 size6\"><\/span><\/span><span class=\"mord mtight\"><span class=\"mopen nulldelimiter sizing reset-size3 size6\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.28641em;\"><span class=\"\" style=\"top: -2.50619em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"sizing reset-size3 size1 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.03588em;\">\u03c3<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.93844em;\"><span class=\"\" style=\"top: -2.93844em; margin-right: 0.1em;\"><span class=\"pstrut\" style=\"height: 2.64444em;\"><\/span><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.2255em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"frac-line mtight\" style=\"border-bottom-width: 0.049em;\"><\/span><\/span><span class=\"\" style=\"top: -3.53753em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"sizing reset-size3 size1 mtight\"><span class=\"mord mtight\"><span class=\"mopen mtight\">(<\/span><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.04398em;\">z<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3448em;\"><span class=\"\" style=\"top: -2.3448em; margin-left: -0.04398em; margin-right: 0.1em;\"><span class=\"pstrut\" style=\"height: 2.64444em;\"><\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.29964em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord mtight\">\u2212<\/span><span class=\"mord mtight\">1<\/span><span class=\"mord mtight\">.<\/span><span class=\"mord mtight\">8<\/span><span class=\"mclose mtight\"><span class=\"mclose mtight\">)<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.04844em;\"><span class=\"\" style=\"top: -3.04844em; margin-right: 0.1em;\"><span class=\"pstrut\" style=\"height: 2.64444em;\"><\/span><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.493814em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter sizing reset-size3 size6\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><span class=\"mbin\">\u00d7<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1.35391em; vertical-align: 0em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">e<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.35391em;\"><span class=\"\" style=\"top: -3.45342em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">\u2212<\/span><span class=\"mord mtight\"><span class=\"mopen nulldelimiter sizing reset-size3 size6\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.844314em;\"><span class=\"\" style=\"top: -2.656em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"sizing reset-size3 size1 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.2255em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"frac-line mtight\" style=\"border-bottom-width: 0.049em;\"><\/span><\/span><span class=\"\" style=\"top: -3.384em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"sizing reset-size3 size1 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.344em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter sizing reset-size3 size6\"><\/span><\/span><span class=\"mord mtight\"><span class=\"mopen nulldelimiter sizing reset-size3 size6\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.28641em;\"><span class=\"\" style=\"top: -2.50619em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"sizing reset-size3 size1 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.03588em;\">\u03c3<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.93844em;\"><span class=\"\" style=\"top: -2.93844em; margin-right: 0.1em;\"><span class=\"pstrut\" style=\"height: 2.64444em;\"><\/span><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.2255em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"frac-line mtight\" style=\"border-bottom-width: 0.049em;\"><\/span><\/span><span class=\"\" style=\"top: -3.53753em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"sizing reset-size3 size1 mtight\"><span class=\"mord mtight\"><span class=\"mopen mtight\">(<\/span><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.04398em;\">z<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3448em;\"><span class=\"\" style=\"top: -2.3448em; margin-left: -0.04398em; margin-right: 0.1em;\"><span class=\"pstrut\" style=\"height: 2.64444em;\"><\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.29964em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord mtight\">\u2212<\/span><span class=\"mord mtight\">2<\/span><span class=\"mord mtight\">.<\/span><span class=\"mord mtight\">2<\/span><span class=\"mclose mtight\"><span class=\"mclose mtight\">)<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.04844em;\"><span class=\"\" style=\"top: -3.04844em; margin-right: 0.1em;\"><span class=\"pstrut\" style=\"height: 2.64444em;\"><\/span><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.493814em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter sizing reset-size3 size6\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1.35391em; vertical-align: 0em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">e<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.35391em;\"><span class=\"\" style=\"top: -3.45342em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">\u2212<\/span><span class=\"mord mtight\"><span class=\"mopen nulldelimiter sizing reset-size3 size6\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.844314em;\"><span class=\"\" style=\"top: -2.656em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"sizing reset-size3 size1 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.2255em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"frac-line mtight\" style=\"border-bottom-width: 0.049em;\"><\/span><\/span><span class=\"\" style=\"top: -3.384em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"sizing reset-size3 size1 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.344em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter sizing reset-size3 size6\"><\/span><\/span><span class=\"mord mtight\"><span class=\"mopen nulldelimiter sizing reset-size3 size6\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.28641em;\"><span class=\"\" style=\"top: -2.50619em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"sizing reset-size3 size1 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.03588em;\">\u03c3<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.93844em;\"><span class=\"\" style=\"top: -2.93844em; margin-right: 0.1em;\"><span class=\"pstrut\" style=\"height: 2.64444em;\"><\/span><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.2255em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"frac-line mtight\" style=\"border-bottom-width: 0.049em;\"><\/span><\/span><span class=\"\" style=\"top: -3.53753em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"sizing reset-size3 size1 mtight\"><span class=\"mord mtight\"><span class=\"mopen mtight\">(<\/span><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.04398em;\">z<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3448em;\"><span class=\"\" style=\"top: -2.3448em; margin-left: -0.04398em; margin-right: 0.1em;\"><span class=\"pstrut\" style=\"height: 2.64444em;\"><\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.29964em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord mtight\">\u2212<\/span><span class=\"mord mtight\">1<\/span><span class=\"mord mtight\">.<\/span><span class=\"mord mtight\">8<\/span><span class=\"mclose mtight\"><span class=\"mclose mtight\">)<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.04844em;\"><span class=\"\" style=\"top: -3.04844em; margin-right: 0.1em;\"><span class=\"pstrut\" style=\"height: 2.64444em;\"><\/span><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.493814em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter sizing reset-size3 size6\"><\/span><\/span><span class=\"mbin mtight\">\u2212<\/span><span class=\"mord mtight\"><span class=\"mopen nulldelimiter sizing reset-size3 size6\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.844314em;\"><span class=\"\" style=\"top: -2.656em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"sizing reset-size3 size1 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.2255em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"frac-line mtight\" style=\"border-bottom-width: 0.049em;\"><\/span><\/span><span class=\"\" style=\"top: -3.384em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"sizing reset-size3 size1 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.344em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter sizing reset-size3 size6\"><\/span><\/span><span class=\"mord mtight\"><span class=\"mopen nulldelimiter sizing reset-size3 size6\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.28641em;\"><span class=\"\" style=\"top: -2.50619em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"sizing reset-size3 size1 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.03588em;\">\u03c3<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.93844em;\"><span class=\"\" style=\"top: -2.93844em; margin-right: 0.1em;\"><span class=\"pstrut\" style=\"height: 2.64444em;\"><\/span><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.2255em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"frac-line mtight\" style=\"border-bottom-width: 0.049em;\"><\/span><\/span><span class=\"\" style=\"top: -3.53753em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"sizing reset-size3 size1 mtight\"><span class=\"mord mtight\"><span class=\"mopen mtight\">(<\/span><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.04398em;\">z<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3448em;\"><span class=\"\" style=\"top: -2.3448em; margin-left: -0.04398em; margin-right: 0.1em;\"><span class=\"pstrut\" style=\"height: 2.64444em;\"><\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.29964em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord mtight\">\u2212<\/span><span class=\"mord mtight\">2<\/span><span class=\"mord mtight\">.<\/span><span class=\"mord mtight\">2<\/span><span class=\"mclose mtight\"><span class=\"mclose mtight\">)<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.04844em;\"><span class=\"\" style=\"top: -3.04844em; margin-right: 0.1em;\"><span class=\"pstrut\" style=\"height: 2.64444em;\"><\/span><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.493814em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter sizing reset-size3 size6\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p>\u63a5\u4e0b\u6765\uff0c\u6211\u4eec\u4e0d\u7528\u81ea\u7136\u5bf9\u6570\uff0c\u800c\u662f\u53d6\u5176\u81ea\u7136\u5bf9\u6570\u5e76\u5bf9\u5176\u8fdb\u884c\u5904\u7406\u3002<br \/> <span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"> ln \u2061 ( e \u2212 1 2 ( z 1 \u2212 1.8 ) 2 \u03c3 2 \u00d7 e \u2212 1 2 ( z 1 \u2212 2.2 ) 2 \u03c3 2 ) = \u2212 1 2 ( z 1 \u2212 1.8 ) 2 \u03c3 2 \u2212 1 2 ( z 1 \u2212 2.2 ) 2 \u03c3 2 \\ln (e^{-\\frac{1}{2}\\frac{(z_1\u22121.8)^2}{\u03c3^2}}\\times e^{-\\frac{1}{2}\\frac{(z_1\u22122.2)^2}{\u03c3^2}} )= {-\\frac{1}{2}\\frac{(z_1\u22121.8)^2}{\u03c3^2}-\\frac{1}{2}\\frac{(z_1\u22122.2)^2}{\u03c3^2}} <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.60391em; vertical-align: -0.25em;\"><\/span><span class=\"mop\">ln<\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathdefault\">e<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.35391em;\"><span class=\"\" style=\"top: -3.45342em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">\u2212<\/span><span class=\"mord mtight\"><span class=\"mopen nulldelimiter sizing reset-size3 size6\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.844314em;\"><span class=\"\" style=\"top: -2.656em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"sizing reset-size3 size1 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.2255em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"frac-line mtight\" style=\"border-bottom-width: 0.049em;\"><\/span><\/span><span class=\"\" style=\"top: -3.384em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"sizing reset-size3 size1 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.344em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter sizing reset-size3 size6\"><\/span><\/span><span class=\"mord mtight\"><span class=\"mopen nulldelimiter sizing reset-size3 size6\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.28641em;\"><span class=\"\" style=\"top: -2.50619em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"sizing reset-size3 size1 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.03588em;\">\u03c3<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.93844em;\"><span class=\"\" style=\"top: -2.93844em; margin-right: 0.1em;\"><span class=\"pstrut\" style=\"height: 2.64444em;\"><\/span><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.2255em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"frac-line mtight\" style=\"border-bottom-width: 0.049em;\"><\/span><\/span><span class=\"\" style=\"top: -3.53753em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"sizing reset-size3 size1 mtight\"><span class=\"mord mtight\"><span class=\"mopen mtight\">(<\/span><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.04398em;\">z<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3448em;\"><span class=\"\" style=\"top: -2.3448em; margin-left: -0.04398em; margin-right: 0.1em;\"><span class=\"pstrut\" style=\"height: 2.64444em;\"><\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.29964em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord mtight\">\u2212<\/span><span class=\"mord mtight\">1<\/span><span class=\"mord mtight\">.<\/span><span class=\"mord mtight\">8<\/span><span class=\"mclose mtight\"><span class=\"mclose mtight\">)<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.04844em;\"><span class=\"\" style=\"top: -3.04844em; margin-right: 0.1em;\"><span class=\"pstrut\" style=\"height: 2.64444em;\"><\/span><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.493814em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter sizing reset-size3 size6\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><span class=\"mbin\">\u00d7<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1.60391em; vertical-align: -0.25em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">e<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.35391em;\"><span class=\"\" style=\"top: -3.45342em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">\u2212<\/span><span class=\"mord mtight\"><span class=\"mopen nulldelimiter sizing reset-size3 size6\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.844314em;\"><span class=\"\" style=\"top: -2.656em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"sizing reset-size3 size1 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.2255em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"frac-line mtight\" style=\"border-bottom-width: 0.049em;\"><\/span><\/span><span class=\"\" style=\"top: -3.384em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"sizing reset-size3 size1 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.344em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter sizing reset-size3 size6\"><\/span><\/span><span class=\"mord mtight\"><span class=\"mopen nulldelimiter sizing reset-size3 size6\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.28641em;\"><span class=\"\" style=\"top: -2.50619em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"sizing reset-size3 size1 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.03588em;\">\u03c3<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.93844em;\"><span class=\"\" style=\"top: -2.93844em; margin-right: 0.1em;\"><span class=\"pstrut\" style=\"height: 2.64444em;\"><\/span><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.2255em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"frac-line mtight\" style=\"border-bottom-width: 0.049em;\"><\/span><\/span><span class=\"\" style=\"top: -3.53753em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"sizing reset-size3 size1 mtight\"><span class=\"mord mtight\"><span class=\"mopen mtight\">(<\/span><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.04398em;\">z<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3448em;\"><span class=\"\" style=\"top: -2.3448em; margin-left: -0.04398em; margin-right: 0.1em;\"><span class=\"pstrut\" style=\"height: 2.64444em;\"><\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.29964em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord mtight\">\u2212<\/span><span class=\"mord mtight\">2<\/span><span class=\"mord mtight\">.<\/span><span class=\"mord mtight\">2<\/span><span class=\"mclose mtight\"><span class=\"mclose mtight\">)<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.04844em;\"><span class=\"\" style=\"top: -3.04844em; margin-right: 0.1em;\"><span class=\"pstrut\" style=\"height: 2.64444em;\"><\/span><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.493814em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter sizing reset-size3 size6\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 2.17711em; vertical-align: -0.686em;\"><\/span><span class=\"mord\"><span class=\"mord\">\u2212<\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.32144em;\"><span class=\"\" style=\"top: -2.314em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"mord\"><span class=\"mord\">2<\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em;\"><\/span><\/span><span class=\"\" style=\"top: -3.677em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"mord\"><span class=\"mord\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.686em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.49111em;\"><span class=\"\" style=\"top: -2.314em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"mord\"><span class=\"mord\"><span class=\"mord mathdefault\" style=\"margin-right: 0.03588em;\">\u03c3<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.740108em;\"><span class=\"\" style=\"top: -2.989em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em;\"><\/span><\/span><span class=\"\" style=\"top: -3.677em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"mord\"><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathdefault\" style=\"margin-right: 0.04398em;\">z<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.301108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: -0.04398em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\">\u2212<\/span><span class=\"mord\">1<\/span><span class=\"mord\">.<\/span><span class=\"mord\">8<\/span><span class=\"mclose\"><span class=\"mclose\">)<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.814108em;\"><span class=\"\" style=\"top: -3.063em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.686em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.32144em;\"><span class=\"\" style=\"top: -2.314em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"mord\"><span class=\"mord\">2<\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em;\"><\/span><\/span><span class=\"\" style=\"top: -3.677em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"mord\"><span class=\"mord\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.686em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.49111em;\"><span class=\"\" style=\"top: -2.314em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"mord\"><span class=\"mord\"><span class=\"mord mathdefault\" style=\"margin-right: 0.03588em;\">\u03c3<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.740108em;\"><span class=\"\" style=\"top: -2.989em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em;\"><\/span><\/span><span class=\"\" style=\"top: -3.677em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"mord\"><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathdefault\" style=\"margin-right: 0.04398em;\">z<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.301108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: -0.04398em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\">\u2212<\/span><span class=\"mord\">2<\/span><span class=\"mord\">.<\/span><span class=\"mord\">2<\/span><span class=\"mclose\"><span class=\"mclose\">)<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.814108em;\"><span class=\"\" style=\"top: -3.063em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.686em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><br \/> \u81ea\u7136\u5bf9\u6570\u662f\u4e00\u4e2a\u5355\u8c03\u51fd\u6570\u2014\u2014\u5728\u5bf9\u6570\u7684\u60c5\u51b5\u4e0b\u2014\u2014\u5b83\u603b\u662f\u9012\u589e\u7684\u2014\u2014\u5982\u4e0b\u56fe\u6240\u793a\u3002\u5b83\u7684\u503c\u53ea\u80fd\u6709\u4e00\u4e2a\u4e00\u5bf9\u4e00\u7684\u6620\u5c04\u3002\u8fd9\u610f\u5473\u7740\u4f18\u5316\u53ef\u80fd\u6027\u7684\u5bf9\u6570\u4e0e\u6700\u5927\u5316\u53ef\u80fd\u6027\u672c\u8eab\u6ca1\u6709\u4ec0\u4e48\u4e0d\u540c\u3002<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/img-blog.csdnimg.cn\/20200521005135571.png\" =\"\" =\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" alt=\"autostore\u673a\u5668\u4eba\u7a0b\u5e8f_\u673a\u5668\u4eba\u5de5\u7a0b\u5e08\u662f\u505a\u4ec0\u4e48\u7684 (https:\/\/mushiming.com\/) \u7b2c2\u5f20\" title=\"autostore\u673a\u5668\u4eba\u7a0b\u5e8f_\u673a\u5668\u4eba\u5de5\u7a0b\u5e08\u662f\u505a\u4ec0\u4e48\u7684 \u7b2c2\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" ><\/p>\n<p>\u5904\u7406\u4f3c\u7136\u8bb0\u5f55\u65f6\u8981\u6ce8\u610f\u7684\u4e00\u4ef6\u4e8b\u662f\uff0c\u5b83\u4eec\u59cb\u7ec8\u662f\u8d1f\u6570\u3002\u8fd9\u662f\u56e0\u4e3a\u6982\u7387\u5047\u5b9a\u503c\u4e3a0\u52301\u4e4b\u95f4\uff0c\u5e76\u4e140\u52301\u4e4b\u95f4\u7684\u4efb\u4f55\u503c\u7684\u5bf9\u6570\u5747\u4e3a\u8d1f\u3002\u53ef\u4ee5\u5728\u4e0a\u56fe\u4e2d\u770b\u5230\u3002\u51fa\u4e8e\u8fd9\u4e2a\u539f\u56e0\uff0c\u4e0e\u6570\u4f3c\u7136\u5de5\u4f5c\u65f6\uff0c\u4f18\u5316\u9650\u55e3\u7ee7\u627f\u51cf\u5c11\u7684\u8d1f\u5bf9\u6570\u4f3c\u7136; \u800c\u5728\u8fc7\u53bb\uff0c\u6211\u4eec\u8bd5\u56fe\u5c06\u53ef\u80fd\u6027\u6700\u5927\u5316\u3002<\/p>\n<p>\u6700\u540e\uff0c\u5982\u4e4b\u524d\u6240\u505a\u7684\u90a3\u6837\uff0c\u53ef\u4ee5\u65e0\u6761\u4ef6\u5220\u9664\u7b49\u5f0f\u524d\u9762\u7684\u5e38\u6570\u3002\u540c\u6837\uff0c\u51fa\u4e8e\u672c\u793a\u4f8b\u7684\u76ee\u7684\uff0c\u6211\u4eec\u5c06\u5047\u8bbe\u5728\u83b7\u5f97\u4e24\u4e2a\u6d4b\u91cf\u503c\u65f6\u4f7f\u7528\u4e86\u76f8\u540c\u7684\u4f20\u611f\u5668-\u56e0\u6b64\u5c06\u5ffd\u7565\u65b9\u7a0b\u5f0f\u4e2d\u7684\u65b9\u5dee\u3002<br \/> <span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"> ( z 1 \u2212 1.8 ) 2 + ( z 1 \u2212 2.2 ) 2 (z_1 \u22121.8)^2 +(z_1\u22122.2) ^2 <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.11411em; vertical-align: -0.25em;\"><\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathdefault\" style=\"margin-right: 0.04398em;\">z<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.301108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: -0.04398em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\">\u2212<\/span><span class=\"mord\">1<\/span><span class=\"mord\">.<\/span><span class=\"mord\">8<\/span><span class=\"mclose\"><span class=\"mclose\">)<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.864108em;\"><span class=\"\" style=\"top: -3.113em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><span class=\"mbin\">+<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1.11411em; vertical-align: -0.25em;\"><\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathdefault\" style=\"margin-right: 0.04398em;\">z<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.301108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: -0.04398em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\">\u2212<\/span><span class=\"mord\">2<\/span><span class=\"mord\">.<\/span><span class=\"mord\">2<\/span><span class=\"mclose\"><span class=\"mclose\">)<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.864108em;\"><span class=\"\" style=\"top: -3.113em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<h6>\u4f18\u5316<\/h6>\n<p>\u5728\u8fd9\u4e00\u70b9\u4e0a\uff0c\u65b9\u7a0b\u5df2\u7ecf\u5927\u5927\u7b80\u5316\u4e86\u3002\u4e3a\u4e86\u5f97\u5230\u5b83\u7684\u6700\u7b80\u5f62\u5f0f\uff0c\u5269\u4e0b\u7684\u5c31\u662f\u628a\u6240\u6709\u9879\u76f8\u4e58\u3002<br \/> <span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"> 2 z 1 2 \u2212 8 z 1 + 8.08 2z_1^2\u22128z_1+8.08 <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.11111em; vertical-align: -0.247em;\"><\/span><span class=\"mord\">2<\/span><span class=\"mord\"><span class=\"mord mathdefault\" style=\"margin-right: 0.04398em;\">z<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.864108em;\"><span class=\"\" style=\"top: -2.453em; margin-left: -0.04398em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><span class=\"\" style=\"top: -3.113em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.247em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\">\u2212<\/span><span class=\"mord\">8<\/span><span class=\"mord\"><span class=\"mord mathdefault\" style=\"margin-right: 0.04398em;\">z<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.301108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: -0.04398em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><span class=\"mbin\">+<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.64444em; vertical-align: 0em;\"><\/span><span class=\"mord\">8<\/span><span class=\"mord\">.<\/span><span class=\"mord\">0<\/span><span class=\"mord\">8<\/span><\/span><\/span><\/span><\/span><\/span><br \/> \u4e3a\u4e86\u627e\u5230\u8fd9\u4e2a\u65b9\u7a0b\u7684\u6700\u5c0f\u503c\uff0c\u4f60\u53ef\u4ee5\u5bf9\u65b9\u7a0b\u6c42\u4e00\u9636\u5bfc\u6570\u5e76\u4ee4\u5b83\u7b49\u4e8e0\u3002<br \/> <span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"> 4 z 1 \u2212 8 = 0 4 z 1 = 8 z 1 = 2 4z_1\u22128=0\\\\ 4z_1 = 8\\\\ z_1 = 2 <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.79444em; vertical-align: -0.15em;\"><\/span><span class=\"mord\">4<\/span><span class=\"mord\"><span class=\"mord mathdefault\" style=\"margin-right: 0.04398em;\">z<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.301108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: -0.04398em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\">\u2212<\/span><span class=\"mord\">8<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.64444em; vertical-align: 0em;\"><\/span><span class=\"mord\">0<\/span><\/span><span class=\"mspace newline\"><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.79444em; vertical-align: -0.15em;\"><\/span><span class=\"mord\">4<\/span><span class=\"mord\"><span class=\"mord mathdefault\" style=\"margin-right: 0.04398em;\">z<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.301108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: -0.04398em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.64444em; vertical-align: 0em;\"><\/span><span class=\"mord\">8<\/span><\/span><span class=\"mspace newline\"><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.58056em; vertical-align: -0.15em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\" style=\"margin-right: 0.04398em;\">z<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.301108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: -0.04398em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.64444em; vertical-align: 0em;\"><\/span><span class=\"mord\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p>\u901a\u8fc7\u8fd9\u6837\u505a\uff0c\u53ef\u4ee5\u8f7b\u6613\u5730\u627e\u5230\u66f2\u7ebf\u4e0a\u7684\u4f4d\u7f6e\uff0c\u5176\u4e2d\u7684\u659c\u7387(\u6216\u68af\u5ea6\uff0c\u5728\u591a\u7ef4\u65b9\u7a0b\u4e2d)\u7b49\u4e8e\u96f6\u5373\u6ce2\u8c37\u3002\u901a\u8fc7\u67e5\u770b\u9519\u8bef\u51fd\u6570\u7684\u56fe\u5f62\uff0c\u53ef\u4ee5\u5f88\u5bb9\u6613\u5730\u53ef\u89c6\u5316\u6b64\u5c5e\u6027\u3002<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/img-blog.csdnimg.cn\/2020052100515388.png\" =\"\" =\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" alt=\"autostore\u673a\u5668\u4eba\u7a0b\u5e8f_\u673a\u5668\u4eba\u5de5\u7a0b\u5e08\u662f\u505a\u4ec0\u4e48\u7684 (https:\/\/mushiming.com\/) \u7b2c3\u5f20\" title=\"autostore\u673a\u5668\u4eba\u7a0b\u5e8f_\u673a\u5668\u4eba\u5de5\u7a0b\u5e08\u662f\u505a\u4ec0\u4e48\u7684 \u7b2c3\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" ><\/p>\n<h6>\u603b\u89c8<\/h6>\n<p>\u8fd9\u91cc\u6267\u884c\u7684\u8fc7\u7a0b\u662fMLE\u95ee\u9898\u7684\u89e3\u6790\u89e3\u3002\u5305\u62ec\u7684\u6b65\u9aa4\uff1a<\/p>\n<ul>\n<li>\u5220\u9664\u65e0\u5173\u7d27\u8981\u7684\u5e38\u6570,<\/li>\n<li>\u5c06\u4e00\u4e2a\u4f3c\u7136\u4f30\u8ba1\u7684\u65b9\u7a0b\u8f6c\u6362\u4e3a\u8d1f\u5bf9\u6570\u4f3c\u7136\u4f30\u8ba1\u7684\u65b9\u7a0b<\/li>\n<li>\u8ba1\u7b97\u51fd\u6570\u7684\u4e00\u9636\u5bfc\u6570\u5e76\u4f7f\u5176\u7b49\u4e8e\u96f6\uff0c\u4ece\u800c\u6c42\u51fa\u6781\u503c\u3002<\/li>\n<\/ul>\n<p>\u5728GraphSLAM\u4e2d\uff0c\u524d\u4e24\u4e2a\u6b65\u9aa4\u53ef\u4ee5\u5e94\u7528\u4e8e\u6bcf\u4e2a\u7ea6\u675f\u3002\u56e0\u6b64\uff0c\u4efb\u4f55\u6d4b\u91cf\u6216\u8fd0\u52a8\u7ea6\u675f\u90fd\u53ef\u4ee5\u7b80\u5355\u5730\u6807\u8bb0\u4e3a\u8d1f\u5bf9\u6570\u4f3c\u7136\u8bef\u5dee\u3002\u5bf9\u4e8e\u4e00\u4e2a\u5ea6\u91cf\u7ea6\u675f\uff0c\u8fd9\u7c7b\u4f3c\u4e8e\u4ee5\u4e0b\uff0c<br \/> <span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"> ( z t \u2212 ( x t + m t ) ) 2 \u03c3 2 \\frac{(z_t\u2212(x_t+m_t))^2}{\u03c3^2} <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 2.17711em; vertical-align: -0.686em;\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.49111em;\"><span class=\"\" style=\"top: -2.314em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"mord\"><span class=\"mord\"><span class=\"mord mathdefault\" style=\"margin-right: 0.03588em;\">\u03c3<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.740108em;\"><span class=\"\" style=\"top: -2.989em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em;\"><\/span><\/span><span class=\"\" style=\"top: -3.677em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"mord\"><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathdefault\" style=\"margin-right: 0.04398em;\">z<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.280556em;\"><span class=\"\" style=\"top: -2.55em; margin-left: -0.04398em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">t<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\">\u2212<\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathdefault\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.280556em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">t<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><span class=\"mbin\">+<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">m<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.280556em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">t<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)<\/span><span class=\"mclose\"><span class=\"mclose\">)<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.814108em;\"><span class=\"\" style=\"top: -3.063em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.686em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><br \/> \u5bf9\u4e8e\u8fd0\u52a8\u7ea6\u675f\uff0c<br \/> <span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"> ( x t \u2212 ( x t \u2212 1 + u t ) ) 2 \u03c3 2 \\frac{(x_t\u2212(x_t\u22121+u_t))^2}{\u03c3^2} <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 2.17711em; vertical-align: -0.686em;\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.49111em;\"><span class=\"\" style=\"top: -2.314em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"mord\"><span class=\"mord\"><span class=\"mord mathdefault\" style=\"margin-right: 0.03588em;\">\u03c3<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.740108em;\"><span class=\"\" style=\"top: -2.989em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em;\"><\/span><\/span><span class=\"\" style=\"top: -3.677em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"mord\"><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathdefault\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.280556em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">t<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\">\u2212<\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathdefault\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.280556em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">t<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\">\u2212<\/span><span class=\"mord\">1<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><span class=\"mbin\">+<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">u<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.280556em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">t<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)<\/span><span class=\"mclose\"><span class=\"mclose\">)<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.814108em;\"><span class=\"\" style=\"top: -3.063em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.686em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><br \/> \u56e0\u6b64\uff0c\u7ea6\u675f\u5c06\u88ab\u6807\u8bb0\u4e3a\u8d1f\u5bf9\u6570\u4f3c\u7136\u8bef\u5dee\uff0c<br \/> <img decoding=\"async\" src=\"https:\/\/img-blog.csdnimg.cn\/20200521005543922.png\" =\"\" =\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" alt=\"autostore\u673a\u5668\u4eba\u7a0b\u5e8f_\u673a\u5668\u4eba\u5de5\u7a0b\u5e08\u662f\u505a\u4ec0\u4e48\u7684 (https:\/\/mushiming.com\/) \u7b2c4\u5f20\" title=\"autostore\u673a\u5668\u4eba\u7a0b\u5e8f_\u673a\u5668\u4eba\u5de5\u7a0b\u5e08\u662f\u505a\u4ec0\u4e48\u7684 \u7b2c4\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" ><\/p>\n<p>\u4f30\u8ba1\u51fd\u6570\u8bd5\u56fe\u6700\u5c0f\u5316\u6240\u6709\u7ea6\u675f\u7684\u548c\uff0c<br \/> <span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"> J G r a p h S L A M = \u2211 t ( x t \u2212 ( x t \u2212 1 + u t ) ) 2 \u03c3 2 + \u2211 t ( z t \u2212 ( x t + m t ) ) 2 \u03c3 2 J_{GraphSLAM}=\u2211_{t}\\frac{(x_t\u2212(x_t\u22121+u_t))^2}{\u03c3^2}+\u2211_t\\frac{(z_t\u2212(x_t+m_t))^2}{\u03c3^2} <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.969438em; vertical-align: -0.286108em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\" style=\"margin-right: 0.09618em;\">J<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.336108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: -0.09618em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">G<\/span><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.02778em;\">r<\/span><span class=\"mord mathdefault mtight\">a<\/span><span class=\"mord mathdefault mtight\">p<\/span><span class=\"mord mathdefault mtight\">h<\/span><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.05764em;\">S<\/span><span class=\"mord mathdefault mtight\">L<\/span><span class=\"mord mathdefault mtight\">A<\/span><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.10903em;\">M<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.286108em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 2.74111em; vertical-align: -1.25001em;\"><\/span><span class=\"mop op-limits\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.05001em;\"><span class=\"\" style=\"top: -1.89999em; margin-left: 0em;\"><span class=\"pstrut\" style=\"height: 3.05em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">t<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.05em;\"><span class=\"pstrut\" style=\"height: 3.05em;\"><\/span><span class=\"\"><span class=\"mop op-symbol large-op\">\u2211<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.25001em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.49111em;\"><span class=\"\" style=\"top: -2.314em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"mord\"><span class=\"mord\"><span class=\"mord mathdefault\" style=\"margin-right: 0.03588em;\">\u03c3<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.740108em;\"><span class=\"\" style=\"top: -2.989em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em;\"><\/span><\/span><span class=\"\" style=\"top: -3.677em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"mord\"><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathdefault\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.280556em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">t<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\">\u2212<\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathdefault\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.280556em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">t<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\">\u2212<\/span><span class=\"mord\">1<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><span class=\"mbin\">+<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">u<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.280556em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">t<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)<\/span><span class=\"mclose\"><span class=\"mclose\">)<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.814108em;\"><span class=\"\" style=\"top: -3.063em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.686em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><span class=\"mbin\">+<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 2.74111em; vertical-align: -1.25001em;\"><\/span><span class=\"mop op-limits\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.05001em;\"><span class=\"\" style=\"top: -1.89999em; margin-left: 0em;\"><span class=\"pstrut\" style=\"height: 3.05em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">t<\/span><\/span><\/span><span class=\"\" style=\"top: -3.05em;\"><span class=\"pstrut\" style=\"height: 3.05em;\"><\/span><span class=\"\"><span class=\"mop op-symbol large-op\">\u2211<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.25001em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.49111em;\"><span class=\"\" style=\"top: -2.314em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"mord\"><span class=\"mord\"><span class=\"mord mathdefault\" style=\"margin-right: 0.03588em;\">\u03c3<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.740108em;\"><span class=\"\" style=\"top: -2.989em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em;\"><\/span><\/span><span class=\"\" style=\"top: -3.677em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"mord\"><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathdefault\" style=\"margin-right: 0.04398em;\">z<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.280556em;\"><span class=\"\" style=\"top: -2.55em; margin-left: -0.04398em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">t<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\">\u2212<\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathdefault\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.280556em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">t<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><span class=\"mbin\">+<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">m<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.280556em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">t<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)<\/span><span class=\"mclose\"><span class=\"mclose\">)<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.814108em;\"><span class=\"\" style=\"top: -3.063em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.686em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<h5>\uff082\uff09MLE\u7684\u6570\u503c\u89e3<\/h5>\n<p>\u5728\u66f4\u590d\u6742\u7684\u95ee\u9898\u4e2d\uff0c\u627e\u5230\u89e3\u6790\u89e3\u53ef\u80fd\u9700\u8981\u5197\u957f\u7684\u8ba1\u7b97\u3002\u5e78\u8fd0\u7684\u662f\uff0c\u8fd8\u6709\u53e6\u4e00\u79cd\u9009\u62e9-\u53ef\u4ee5\u5728\u77ed\u65f6\u95f4\u5185\u627e\u5230\u6700\u5927\u4f3c\u7136\u95ee\u9898\u7684\u6570\u503c\u89e3\u3002\u6211\u4eec\u5c06\u63a2\u8ba8\u4e0a\u4e00\u4e2a\u793a\u4f8b\u7684\u6570\u503c\u89e3\u51b3\u65b9\u6848\u3002<\/p>\n<h6>\u6570\u503c\u89e3<\/h6>\n<p>\u4e0b\u4f8b\u663e\u793a\u4e86\u8bef\u5dee\u51fd\u6570\u7684\u56fe\u5f62\u3002\u5728\u6b64\u793a\u4f8b\u4e2d\uff0c\u5f88\u5bb9\u6613\u770b\u5230\u5168\u5c40\u6700\u5c0f\u503c\u4f4d\u4e8e\u4f55\u5904\u3002\u4f46\u662f\uff0c\u5728\u5177\u6709\u591a\u4e2a\u7ef4\u5ea6\u7684\u66f4\u590d\u6742\u7684\u793a\u4f8b\u4e2d\uff0c\u8fd9\u5e76\u4e0d\u7b80\u5355\u3002<br \/> <img decoding=\"async\" src=\"https:\/\/img-blog.csdnimg.cn\/20200521010019899.png\" =\"\" =\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" alt=\"autostore\u673a\u5668\u4eba\u7a0b\u5e8f_\u673a\u5668\u4eba\u5de5\u7a0b\u5e08\u662f\u505a\u4ec0\u4e48\u7684 (https:\/\/mushiming.com\/) \u7b2c5\u5f20\" title=\"autostore\u673a\u5668\u4eba\u7a0b\u5e8f_\u673a\u5668\u4eba\u5de5\u7a0b\u5e08\u662f\u505a\u4ec0\u4e48\u7684 \u7b2c5\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" ><\/p>\n<p>\u53ef\u4ee5\u901a\u8fc7\u5e94\u7528\u4f18\u5316\u7b97\u6cd5\u6765\u6570\u503c\u6c42\u89e3\u6b64MLE\u3002\u4f18\u5316\u7b97\u6cd5\u7684\u76ee\u6807\u662f\u5feb\u901f\u627e\u5230\u6700\u4f73\u89e3\u51b3\u65b9\u6848-\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\u4e3a\u5c40\u90e8\u6700\u5c0f\u503c\u3002\u6709\u51e0\u79cd\u4e0d\u540c\u7684\u7b97\u6cd5\u53ef\u4ee5\u89e3\u51b3\u8fd9\u4e2a\u95ee\u9898\u3002\u5728SLAM\u4e2d\uff0c<strong>\u68af\u5ea6\u4e0b\u964d<\/strong>\uff0c<strong>Levenberg-Marquardt<\/strong>\u548c<strong>\u5171\u8f6d\u68af\u5ea6\u7b97\u6cd5<\/strong>\u975e\u5e38\u666e\u904d\u3002<\/p>\n<h6>\u68af\u5ea6\u4e0b\u964d\u7b97\u6cd5<\/h6>\n<p>\u56de\u60f3\u4e00\u4e0b\uff0c\u51fd\u6570\u7684\u68af\u5ea6\u662f\u6307\u5411\u6700\u5927\u53d8\u5316\u7387\u65b9\u5411\u7684\u77e2\u91cf\uff1b\u6216\u5728\u6781\u7aef\u60c5\u51b5\u4e0b\u7b49\u4e8e\u96f6\u3002<\/p>\n<p>\u5728\u68af\u5ea6\u4e0b\u964d\u4e2d-\u8fdb\u884c\u521d\u59cb\u731c\u6d4b\uff0c\u7136\u540e\u6cbf\u4e0e\u68af\u5ea6\u76f8\u53cd\u7684\u65b9\u5411\u8fdb\u884c\u589e\u91cf\u8c03\u6574\u3002\u6700\u7ec8\uff0c\u5e94\u8be5\u8fbe\u5230\u6700\u4f4e\u9650\u5ea6\u7684\u529f\u80fd\u3002<\/p>\n<p>\u8be5\u7b97\u6cd5\u786e\u5b9e\u6709\u4e00\u4e2a\u7f3a\u70b9-\u5728\u590d\u6742\u7684\u5206\u5e03\u4e2d\uff0c\u521d\u59cb\u731c\u6d4b\u53ef\u80fd\u4f1a\u663e\u7740\u6539\u53d8\u6700\u7ec8\u7ed3\u679c\u3002\u6839\u636e\u6700\u521d\u7684\u731c\u6d4b\uff0c\u8be5\u7b97\u6cd5\u6536\u655b\u4e8e\u4e24\u4e2a\u4e0d\u540c\u7684\u5c40\u90e8\u6700\u5c0f\u503c\u3002\u8be5\u7b97\u6cd5\u65e0\u6cd5\u786e\u5b9a\u5168\u5c40\u6700\u5c0f\u503c\u5728\u54ea\u91cc-\u5b83\u6cbf\u6700\u9661\u7684\u5761\u5ea6\u5411\u4e0b\u79fb\u52a8\uff0c\u5e76\u4e14\u5f53\u8fbe\u5230\u5c40\u90e8\u6700\u5c0f\u503c\u65f6\uff0c\u5b83\u8ba4\u4e3a\u5176\u4efb\u52a1\u5df2\u5b8c\u6210\u3002\u89e3\u51b3\u6b64\u95ee\u9898\u7684\u4e00\u79cd\u65b9\u6cd5\u662f\u4f7f\u7528<strong>\u968f\u673a\u68af\u5ea6\u4e0b\u964d\u7b97\u6cd5<\/strong>\uff08SGD\uff09\u3002<\/p>\n<h4>2. \u4e00\u7ef4\u5230\u591a\u7ef4<\/h4>\n<p>\u5728\u524d\u9762\u7684\u793a\u4f8b\u4e2d\uff0c\u60a8\u6b63\u5728\u4f7f\u7528\u4e00\u7ef4\u56fe\u3002\u673a\u5668\u4eba\u7684\u8fd0\u52a8\u548c\u6d4b\u91cf\u4ec5\u9650\u4e8e\u4e00\u7ef4-\u5b83\u4eec\u53ef\u4ee5\u5411\u524d\u6216\u5411\u540e\u6267\u884c\u3002<\/p>\n<h5>\uff081\uff091-Dimensional Graphs<\/h5>\n<p>\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c\u6bcf\u4e2a\u7ea6\u675f\u53ef\u4ee5\u7528\u4ee5\u4e0b\u5f62\u5f0f\u8868\u793a\uff1a<br \/> <strong>1-D \u6d4b\u91cf\u7ea6\u675f<\/strong>: <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> ( z t \u2212 ( x t + m t ) ) 2 \u03c3 2 \\large \\frac{(z_t - (x_t + m_t))^2}{\\sigma^2} <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.71746em; vertical-align: -0.414em;\"><\/span><span class=\"mord sizing reset-size6 size7\"><span class=\"mopen nulldelimiter sizing reset-size7 size6\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.08622em;\"><span class=\"\" style=\"top: -2.655em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"sizing reset-size7 size4 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.03588em;\">\u03c3<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.76933em;\"><span class=\"\" style=\"top: -2.886em; margin-right: 0.0625em;\"><span class=\"pstrut\" style=\"height: 2.6em;\"><\/span><span class=\"sizing reset-size4 size2 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em;\"><\/span><\/span><span class=\"\" style=\"top: -3.47667em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"sizing reset-size7 size4 mtight\"><span class=\"mord mtight\"><span class=\"mopen mtight\">(<\/span><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.04398em;\">z<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.31831em;\"><span class=\"\" style=\"top: -2.457em; margin-left: -0.04398em; margin-right: 0.0625em;\"><span class=\"pstrut\" style=\"height: 2.6em;\"><\/span><span class=\"sizing reset-size4 size2 mtight\"><span class=\"mord mathdefault mtight\">t<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.143em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mbin mtight\">\u2212<\/span><span class=\"mopen mtight\">(<\/span><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.31831em;\"><span class=\"\" style=\"top: -2.457em; margin-left: 0em; margin-right: 0.0625em;\"><span class=\"pstrut\" style=\"height: 2.6em;\"><\/span><span class=\"sizing reset-size4 size2 mtight\"><span class=\"mord mathdefault mtight\">t<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.143em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mbin mtight\">+<\/span><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">m<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.31831em;\"><span class=\"\" style=\"top: -2.457em; margin-left: 0em; margin-right: 0.0625em;\"><span class=\"pstrut\" style=\"height: 2.6em;\"><\/span><span class=\"sizing reset-size4 size2 mtight\"><span class=\"mord mathdefault mtight\">t<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.143em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose mtight\">)<\/span><span class=\"mclose mtight\"><span class=\"mclose mtight\">)<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.91433em;\"><span class=\"\" style=\"top: -3.031em; margin-right: 0.0625em;\"><span class=\"pstrut\" style=\"height: 2.6em;\"><\/span><span class=\"sizing reset-size4 size2 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.345em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter sizing reset-size7 size6\"><\/span><\/span><\/span><\/span><\/span><\/span><br \/> <strong>1-D \u8fd0\u52a8\u7ea6\u675f<\/strong>:<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> ( x t \u2212 ( x t \u2212 1 + u t ) ) 2 \u03c3 2 \\large \\frac{(x_t - (x_{t-1} + u_t))^2}{\\sigma^2} <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.71746em; vertical-align: -0.414em;\"><\/span><span class=\"mord sizing reset-size6 size7\"><span class=\"mopen nulldelimiter sizing reset-size7 size6\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.08622em;\"><span class=\"\" style=\"top: -2.655em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"sizing reset-size7 size4 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.03588em;\">\u03c3<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.76933em;\"><span class=\"\" style=\"top: -2.886em; margin-right: 0.0625em;\"><span class=\"pstrut\" style=\"height: 2.6em;\"><\/span><span class=\"sizing reset-size4 size2 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em;\"><\/span><\/span><span class=\"\" style=\"top: -3.47667em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"sizing reset-size7 size4 mtight\"><span class=\"mord mtight\"><span class=\"mopen mtight\">(<\/span><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.31831em;\"><span class=\"\" style=\"top: -2.457em; margin-left: 0em; margin-right: 0.0625em;\"><span class=\"pstrut\" style=\"height: 2.6em;\"><\/span><span class=\"sizing reset-size4 size2 mtight\"><span class=\"mord mathdefault mtight\">t<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.143em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mbin mtight\">\u2212<\/span><span class=\"mopen mtight\">(<\/span><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.34033em;\"><span class=\"\" style=\"top: -2.457em; margin-left: 0em; margin-right: 0.0625em;\"><span class=\"pstrut\" style=\"height: 2.6em;\"><\/span><span class=\"sizing reset-size4 size2 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">t<\/span><span class=\"mbin mtight\">\u2212<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.205497em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mbin mtight\">+<\/span><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">u<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.31831em;\"><span class=\"\" style=\"top: -2.457em; margin-left: 0em; margin-right: 0.0625em;\"><span class=\"pstrut\" style=\"height: 2.6em;\"><\/span><span class=\"sizing reset-size4 size2 mtight\"><span class=\"mord mathdefault mtight\">t<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.143em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose mtight\">)<\/span><span class=\"mclose mtight\"><span class=\"mclose mtight\">)<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.91433em;\"><span class=\"\" style=\"top: -3.031em; margin-right: 0.0625em;\"><span class=\"pstrut\" style=\"height: 2.6em;\"><\/span><span class=\"sizing reset-size4 size2 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.345em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter sizing reset-size7 size6\"><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<h5>\uff082\uff09n-Dimensional Graphs<\/h5>\n<p>\u5728\u591a\u7ef4\u7cfb\u7edf\u4e2d\uff0c\u6211\u4eec\u5fc5\u987b\u4f7f\u7528\u77e9\u9635\u548c\u534f\u65b9\u5dee\u6765\u8868\u793a\u7ea6\u675f\u3002\u8fd9\u79cd\u6982\u62ec\u53ef\u4ee5\u5e94\u7528\u4e8e\u4e8c\u7ef4\uff0c\u4e09\u7ef4\u548c\u5b9e\u9645\u4e0a\u4efb\u4f55n\u4e2a\u7ef4\u7684\u7cfb\u7edf\u3002\u7ea6\u675f\u65b9\u7a0b\u770b\u8d77\u6765\u50cf\u8fd9\u6837\uff0c<\/p>\n<p><strong>n-D \u6d4b\u91cf\u7ea6\u675f:<\/strong> <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> ( z t \u2212 h ( x t , m j ) ) T Q t \u2212 1 ( z t \u2212 h ( x t , m j ) ) ( z t \u2212 h ( x t , m j ) ) (z_t-h(x_t,m_j))^TQ_t^{-1}(z_t-h(x_t,m_j))(zt\u2212h(xt,mj)) <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em; vertical-align: -0.25em;\"><\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathdefault\" style=\"margin-right: 0.04398em;\">z<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.280556em;\"><span class=\"\" style=\"top: -2.55em; margin-left: -0.04398em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">t<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1.14035em; vertical-align: -0.286108em;\"><\/span><span class=\"mord mathdefault\">h<\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathdefault\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.280556em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">t<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">m<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.311664em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.05724em;\">j<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.286108em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)<\/span><span class=\"mclose\"><span class=\"mclose\">)<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.841331em;\"><span class=\"\" style=\"top: -3.063em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.13889em;\">T<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\"><span class=\"mord mathdefault\">Q<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.854239em;\"><span class=\"\" style=\"top: -2.45424em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">t<\/span><\/span><\/span><span class=\"\" style=\"top: -3.10313em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">\u2212<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.245756em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathdefault\" style=\"margin-right: 0.04398em;\">z<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.280556em;\"><span class=\"\" style=\"top: -2.55em; margin-left: -0.04398em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">t<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1.03611em; vertical-align: -0.286108em;\"><\/span><span class=\"mord mathdefault\">h<\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathdefault\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.280556em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">t<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">m<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.311664em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.05724em;\">j<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.286108em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)<\/span><span class=\"mclose\">)<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.04398em;\">z<\/span><span class=\"mord mathdefault\">t<\/span><span class=\"mord\">\u2212<\/span><span class=\"mord mathdefault\">h<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathdefault\">x<\/span><span class=\"mord mathdefault\">t<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord mathdefault\">m<\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.05724em;\">j<\/span><span class=\"mclose\">)<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span><br \/> <strong>n-D \u8fd0\u52a8\u7ea6\u675f<\/strong>: <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> ( x t \u2212 g ( u t , x t \u2212 1 ) ) T R t \u2212 1 ( x t \u2212 g ( u t , x t \u2212 1 ) ) ( x t \u2212 g ( u t , x t \u2212 1 ) ) (x_t-g(u_t,x_{t-1}))^TR_t^{-1}(x_t-g(u_t,x_{t-1}))(xt\u2212g(ut,xt\u22121)) <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em; vertical-align: -0.25em;\"><\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathdefault\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.280556em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">t<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1.10424em; vertical-align: -0.25em;\"><\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.03588em;\">g<\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathdefault\">u<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.280556em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">t<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.301108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">t<\/span><span class=\"mbin mtight\">\u2212<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.208331em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)<\/span><span class=\"mclose\"><span class=\"mclose\">)<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.841331em;\"><span class=\"\" style=\"top: -3.063em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.13889em;\">T<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\"><span class=\"mord mathdefault\" style=\"margin-right: 0.00773em;\">R<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.854239em;\"><span class=\"\" style=\"top: -2.45424em; margin-left: -0.00773em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">t<\/span><\/span><\/span><span class=\"\" style=\"top: -3.10313em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">\u2212<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.245756em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathdefault\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.280556em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">t<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em; vertical-align: -0.25em;\"><\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.03588em;\">g<\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathdefault\">u<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.280556em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">t<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.301108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">t<\/span><span class=\"mbin mtight\">\u2212<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.208331em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)<\/span><span class=\"mclose\">)<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathdefault\">x<\/span><span class=\"mord mathdefault\">t<\/span><span class=\"mord\">\u2212<\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.03588em;\">g<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathdefault\">u<\/span><span class=\"mord mathdefault\">t<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord mathdefault\">x<\/span><span class=\"mord mathdefault\">t<\/span><span class=\"mord\">\u2212<\/span><span class=\"mord\">1<\/span><span class=\"mclose\">)<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span><\/p>\n<p>\u5176\u4e2d<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> h ( ) h() <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em; vertical-align: -0.25em;\"><\/span><span class=\"mord mathdefault\">h<\/span><span class=\"mopen\">(<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span>\u548c<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> g ( ) g() <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em; vertical-align: -0.25em;\"><\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.03588em;\">g<\/span><span class=\"mopen\">(<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span>\u8868\u793a\u6d4b\u91cf\u548c\u8fd0\u52a8\u51fd\u6570\uff0c<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> Q t Q_t <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.87777em; vertical-align: -0.19444em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">Q<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.280556em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">t<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u548c<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> R t R_t <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.83333em; vertical-align: -0.15em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\" style=\"margin-right: 0.00773em;\">R<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.280556em;\"><span class=\"\" style=\"top: -2.55em; margin-left: -0.00773em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">t<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u4e3a\u6d4b\u91cf\u548c\u8fd0\u52a8\u566a\u58f0\u7684\u534f\u65b9\u5dee\u3002<\/p>\n<p>\u6240\u6709\u7ea6\u675f\u7684\u548c\u7684\u591a\u7ef4\u516c\u5f0f\u5982\u4e0b\u6240\u793a\u3002<br \/> <span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"> J G r a p h S L A M = x 0 T \u03a9 x 0 + \u2211 t ( x t \u2212 g ( u t , x t \u2212 1 ) ) T R t \u2212 1 ( x t \u2212 g ( u t , x t \u2212 1 ) ) + \u2211 t ( z t \u2212 h ( x t , m j ) ) T Q t \u2212 1 ( z t \u2212 h ( x t , m j ) ) J_{GraphSLAM} = x_0^T \\Omega x_0 + \\sum_t(x_t-g(u_t,x_{t-1}))^T R_t^{-1}(x_t-g(u_t,x_{t-1}))\\\\ \\quad + \\sum_t(z_t-h(x_t,m_j))^TQ_t^{-1}(z_t-h(x_t,m_j)) <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.969438em; vertical-align: -0.286108em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\" style=\"margin-right: 0.09618em;\">J<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.336108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: -0.09618em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">G<\/span><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.02778em;\">r<\/span><span class=\"mord mathdefault mtight\">a<\/span><span class=\"mord mathdefault mtight\">p<\/span><span class=\"mord mathdefault mtight\">h<\/span><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.05764em;\">S<\/span><span class=\"mord mathdefault mtight\">L<\/span><span class=\"mord mathdefault mtight\">A<\/span><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.10903em;\">M<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.286108em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1.13833em; vertical-align: -0.247em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.891331em;\"><span class=\"\" style=\"top: -2.453em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">0<\/span><\/span><\/span><span class=\"\" style=\"top: -3.113em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.13889em;\">T<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.247em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\">\u03a9<\/span><span class=\"mord\"><span class=\"mord mathdefault\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.301108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">0<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><span class=\"mbin\">+<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 2.30001em; vertical-align: -1.25001em;\"><\/span><span class=\"mop op-limits\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.05001em;\"><span class=\"\" style=\"top: -1.89999em; margin-left: 0em;\"><span class=\"pstrut\" style=\"height: 3.05em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">t<\/span><\/span><\/span><span class=\"\" style=\"top: -3.05em;\"><span class=\"pstrut\" style=\"height: 3.05em;\"><\/span><span class=\"\"><span class=\"mop op-symbol large-op\">\u2211<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.25001em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathdefault\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.280556em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">t<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1.14133em; vertical-align: -0.25em;\"><\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.03588em;\">g<\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathdefault\">u<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.280556em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">t<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.301108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">t<\/span><span class=\"mbin mtight\">\u2212<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.208331em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)<\/span><span class=\"mclose\"><span class=\"mclose\">)<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.891331em;\"><span class=\"\" style=\"top: -3.113em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.13889em;\">T<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\"><span class=\"mord mathdefault\" style=\"margin-right: 0.00773em;\">R<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.864108em;\"><span class=\"\" style=\"top: -2.453em; margin-left: -0.00773em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">t<\/span><\/span><\/span><span class=\"\" style=\"top: -3.113em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">\u2212<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.247em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathdefault\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.280556em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">t<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em; vertical-align: -0.25em;\"><\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.03588em;\">g<\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathdefault\">u<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.280556em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">t<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.301108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">t<\/span><span class=\"mbin mtight\">\u2212<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.208331em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><\/span><span class=\"mspace newline\"><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.66666em; vertical-align: -0.08333em;\"><\/span><span class=\"mspace\" style=\"margin-right: 1em;\"><\/span><span class=\"mbin\">+<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 2.30001em; vertical-align: -1.25001em;\"><\/span><span class=\"mop op-limits\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.05001em;\"><span class=\"\" style=\"top: -1.89999em; margin-left: 0em;\"><span class=\"pstrut\" style=\"height: 3.05em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">t<\/span><\/span><\/span><span class=\"\" style=\"top: -3.05em;\"><span class=\"pstrut\" style=\"height: 3.05em;\"><\/span><span class=\"\"><span class=\"mop op-symbol large-op\">\u2211<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.25001em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathdefault\" style=\"margin-right: 0.04398em;\">z<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.280556em;\"><span class=\"\" style=\"top: -2.55em; margin-left: -0.04398em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">t<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1.17744em; vertical-align: -0.286108em;\"><\/span><span class=\"mord mathdefault\">h<\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathdefault\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.280556em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">t<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">m<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.311664em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.05724em;\">j<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.286108em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)<\/span><span class=\"mclose\"><span class=\"mclose\">)<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.891331em;\"><span class=\"\" style=\"top: -3.113em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.13889em;\">T<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\"><span class=\"mord mathdefault\">Q<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.864108em;\"><span class=\"\" style=\"top: -2.453em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">t<\/span><\/span><\/span><span class=\"\" style=\"top: -3.113em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">\u2212<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.247em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathdefault\" style=\"margin-right: 0.04398em;\">z<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.280556em;\"><span class=\"\" style=\"top: -2.55em; margin-left: -0.04398em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">t<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1.03611em; vertical-align: -0.286108em;\"><\/span><span class=\"mord mathdefault\">h<\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathdefault\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.280556em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">t<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">m<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.311664em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.05724em;\">j<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.286108em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span><\/span><br \/> sum\u4e2d\u7684\u7b2c\u4e00\u4e2a\u5143\u7d20\u662f\u521d\u59cb\u7ea6\u675f\u2014\u5b83\u5c06\u7b2c\u4e00\u4e2a\u673a\u5668\u4eba\u59ff\u6001\u8bbe\u7f6e\u4e3a\u4e0e\u5730\u56fe\u7684\u539f\u70b9\u76f8\u7b49\u3002\u534f\u65b9\u5dee<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> \u03a9 0 \\Omega_0 <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.83333em; vertical-align: -0.15em;\"><\/span><span class=\"mord\"><span class=\"mord\">\u03a9<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.301108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">0<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u8868\u793a\u5b8c\u5168\u7f6e\u4fe1\u5ea6\u3002<br \/> \u672c\u8d28\u4e0a,<br \/> <span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"> \u03a9 0 = [ \u221e 0 0 0 \u221e 0 0 0 \u221e ] \\Omega_0 = \\begin{bmatrix} \\infty &0 & 0 \\\\ 0 & \\infty & 0\\\\ 0 & 0 & \\infty \\end{bmatrix} <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.83333em; vertical-align: -0.15em;\"><\/span><span class=\"mord\"><span class=\"mord\">\u03a9<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.301108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">0<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 3.60004em; vertical-align: -1.55002em;\"><\/span><span class=\"minner\"><span class=\"mopen\"><span class=\"delimsizing mult\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 2.05002em;\"><span class=\"\" style=\"top: -2.25em;\"><span class=\"pstrut\" style=\"height: 3.155em;\"><\/span><span class=\"delimsizinginner delim-size4\"><span class=\"\">\u23a3<\/span><\/span><\/span><span class=\"\" style=\"top: -4.05002em;\"><span class=\"pstrut\" style=\"height: 3.155em;\"><\/span><span class=\"delimsizinginner delim-size4\"><span class=\"\">\u23a1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.55002em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\"><span class=\"mtable\"><span class=\"col-align-c\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 2.05em;\"><span class=\"\" style=\"top: -4.21em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"mord\"><span class=\"mord\">\u221e<\/span><\/span><\/span><span class=\"\" style=\"top: -3.01em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"mord\"><span class=\"mord\">0<\/span><\/span><\/span><span class=\"\" style=\"top: -1.81em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"mord\"><span class=\"mord\">0<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.55em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"arraycolsep\" style=\"width: 0.5em;\"><\/span><span class=\"arraycolsep\" style=\"width: 0.5em;\"><\/span><span class=\"col-align-c\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 2.05em;\"><span class=\"\" style=\"top: -4.21em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"mord\"><span class=\"mord\">0<\/span><\/span><\/span><span class=\"\" style=\"top: -3.01em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"mord\"><span class=\"mord\">\u221e<\/span><\/span><\/span><span class=\"\" style=\"top: -1.81em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"mord\"><span class=\"mord\">0<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.55em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"arraycolsep\" style=\"width: 0.5em;\"><\/span><span class=\"arraycolsep\" style=\"width: 0.5em;\"><\/span><span class=\"col-align-c\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 2.05em;\"><span class=\"\" style=\"top: -4.21em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"mord\"><span class=\"mord\">0<\/span><\/span><\/span><span class=\"\" style=\"top: -3.01em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"mord\"><span class=\"mord\">0<\/span><\/span><\/span><span class=\"\" style=\"top: -1.81em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"mord\"><span class=\"mord\">\u221e<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.55em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\"><span class=\"delimsizing mult\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 2.05002em;\"><span class=\"\" style=\"top: -2.25em;\"><span class=\"pstrut\" style=\"height: 3.155em;\"><\/span><span class=\"delimsizinginner delim-size4\"><span class=\"\">\u23a6<\/span><\/span><\/span><span class=\"\" style=\"top: -4.05002em;\"><span class=\"pstrut\" style=\"height: 3.155em;\"><\/span><span class=\"delimsizinginner delim-size4\"><span class=\"\">\u23a4<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.55002em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><br \/> \u65e2\u7136\u6211\u4eec\u6b63\u5728\u5904\u7406\u591a\u7ef4\u56fe\u548c\u591a\u7ef4\u7ea6\u675f\uff0c\u90a3\u4e48\u4f7f\u7528\u66f4\u667a\u80fd\u7684\u6570\u636e\u7ed3\u6784\u6765\u5904\u7406\u6211\u4eec\u7684\u6570\u636e\u5c31\u5f88\u6709\u610f\u4e49\u3002<\/p>\n<h3>\u4e09\u3001GraphSLAM\u7b97\u6cd5<\/h3>\n<p>\u4e2a\u4eba\u8ba4\u4e3a\u8bfe\u7a0b\u5728\u8fd9\u4e2a\u90e8\u5206\u8bb2\u7684\u4e0d\u662f\u592a\u6e05\u695a\uff0c\u53ef\u80fd\u56e0\u4e3a\u5176\u907f\u514d\u6d89\u53ca\u6bd4\u8f83\u590d\u6742\u7684\u516c\u5f0f\u548c\u63a8\u5bfc\u3002\u4f46\u662f\u6211\u89c9\u5f97\u6a21\u578b\u8fd8\u662f\u6bd4\u8f83\u91cd\u8981\u7684\uff0c\u6240\u4ee5\u6211\u5c06\u5728\u8fd9\u4e2a\u90e8\u5206\u4f1a\u6574\u5408\u300a\u6982\u7387\u673a\u5668\u4eba\u300b\u4e2d\u7684\u5185\u5bb9\u3002<\/p>\n<blockquote>\n<p>1.\u300a\u6982\u7387\u673a\u5668\u4eba\u300b<br \/> 2. \u65e0\u5904\u4e0d\u5728\u7684\u5c0f\u571f\u7ffb\u8bd1\u7248<\/p>\n<\/blockquote>\n<h4>1. \u7b97\u6cd5\u601d\u60f3<\/h4>\n<p>GraphSLAM\u80cc\u540e\u7684\u601d\u60f3\u975e\u5e38\u7b80\u5355\uff0c\u4ece\u6570\u636e\u4e2d\u63d0\u53d6\u8f6f\u7ea6\u675f\uff0c\u5e76\u5c06\u4e4b\u7528\u7a00\u758f\u56fe\u7684\u5f62\u5f0f\u8868\u793a\u51fa\u6765\u3002\u5b83\u901a\u8fc7\u5c06\u8fd9\u4e9b\u7ea6\u675f\u8f6c\u6362\u5230\u5168\u5c40\u7684\u5173\u8054\u5ea6\u4f30\u8ba1\uff0c\u4ece\u800c\u83b7\u5f97\u5730\u56fe\u548c\u673a\u5668\u4eba\u7684\u8def\u5f84\u3002\u8fd9\u4e9b\u7ea6\u675f\u901a\u5e38\u90fd\u662f\u975e\u7ebf\u6027\u7684\uff0c \u4f46\u5728\u6c42\u89e3\u5b83\u4eec\u7684\u65f6\u5019\u90fd\u8981\u5bf9\u5176\u7ebf\u6027\u5316\uff0c\u5c06\u4e4b\u8f6c\u6362\u4e3a\u4fe1\u606f\u77e9\u9635\u7684\u5f62\u5f0f\u3002\u56e0\u6b64GraphSLAM\u672c\u8d28\u4e0a\u662f\u57fa\u4e8e\u4fe1\u606f\u8bba\u7684\u6280\u672f\u3002\u6211\u4eec\u5c06\u4ece\u4e24\u4e2a\u65b9\u9762\u6765\u8ba8\u8bbaGraphSLAM\uff1a<strong>\u6784\u5efa\u5177\u6709\u975e\u7ebf\u6027\u7ea6\u675f\u7684\u7a00\u758f\u56fe<\/strong>\u3001 <strong>\u7ebf\u6027\u5316\u7ea6\u675f\u7684\u7a00\u758f\u4fe1\u606f\u77e9\u9635<\/strong>\u3002<\/p>\n<h4>(1)\u5efa\u7acb\u56fe\u5f62<\/h4>\n<p>\u5047\u8bbe\u6211\u4eec\u6709\u4e00\u7ec4\u6d4b\u91cf\u503c<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> z 1 : t z_{1:t} <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.58056em; vertical-align: -0.15em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\" style=\"margin-right: 0.04398em;\">z<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.301108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: -0.04398em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">1<\/span><span class=\"mrel mtight\">:<\/span><span class=\"mord mathdefault mtight\">t<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u53ca\u5176\u5bf9\u5e94\u7684\u5173\u8054\u5ea6\u53d8\u91cf<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> c 1 : t c_{1:t} <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.58056em; vertical-align: -0.15em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">c<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.301108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">1<\/span><span class=\"mrel mtight\">:<\/span><span class=\"mord mathdefault mtight\">t<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\uff0c\u4ee5\u53ca\u63a7\u5236\u91cf\u96c6\u5408<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> u 1 : t u_{1:t} <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.58056em; vertical-align: -0.15em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">u<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.301108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">1<\/span><span class=\"mrel mtight\">:<\/span><span class=\"mord mathdefault mtight\">t<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u3002GraphSLAM\u5c06\u8fd9\u4e9b\u6570\u636e\u8f6c\u6362\u4e3a\u56fe\uff0c\u56fe\u4e2d\u7684\u8282\u70b9\u5c31\u662f\u673a\u5668\u4eba\u7684\u4f4d\u59ff<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> x 1 : t x_{1:t} <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.58056em; vertical-align: -0.15em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.301108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">1<\/span><span class=\"mrel mtight\">:<\/span><span class=\"mord mathdefault mtight\">t<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\uff0c \u4ee5\u53ca\u5730\u56fe\u7684\u7279\u5f81<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> m = m j m = {m_j} <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.43056em; vertical-align: 0em;\"><\/span><span class=\"mord mathdefault\">m<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.716668em; vertical-align: -0.286108em;\"><\/span><span class=\"mord\"><span class=\"mord\"><span class=\"mord mathdefault\">m<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.311664em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.05724em;\">j<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.286108em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u3002\u56fe\u4e2d\u7684\u6bcf\u4e00\u6761\u8fb9\u90fd\u5bf9\u5e94\u7740\u4e00\u4e2a\u4e8b\u4ef6\uff0c\u8fd0\u52a8\u4e8b\u4ef6\u751f\u6210\u4e00\u6761\u8fde\u63a5\u7740\u4e24\u4e2a\u673a\u5668\u4eba\u4f4d\u59ff\u7684\u8fb9\uff0c\u6d4b\u91cf\u4e8b\u4ef6\u5219\u5728\u4f4d\u59ff\u548c\u5730\u56fe\u4e2d\u7684\u7279\u5f81\u4e4b\u95f4\u6784\u5efa\u4e86\u8fb9\u3002 \u8fb9\u8868\u793aGraphSLAM\u4e2d\u4f4d\u59ff\u548c\u7279\u5f81\u4e4b\u95f4\u7684\u8f6f\u7ea6\u675f\u3002<\/p>\n<p>\u5bf9\u4e8e\u4e00\u4e2a\u7ebf\u6027\u7cfb\u7edf\uff0c\u8fd9\u4e9b\u7ea6\u675f\u5bf9\u5e94\u7740\u5927\u7cfb\u7edf\u65b9\u7a0b\u4e2d\u7684\u4fe1\u606f\u77e9\u9635\u548c\u4fe1\u606f\u5411\u91cf\u7684\u5143\u7d20\u3002\u6309\u7167\u60ef\u4f8b\uff0c\u4ee4<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> \u03a9 \\Omega <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.68333em; vertical-align: 0em;\"><\/span><span class=\"mord\">\u03a9<\/span><\/span><\/span><\/span><\/span>\u8868\u793a\u4fe1\u606f\u77e9\u9635\uff0c<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> \u03be \\xi <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.88888em; vertical-align: -0.19444em;\"><\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.04601em;\">\u03be<\/span><\/span><\/span><\/span><\/span>\u8868\u793a\u4fe1\u606f\u5411\u91cf\u3002\u540e\u9762\u6211\u4eec\u4f1a\u63d0\u5230\uff0c \u6bcf\u4e2a\u6d4b\u91cf\u503c\u548c\u63a7\u5236\u91cf\u90fd\u4f1a\u5bf9<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> \u03a9 \\Omega <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.68333em; vertical-align: 0em;\"><\/span><span class=\"mord\">\u03a9<\/span><\/span><\/span><\/span><\/span>\u548c<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> \u03be \\xi <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.88888em; vertical-align: -0.19444em;\"><\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.04601em;\">\u03be<\/span><\/span><\/span><\/span><\/span>\u8fdb\u884c\u4e00\u6b21<strong>\u5c40\u90e8\u66f4\u65b0<\/strong>\uff08local update\uff09\uff0c\u5176\u8868\u73b0\u5f62\u5f0f\u5c31\u662f\u5728\u56fe\u4e2d\u589e\u52a0\u4e86\u4e00\u6761\u8fb9\u3002 \u5b9e\u9645\u4e0a\uff0c\u5c06\u63a7\u5236\u91cf\u548c\u6d4b\u91cf\u503c\u6574\u5408\u8fdb<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> \u03a9 \\Omega <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.68333em; vertical-align: 0em;\"><\/span><span class=\"mord\">\u03a9<\/span><\/span><\/span><\/span><\/span>\u548c<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> \u03be \\xi <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.88888em; vertical-align: -0.19444em;\"><\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.04601em;\">\u03be<\/span><\/span><\/span><\/span><\/span>\u7684\u89c4\u5219\u5c31\u662f\u5c40\u90e8\u5730\u589e\u52a0\uff0c\u5728\u4e00\u5b9a\u7a0b\u5ea6\u4e0a\u5c06\u4fe1\u606f\u8868\u793a\u4e3a\u4e00\u79cd<strong>\u589e\u91cf<\/strong>\uff08additive quantity\uff09\u3002<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/imgconvert.csdnimg.cn\/aHR0cHM6Ly9nYW95aWNoYW8uY29tL1hpYW90dS9pbWcvcHJfZmlndXJlXzExLjJhLnBuZw\" =\"\" =\"\" alt=\"autostore\u673a\u5668\u4eba\u7a0b\u5e8f_\u673a\u5668\u4eba\u5de5\u7a0b\u5e08\u662f\u505a\u4ec0\u4e48\u7684 (https:\/\/mushiming.com\/) \u7b2c6\u5f20\" title=\"autostore\u673a\u5668\u4eba\u7a0b\u5e8f_\u673a\u5668\u4eba\u5de5\u7a0b\u5e08\u662f\u505a\u4ec0\u4e48\u7684 \u7b2c6\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" ><\/p>\n<p>\u56fe3.1.1a. \u89c2\u6d4b\u5230\u8def\u6807<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> m 1 m_1 <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.58056em; vertical-align: -0.15em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">m<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.301108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p>\u56fe3.1.1\u4e3e\u4f8b\u8bf4\u660e\u4e86\u6784\u5efa\u56fe\u53ca\u5176\u4fe1\u606f\u77e9\u9635\u7684\u8fc7\u7a0b\u3002\u9996\u5148\u8003\u8651\u4e00\u4e2a\u6d4b\u91cf\u503c<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> z t i z_t^i <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.07166em; vertical-align: -0.247em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\" style=\"margin-right: 0.04398em;\">z<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.824664em;\"><span class=\"\" style=\"top: -2.453em; margin-left: -0.04398em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">t<\/span><\/span><\/span><span class=\"\" style=\"top: -3.063em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">i<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.247em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\uff0c\u5b83\u63d0\u4f9b\u4e86<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> t t <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.61508em; vertical-align: 0em;\"><\/span><span class=\"mord mathdefault\">t<\/span><\/span><\/span><\/span><\/span>\u65f6\u523b\u673a\u5668\u4eba\u4f4d\u59ff<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> x t x_t <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.58056em; vertical-align: -0.15em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.280556em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">t<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u548c\u7279\u5f81<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> j = c t i j = c_t^i <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.85396em; vertical-align: -0.19444em;\"><\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.05724em;\">j<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1.07166em; vertical-align: -0.247em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">c<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.824664em;\"><span class=\"\" style=\"top: -2.453em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">t<\/span><\/span><\/span><span class=\"\" style=\"top: -3.063em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">i<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.247em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u4e4b\u95f4\u7684\u4fe1\u606f\u3002 \u5728GraphSLAM\u4e2d\u8fd9\u4e00\u4fe1\u606f\u4f1a\u88ab\u8868\u8ff0\u4e3a<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> x t x_t <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.58056em; vertical-align: -0.15em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.280556em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">t<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u548c<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> m j m_j <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.716668em; vertical-align: -0.286108em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">m<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.311664em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.05724em;\">j<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.286108em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u4e4b\u95f4\u7684\u4e00\u4e2a\u7ea6\u675f\u3002\u6211\u4eec\u53ef\u4ee5\u5c06\u8fd9\u4e2a\u8fb9\u770b\u4f5c\u662f<strong>\u5f39\u7c27-\u8d28\u5757\u6a21\u578b<\/strong>(spring-mass model)\u4e2d\u7684\u5f39\u7c27\uff0c\u7ea6\u675f\u5f62\u5f0f\u4e3a <span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"> ( z t i \u2212 h ( x t , m j ) ) T Q t \u2212 1 ( z t i \u2212 h ( x t , m j ) ) \\left(z_t^i - h(x_t, m_j) \\right)^T Q_t^{-1} \\left(z_t^i - h(x_t, m_j) \\right) <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.4559em; vertical-align: -0.35001em;\"><\/span><span class=\"minner\"><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top: 0em;\"><span class=\"delimsizing size1\">(<\/span><\/span><span class=\"mord\"><span class=\"mord mathdefault\" style=\"margin-right: 0.04398em;\">z<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.874664em;\"><span class=\"\" style=\"top: -2.453em; margin-left: -0.04398em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">t<\/span><\/span><\/span><span class=\"\" style=\"top: -3.113em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">i<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.247em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><span class=\"mord mathdefault\">h<\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathdefault\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.280556em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">t<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">m<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.311664em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.05724em;\">j<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.286108em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)<\/span><span class=\"mclose delimcenter\" style=\"top: 0em;\"><span class=\"delimsizing size1\">)<\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.10589em;\"><span class=\"\" style=\"top: -3.32756em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.13889em;\">T<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">Q<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.864108em;\"><span class=\"\" style=\"top: -2.453em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">t<\/span><\/span><\/span><span class=\"\" style=\"top: -3.113em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">\u2212<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.247em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top: 0em;\"><span class=\"delimsizing size1\">(<\/span><\/span><span class=\"mord\"><span class=\"mord mathdefault\" style=\"margin-right: 0.04398em;\">z<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.874664em;\"><span class=\"\" style=\"top: -2.453em; margin-left: -0.04398em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">t<\/span><\/span><\/span><span class=\"\" style=\"top: -3.113em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">i<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.247em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><span class=\"mord mathdefault\">h<\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathdefault\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.280556em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">t<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">m<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.311664em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.05724em;\">j<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.286108em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)<\/span><span class=\"mclose delimcenter\" style=\"top: 0em;\"><span class=\"delimsizing size1\">)<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u5176\u4e2d<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> h h <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.69444em; vertical-align: 0em;\"><\/span><span class=\"mord mathdefault\">h<\/span><\/span><\/span><\/span><\/span>\u662f\u5df2\u7ecf\u5f88\u719f\u6089\u7684\u6d4b\u91cf\u65b9\u7a0b\uff0c<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> Q t Q_t <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.87777em; vertical-align: -0.19444em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">Q<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.280556em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">t<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u5219\u662f\u6d4b\u91cf\u566a\u58f0\u4e2d\u7684\u534f\u65b9\u5dee\u3002\u56fe3.1.1a\u4e2d\u663e\u793a\u4e86GraphSLAM\u5c06\u8fd9\u6837\u7684\u4e00\u6761\u8fb9\u6dfb\u52a0\u8fdb\u56fe\u7684\u8fc7\u7a0b\u3002<\/p>\n<p>\u73b0\u5728\u8003\u8651\u673a\u5668\u4eba\u7684\u8fd0\u52a8\u3002\u63a7\u5236\u91cf<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> u t u_t <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.58056em; vertical-align: -0.15em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">u<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.280556em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">t<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u63d0\u4f9b\u4e86<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> t \u2212 1 t-1 <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.69841em; vertical-align: -0.08333em;\"><\/span><span class=\"mord mathdefault\">t<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.64444em; vertical-align: 0em;\"><\/span><span class=\"mord\">1<\/span><\/span><\/span><\/span><\/span>\u65f6\u523b\u548c<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> t t <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.61508em; vertical-align: 0em;\"><\/span><span class=\"mord mathdefault\">t<\/span><\/span><\/span><\/span><\/span>\u65f6\u523b\u673a\u5668\u4eba\u7684\u76f8\u5bf9\u4f4d\u7f6e\u5173\u7cfb\u7684\u4fe1\u606f\u3002\u8fd9\u4e00\u4fe1\u606f\u53ef\u4ee5\u4ee5\u5982\u4e0b\u7684\u5f62\u5f0f\u4f5c\u4e3a\u4e00\u4e2a\u7ea6\u675f\u6dfb\u52a0\u5230\u56fe\u4e2d: <span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"> ( x t \u2212 g ( u t , x t \u2212 1 ) ) T R t \u2212 1 ( x t \u2212 g ( u t , x t \u2212 1 ) ) \\left(x_t - g(u_t, x_{t-1}) \\right)^T R_t^{-1} \\left(x_t - g(u_t, x_{t-1}) \\right) <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.23123em; vertical-align: -0.25em;\"><\/span><span class=\"minner\"><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top: 0em;\">(<\/span><span class=\"mord\"><span class=\"mord mathdefault\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.280556em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">t<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.03588em;\">g<\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathdefault\">u<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.280556em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">t<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.301108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">t<\/span><span class=\"mbin mtight\">\u2212<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.208331em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)<\/span><span class=\"mclose delimcenter\" style=\"top: 0em;\">)<\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.981231em;\"><span class=\"\" style=\"top: -3.2029em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.13889em;\">T<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\" style=\"margin-right: 0.00773em;\">R<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.864108em;\"><span class=\"\" style=\"top: -2.453em; margin-left: -0.00773em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">t<\/span><\/span><\/span><span class=\"\" style=\"top: -3.113em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">\u2212<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.247em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top: 0em;\">(<\/span><span class=\"mord\"><span class=\"mord mathdefault\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.280556em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">t<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.03588em;\">g<\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathdefault\">u<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.280556em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">t<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.301108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">t<\/span><span class=\"mbin mtight\">\u2212<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.208331em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)<\/span><span class=\"mclose delimcenter\" style=\"top: 0em;\">)<\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u5176\u4e2d\uff0c<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> g g <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.625em; vertical-align: -0.19444em;\"><\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.03588em;\">g<\/span><\/span><\/span><\/span><\/span>\u5c31\u662f\u673a\u5668\u4eba\u8fd0\u52a8\u5b66\u6a21\u578b\uff0c<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> R t R_t <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.83333em; vertical-align: -0.15em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\" style=\"margin-right: 0.00773em;\">R<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.280556em;\"><span class=\"\" style=\"top: -2.55em; margin-left: -0.00773em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">t<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u5219\u662f\u8fd0\u52a8\u566a\u58f0\u7684\u534f\u65b9\u5dee\u3002\u5982\u56fe3.1.1b\u6240\u793a\uff0c\u6dfb\u52a0\u4e00\u4e2a\u8fd9\u6837\u7684\u8fb9\u5230\u56fe\u4e2d\u3002 \u56fe\u4e2d\u8fd8\u663e\u793a\u4e86\u5728\u4fe1\u606f\u77e9\u9635\u4e2d\u65b0\u589e\u7684\u4ece\u4f4d\u59ff<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> x t \u2212 1 x_{t-1} <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.638891em; vertical-align: -0.208331em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.301108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">t<\/span><span class=\"mbin mtight\">\u2212<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.208331em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u5230<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> x t x_t <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.58056em; vertical-align: -0.15em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.280556em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">t<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u4e4b\u95f4\u7684\u5143\u7d20\u3002\u8fd9\u4e2a\u66f4\u65b0\u8fc7\u7a0b\u4e5f\u662f\u589e\u91cf\u7684\u3002\u8fd9\u4e00\u6570\u503c\u53cd\u6620\u4e86\u56e0\u4e3a\u8fd0\u52a8\u566a\u58f0<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> R t R_t <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.83333em; vertical-align: -0.15em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\" style=\"margin-right: 0.00773em;\">R<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.280556em;\"><span class=\"\" style=\"top: -2.55em; margin-left: -0.00773em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">t<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u800c\u6b8b\u5b58\u7684\u4e0d\u786e\u5b9a\u5ea6\u3002\u566a\u58f0\u8d8a\u5c0f\uff0c \u6dfb\u52a0\u5230<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> \u03a9 \\Omega <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.68333em; vertical-align: 0em;\"><\/span><span class=\"mord\">\u03a9<\/span><\/span><\/span><\/span><\/span>\u548c<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> \u03be \\xi <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.88888em; vertical-align: -0.19444em;\"><\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.04601em;\">\u03be<\/span><\/span><\/span><\/span><\/span>\u7684\u6570\u503c\u5c31\u8d8a\u5927\u3002<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/imgconvert.csdnimg.cn\/aHR0cHM6Ly9nYW95aWNoYW8uY29tL1hpYW90dS9pbWcvcHJfZmlndXJlXzExLjJiLnBuZw\" =\"\" =\"\" alt=\"autostore\u673a\u5668\u4eba\u7a0b\u5e8f_\u673a\u5668\u4eba\u5de5\u7a0b\u5e08\u662f\u505a\u4ec0\u4e48\u7684 (https:\/\/mushiming.com\/) \u7b2c7\u5f20\" title=\"autostore\u673a\u5668\u4eba\u7a0b\u5e8f_\u673a\u5668\u4eba\u5de5\u7a0b\u5e08\u662f\u505a\u4ec0\u4e48\u7684 \u7b2c7\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" ><\/p>\n<p>\u56fe3.1.1b. \u4ece<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> x 1 x_1 <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.58056em; vertical-align: -0.15em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.301108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u5230<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> x 2 x_2 <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.58056em; vertical-align: -0.15em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.301108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u7684\u673a\u5668\u4eba\u8fd0\u52a8<\/p>\n<p>\u7efc\u5408\u4e86\u6240\u6709\u7684\u6d4b\u91cf\u503c<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> z 1 : t z_{1:t} <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.58056em; vertical-align: -0.15em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\" style=\"margin-right: 0.04398em;\">z<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.301108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: -0.04398em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">1<\/span><span class=\"mrel mtight\">:<\/span><span class=\"mord mathdefault mtight\">t<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u548c\u63a7\u5236\u91cf<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> u 1 : t u_{1:t} <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.58056em; vertical-align: -0.15em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">u<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.301108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">1<\/span><span class=\"mrel mtight\">:<\/span><span class=\"mord mathdefault mtight\">t<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\uff0c\u6211\u4eec\u5c31\u5f97\u5230\u4e86\u8f6f\u7ea6\u675f\u5f62\u5f0f\u7684\u7a00\u758f\u56fe\u3002\u56fe\u4e2d\u7ea6\u675f\u7684\u6570\u91cf\u968f\u7740\u65f6\u95f4\u7ebf\u6027\u7684\u589e\u957f\uff0c\u56e0\u6b64\u6240\u5f97\u7684\u56fe\u662f\u7a00\u758f\u7684\u3002\u56fe\u4e2d\u6240\u6709\u7ea6\u675f\u7684\u548c\u4e3a:<\/p>\n<p><span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"> J G r a p h S L A M = x 0 T \u03a9 0 x 0 + \u2211 t ( x t \u2212 g ( u t , x t \u2212 1 ) ) T R t \u2212 1 ( x t \u2212 g ( u t , x t \u2212 1 ) ) + \u2211 t \u2211 i ( z t i \u2212 h ( x t , c t i ) ) T Q t \u2212 1 ( z t i \u2212 h ( x t , c t i ) ) J_{\\mathrm{GraphSLAM}} = x_0^T \\Omega_0 x_0 + \\sum_t \\left(x_t - g(u_t, x_{t-1}) \\right)^T R_t^{-1} \\left(x_t - g(u_t, x_{t-1}) \\right) \\\\+ \\sum_t \\sum_i \\left(z_t^i - h(x_t, c_t^i) \\right)^T Q_t^{-1} \\left(z_t^i - h(x_t, c_t^i) \\right) <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.969438em; vertical-align: -0.286108em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\" style=\"margin-right: 0.09618em;\">J<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.336108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: -0.09618em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\"><span class=\"mord mathrm mtight\">G<\/span><span class=\"mord mathrm mtight\">r<\/span><span class=\"mord mathrm mtight\">a<\/span><span class=\"mord mathrm mtight\">p<\/span><span class=\"mord mathrm mtight\">h<\/span><span class=\"mord mathrm mtight\">S<\/span><span class=\"mord mathrm mtight\">L<\/span><span class=\"mord mathrm mtight\">A<\/span><span class=\"mord mathrm mtight\">M<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.286108em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1.13833em; vertical-align: -0.247em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.891331em;\"><span class=\"\" style=\"top: -2.453em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">0<\/span><\/span><\/span><span class=\"\" style=\"top: -3.113em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.13889em;\">T<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.247em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\"><span class=\"mord\">\u03a9<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.301108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">0<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\"><span class=\"mord mathdefault\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.301108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">0<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><span class=\"mbin\">+<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 2.30001em; vertical-align: -1.25001em;\"><\/span><span class=\"mop op-limits\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.05001em;\"><span class=\"\" style=\"top: -1.89999em; margin-left: 0em;\"><span class=\"pstrut\" style=\"height: 3.05em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">t<\/span><\/span><\/span><span class=\"\" style=\"top: -3.05em;\"><span class=\"pstrut\" style=\"height: 3.05em;\"><\/span><span class=\"\"><span class=\"mop op-symbol large-op\">\u2211<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.25001em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"minner\"><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top: 0em;\">(<\/span><span class=\"mord\"><span class=\"mord mathdefault\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.280556em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">t<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.03588em;\">g<\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathdefault\">u<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.280556em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">t<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.301108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">t<\/span><span class=\"mbin mtight\">\u2212<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.208331em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)<\/span><span class=\"mclose delimcenter\" style=\"top: 0em;\">)<\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.981231em;\"><span class=\"\" style=\"top: -3.2029em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.13889em;\">T<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\" style=\"margin-right: 0.00773em;\">R<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.864108em;\"><span class=\"\" style=\"top: -2.453em; margin-left: -0.00773em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">t<\/span><\/span><\/span><span class=\"\" style=\"top: -3.113em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">\u2212<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.247em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top: 0em;\">(<\/span><span class=\"mord\"><span class=\"mord mathdefault\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.280556em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">t<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.03588em;\">g<\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathdefault\">u<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.280556em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">t<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.301108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">t<\/span><span class=\"mbin mtight\">\u2212<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.208331em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)<\/span><span class=\"mclose delimcenter\" style=\"top: 0em;\">)<\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><\/span><span class=\"mspace newline\"><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.66666em; vertical-align: -0.08333em;\"><\/span><span class=\"mbin\">+<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 2.38356em; vertical-align: -1.27767em;\"><\/span><span class=\"mop op-limits\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.05001em;\"><span class=\"\" style=\"top: -1.89999em; margin-left: 0em;\"><span class=\"pstrut\" style=\"height: 3.05em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">t<\/span><\/span><\/span><span class=\"\" style=\"top: -3.05em;\"><span class=\"pstrut\" style=\"height: 3.05em;\"><\/span><span class=\"\"><span class=\"mop op-symbol large-op\">\u2211<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.25001em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mop op-limits\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.05001em;\"><span class=\"\" style=\"top: -1.87233em; margin-left: 0em;\"><span class=\"pstrut\" style=\"height: 3.05em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">i<\/span><\/span><\/span><span class=\"\" style=\"top: -3.05001em;\"><span class=\"pstrut\" style=\"height: 3.05em;\"><\/span><span class=\"\"><span class=\"mop op-symbol large-op\">\u2211<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.27767em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"minner\"><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top: 0em;\"><span class=\"delimsizing size1\">(<\/span><\/span><span class=\"mord\"><span class=\"mord mathdefault\" style=\"margin-right: 0.04398em;\">z<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.874664em;\"><span class=\"\" style=\"top: -2.453em; margin-left: -0.04398em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">t<\/span><\/span><\/span><span class=\"\" style=\"top: -3.113em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">i<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.247em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><span class=\"mord mathdefault\">h<\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathdefault\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.280556em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">t<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">c<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.874664em;\"><span class=\"\" style=\"top: -2.453em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">t<\/span><\/span><\/span><span class=\"\" style=\"top: -3.113em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">i<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.247em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)<\/span><span class=\"mclose delimcenter\" style=\"top: 0em;\"><span class=\"delimsizing size1\">)<\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.10589em;\"><span class=\"\" style=\"top: -3.32756em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.13889em;\">T<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">Q<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.864108em;\"><span class=\"\" style=\"top: -2.453em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">t<\/span><\/span><\/span><span class=\"\" style=\"top: -3.113em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">\u2212<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.247em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top: 0em;\"><span class=\"delimsizing size1\">(<\/span><\/span><span class=\"mord\"><span class=\"mord mathdefault\" style=\"margin-right: 0.04398em;\">z<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.874664em;\"><span class=\"\" style=\"top: -2.453em; margin-left: -0.04398em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">t<\/span><\/span><\/span><span class=\"\" style=\"top: -3.113em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">i<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.247em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><span class=\"mord mathdefault\">h<\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathdefault\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.280556em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">t<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">c<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.874664em;\"><span class=\"\" style=\"top: -2.453em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">t<\/span><\/span><\/span><span class=\"\" style=\"top: -3.113em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">i<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.247em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)<\/span><span class=\"mclose delimcenter\" style=\"top: 0em;\"><span class=\"delimsizing size1\">)<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p>\u5b83\u662f\u5b9a\u4e49\u5728\u4f4d\u59ff\u53d8\u91cf<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> x 1 : t x_{1:t} <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.58056em; vertical-align: -0.15em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.301108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">1<\/span><span class=\"mrel mtight\">:<\/span><span class=\"mord mathdefault mtight\">t<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u4ee5\u53ca\u5730\u56fe<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> m m <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.43056em; vertical-align: 0em;\"><\/span><span class=\"mord mathdefault\">m<\/span><\/span><\/span><\/span><\/span>\u4e2d\u6240\u6709\u7684\u7279\u5f81\u4e0a\u7684\u51fd\u6570\u3002\u6ce8\u610f\u5230\u8fd9\u4e00\u8868\u8fbe\u5f0f\u8fd8\u6709\u4e00\u4e2a\u5f62\u5982<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> x 0 T \u03a9 0 x 0 x_0^T \\Omega_0 x_0 <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.08944em; vertical-align: -0.248108em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.841331em;\"><span class=\"\" style=\"top: -2.45189em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">0<\/span><\/span><\/span><span class=\"\" style=\"top: -3.063em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.13889em;\">T<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.248108em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\"><span class=\"mord\">\u03a9<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.301108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">0<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\"><span class=\"mord mathdefault\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.301108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">0<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u7684<strong>\u786c\u7ea6\u675f<\/strong>\uff08anchoring constrains\uff09\u3002 \u8be5\u7ea6\u675f\u901a\u8fc7\u5c06\u673a\u5668\u4eba\u7684\u521d\u59cb\u4f4d\u59ff\u521d\u59cb\u5316\u4e3a<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> ( 0 0 0 ) T \\begin{pmatrix} 0 & 0 & 0 \\end{pmatrix}^T <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.43124em; vertical-align: -0.35001em;\"><\/span><span class=\"minner\"><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top: 0em;\"><span class=\"delimsizing size1\">(<\/span><\/span><span class=\"mord\"><span class=\"mtable\"><span class=\"col-align-c\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.85em;\"><span class=\"\" style=\"top: -3.01em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"mord\"><span class=\"mord\">0<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.35em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"arraycolsep\" style=\"width: 0.5em;\"><\/span><span class=\"arraycolsep\" style=\"width: 0.5em;\"><\/span><span class=\"col-align-c\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.85em;\"><span class=\"\" style=\"top: -3.01em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"mord\"><span class=\"mord\">0<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.35em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"arraycolsep\" style=\"width: 0.5em;\"><\/span><span class=\"arraycolsep\" style=\"width: 0.5em;\"><\/span><span class=\"col-align-c\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.85em;\"><span class=\"\" style=\"top: -3.01em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"mord\"><span class=\"mord\">0<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.35em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose delimcenter\" style=\"top: 0em;\"><span class=\"delimsizing size1\">)<\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.08123em;\"><span class=\"\" style=\"top: -3.3029em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.13889em;\">T<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u6765\u56fa\u5b9a\u5730\u56fe\u7684\u7edd\u5bf9\u5750\u6807\u3002<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/imgconvert.csdnimg.cn\/aHR0cHM6Ly9nYW95aWNoYW8uY29tL1hpYW90dS9pbWcvcHJfZmlndXJlXzExLjJjLnBuZw\" =\"\" =\"\" alt=\"autostore\u673a\u5668\u4eba\u7a0b\u5e8f_\u673a\u5668\u4eba\u5de5\u7a0b\u5e08\u662f\u505a\u4ec0\u4e48\u7684 (https:\/\/mushiming.com\/) \u7b2c8\u5f20\" title=\"autostore\u673a\u5668\u4eba\u7a0b\u5e8f_\u673a\u5668\u4eba\u5de5\u7a0b\u5e08\u662f\u505a\u4ec0\u4e48\u7684 \u7b2c8\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" ><\/p>\n<p>\u56fe3.1c. \u51e0\u6b65\u4e4b\u540e\u7684\u7ea6\u675f<\/p>\n<p>\u5728\u76f8\u5173\u7684\u4fe1\u606f\u77e9\u9635<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> \u03a9 \\Omega <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.68333em; vertical-align: 0em;\"><\/span><span class=\"mord\">\u03a9<\/span><\/span><\/span><\/span><\/span>\u4e2d\uff0c\u975e\u5bf9\u89d2\u5143\u7d20\u90fd\u4e3a0, \u4f46\u6709\u4e24\u4e2a\u4f8b\u5916\u3002<\/p>\n<ul>\n<li>\u4efb\u4f55\u4e24\u4e2a\u90bb\u63a5\u7684\u4f4d\u59ff\u72b6\u6001<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> x t \u2212 1 x_{t-1} <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.638891em; vertical-align: -0.208331em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.301108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">t<\/span><span class=\"mbin mtight\">\u2212<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.208331em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u548c<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> x t x_t <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.58056em; vertical-align: -0.15em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.280556em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">t<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u5bf9\u5e94\u7740\u4e00\u4e2a\u975e\u96f6\u7684\u503c\uff0c \u8868\u793a\u7531\u63a7\u5236\u91cf<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> u t u_t <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.58056em; vertical-align: -0.15em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">u<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.280556em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">t<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u6240\u5f15\u5165\u7684\u4fe1\u606f\u8fb9\u3002<\/li>\n<li>\u5982\u679c\u673a\u5668\u4eba\u5728\u4f4d\u59ff<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> x t x_t <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.58056em; vertical-align: -0.15em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.280556em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">t<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u4e0a\u80fd\u591f\u89c2\u6d4b\u5230\u7279\u5f81<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> m j m_j <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.716668em; vertical-align: -0.286108em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">m<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.311664em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.05724em;\">j<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.286108em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u90a3\u4e48\u4fe1\u606f\u77e9\u9635\u4e2d\u5bf9\u5e94\u7740<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> x t x_t <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.58056em; vertical-align: -0.15em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.280556em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">t<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>-<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> m j m_j <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.716668em; vertical-align: -0.286108em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">m<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.311664em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.05724em;\">j<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.286108em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u7684\u5143\u7d20\u5c31\u662f\u975e\u96f6\u7684\u3002<\/li>\n<\/ul>\n<p>\u82e5\u6240\u6709\u7684\u7279\u5f81\u5bf9\u6240\u5bf9\u5e94\u7684\u4fe1\u606f\u77e9\u9635\u5143\u7d20\u90fd\u4e3a0\u3002 \u8fd9\u53cd\u6620\u4e86\u6211\u4eec\u4ece\u6765\u6ca1\u6709\u91c7\u96c6\u5230\u7279\u5f81\u4e4b\u95f4\u7684\u76f8\u5bf9\u4f4d\u7f6e\u5173\u7cfb\uff0c\u5728SLAM\u4e2d\u6211\u4eec\u91c7\u96c6\u5230\u7684\u5168\u662f\u6d4b\u91cf\u503c\u4fe1\u606f\uff0c\u7ea6\u675f\u4e86\u673a\u5668\u4eba\u548c\u7279\u5f81\u4e4b\u95f4\u7684\u4f4d\u7f6e\u5173\u7cfb\u3002\u56e0\u6b64\uff0c\u4fe1\u606f\u77e9\u9635\u5c31\u662f\u7a00\u758f\u7684\uff0c \u9664\u4e86\u7ebf\u6027\u6570\u91cf\u7684\u5143\u7d20\u5916\u5176\u4f59\u5404\u5143\u7d20\u5747\u4e3a0\u3002<\/p>\n<h5>(2) \u63a8\u8bba<\/h5>\n<p>\u663e\u7136\uff0c\u65e0\u8bba\u662f\u56fe\u7684\u5f62\u5f0f\u8fd8\u662f\u4fe1\u606f\u77e9\u9635\u7684\u5f62\u5f0f\u90fd\u53ef\u4ee5\u7ed9\u6211\u4eec\u63d0\u4f9b\u5730\u56fe\u548c\u8def\u5f84\u4fe1\u606f\u3002\u5728GraphSLAM\u4e2d\u5730\u56fe\u548c\u8def\u5f84\u662f\u901a\u8fc7\u7ebf\u6027\u5316\u7684\u4fe1\u606f\u77e9\u9635<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> \u03bc = \u03a9 \u2212 1 \u03be \u03bc = \\Omega^{-1} \\xi <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.625em; vertical-align: -0.19444em;\"><\/span><span class=\"mord mathdefault\">\u03bc<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1.00855em; vertical-align: -0.19444em;\"><\/span><span class=\"mord\"><span class=\"mord\">\u03a9<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.814108em;\"><span class=\"\" style=\"top: -3.063em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">\u2212<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.04601em;\">\u03be<\/span><\/span><\/span><\/span><\/span>\u83b7\u5f97\u7684\u3002 \u8fd9\u4e2a\u64cd\u4f5c\u8981\u6c42\u6211\u4eec\u6c42\u89e3\u4e00\u4e2a\u7531\u7ebf\u6027\u65b9\u7a0b\u6784\u6210\u7684\u7cfb\u7edf\u3002\u8fd9\u5e26\u6765\u4e86\u4e00\u4e2a\u6211\u4eec\u8be5\u5982\u4f55\u9ad8\u6548\u7684\u6062\u590d\u5730\u56fe\u4f30\u8ba1<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> \u03bc \u03bc <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.625em; vertical-align: -0.19444em;\"><\/span><span class=\"mord mathdefault\">\u03bc<\/span><\/span><\/span><\/span><\/span>\u548c\u534f\u65b9\u5dee\u77e9\u9635<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> \u03a3 \\Sigma <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.68333em; vertical-align: 0em;\"><\/span><span class=\"mord\">\u03a3<\/span><\/span><\/span><\/span><\/span>\u7684\u95ee\u9898\u3002<\/p>\n<p>\u8fd9\u4e00\u590d\u6742\u95ee\u9898\u7684\u7b54\u6848\u4f9d\u8d56\u4e8e\u4e16\u754c\u7684\u62d3\u6251\u903b\u8f91\u3002\u5982\u679c\u6bcf\u4e2a\u7279\u5f81\u90fd\u53ea\u80fd\u5728\u4e00\u5904\u770b\u5230\uff0c\u90a3\u4e48\u8fd9\u4e2a\u56fe\u5c31\u662f\u7ebf\u6027\u7ea6\u675f\u8868\u793a\u7684\u3002\u90a3\u4e48<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> \u03a9 \\Omega <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.68333em; vertical-align: 0em;\"><\/span><span class=\"mord\">\u03a9<\/span><\/span><\/span><\/span><\/span>\u5c31\u53ef\u4ee5\u901a\u8fc7\u7ebf\u6027\u53d8\u6362\u5199\u6210<strong>\u5e26\u5bf9\u89d2\u9635<\/strong>(band-diagonal matrix)\u7684\u5f62\u5f0f\uff0c \u6240\u6709\u7684\u975e\u96f6\u5143\u7d20\u90fd\u51fa\u73b0\u5728\u5bf9\u89d2\u5143\u7d20\u7684\u4e24\u4fa7\u3002\u65b9\u7a0b<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> \u03bc = \u03a9 \u2212 1 \u03be \u03bc = \\Omega^{-1} \\xi <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.625em; vertical-align: -0.19444em;\"><\/span><span class=\"mord mathdefault\">\u03bc<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1.00855em; vertical-align: -0.19444em;\"><\/span><span class=\"mord\"><span class=\"mord\">\u03a9<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.814108em;\"><span class=\"\" style=\"top: -3.063em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">\u2212<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.04601em;\">\u03be<\/span><\/span><\/span><\/span><\/span>\u5c31\u53ef\u4ee5\u5728\u7ebf\u6027\u7684\u65f6\u95f4\u91cc\u89e3\u51fa\u3002\u8fd9\u4e00\u601d\u60f3\u63cf\u8ff0\u7684\u662f\u53ea\u904d\u5386\u4e00\u6b21\u7684\u65e0\u73af\u4e16\u754c\uff0c \u56e0\u6b64\u6bcf\u4e2a\u7279\u5f81\u90fd\u53ef\u4ee5\u770b\u4f5c\u662f\u4e00\u4e2a\u77ed\u7684\u8fde\u7eed\u7684\u65f6\u95f4\u6bb5\u5185\u7684\u7279\u5f81\u3002<\/p>\n<p>\u4f46\u662f\uff0c\u66f4\u4e00\u822c\u7684\u60c5\u51b5\u662f\u540c\u4e00\u4e2a\u7279\u5f81\u53ef\u80fd\u88ab\u591a\u6b21\u89c2\u6d4b\u5230\uff0c\u800c\u4e14\u6bcf\u6b21\u89c2\u6d4b\u5230\u7684\u65f6\u95f4\u95f4\u9694\u5f88\u5927\u3002\u8fd9\u53ef\u80fd\u662f\u7531\u4e8e\u673a\u5668\u4eba\u5728\u8d70\u5eca\u91cc\u6765\u6765\u56de\u56de\u7684\u8fd0\u52a8\uff0c\u6216\u8005\u4e16\u754c\u672c\u8eab\u5c31\u662f\u6709\u73af\u7684\u3002 \u5728\u4efb\u4f55\u4e00\u79cd\u60c5\u51b5\u4e0b\uff0c\u90fd\u6709\u7279\u5f81<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> m j m_j <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.716668em; vertical-align: -0.286108em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">m<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.311664em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.05724em;\">j<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.286108em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u5728\u4e24\u4e2a\u5b8c\u5168\u4e0d\u540c\u7684\u65f6\u95f4\u70b9\u6240\u5bf9\u5e94\u7684\u4f4d\u59ff<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> x t 1 , x t 2 x_{t_1}, x_{t_2} <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.68066em; vertical-align: -0.2501em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.280556em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">t<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.317314em;\"><span class=\"\" style=\"top: -2.357em; margin-left: 0em; margin-right: 0.0714286em;\"><span class=\"pstrut\" style=\"height: 2.5em;\"><\/span><span class=\"sizing reset-size3 size1 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.143em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2501em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.280556em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">t<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.317314em;\"><span class=\"\" style=\"top: -2.357em; margin-left: 0em; margin-right: 0.0714286em;\"><span class=\"pstrut\" style=\"height: 2.5em;\"><\/span><span class=\"sizing reset-size3 size1 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.143em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2501em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u4e0a\u88ab\u89c2\u6d4b\u5230\uff0c\u5176\u4e2d<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> t 2 \u226b t 1 t_2 \\gg t_1 <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.76508em; vertical-align: -0.15em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">t<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.301108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><span class=\"mrel\">\u226b<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.76508em; vertical-align: -0.15em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">t<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.301108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u3002\u5728\u6211\u4eec\u7684\u7ea6\u675f\u56fe\u4e2d\uff0c\u8fd9\u5c31\u4ea7\u751f\u4e86\u4e00\u4e2a\u73af\u5f62\u4f9d\u8d56\uff0c <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> x t 1 x_{t_1} <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.68066em; vertical-align: -0.2501em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.280556em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">t<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.317314em;\"><span class=\"\" style=\"top: -2.357em; margin-left: 0em; margin-right: 0.0714286em;\"><span class=\"pstrut\" style=\"height: 2.5em;\"><\/span><span class=\"sizing reset-size3 size1 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.143em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2501em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u548c<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> x t 2 x_{t_2} <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.68066em; vertical-align: -0.2501em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.280556em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">t<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.317314em;\"><span class=\"\" style=\"top: -2.357em; margin-left: 0em; margin-right: 0.0714286em;\"><span class=\"pstrut\" style=\"height: 2.5em;\"><\/span><span class=\"sizing reset-size3 size1 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.143em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2501em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u901a\u8fc7\u63a7\u5236\u5e8f\u5217<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> u t 1 + 1 , u t 1 + 2 , \u22ef \u2009 , u t 2 u_{t_1 + 1}, u_{t_1 + 2}, \\cdots, u_{t_2} <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.68066em; vertical-align: -0.2501em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">u<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.301108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">t<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.317314em;\"><span class=\"\" style=\"top: -2.357em; margin-left: 0em; margin-right: 0.0714286em;\"><span class=\"pstrut\" style=\"height: 2.5em;\"><\/span><span class=\"sizing reset-size3 size1 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.143em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mbin mtight\">+<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2501em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">u<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.301108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">t<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.317314em;\"><span class=\"\" style=\"top: -2.357em; margin-left: 0em; margin-right: 0.0714286em;\"><span class=\"pstrut\" style=\"height: 2.5em;\"><\/span><span class=\"sizing reset-size3 size1 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.143em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mbin mtight\">+<\/span><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2501em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"minner\">\u22ef<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">u<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.280556em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">t<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.317314em;\"><span class=\"\" style=\"top: -2.357em; margin-left: 0em; margin-right: 0.0714286em;\"><span class=\"pstrut\" style=\"height: 2.5em;\"><\/span><span class=\"sizing reset-size3 size1 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.143em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2501em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u8fde\u63a5\u8d77\u6765\uff0c\u5e76\u5206\u522b\u5728<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> x t 1 x_{t_1} <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.68066em; vertical-align: -0.2501em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.280556em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">t<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.317314em;\"><span class=\"\" style=\"top: -2.357em; margin-left: 0em; margin-right: 0.0714286em;\"><span class=\"pstrut\" style=\"height: 2.5em;\"><\/span><span class=\"sizing reset-size3 size1 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.143em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2501em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u548c<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> m j m_j <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.716668em; vertical-align: -0.286108em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">m<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.311664em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.05724em;\">j<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.286108em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u4ee5\u53ca<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> x t 2 x_{t_2} <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.68066em; vertical-align: -0.2501em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.280556em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">t<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.317314em;\"><span class=\"\" style=\"top: -2.357em; margin-left: 0em; margin-right: 0.0714286em;\"><span class=\"pstrut\" style=\"height: 2.5em;\"><\/span><span class=\"sizing reset-size3 size1 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.143em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2501em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u548c<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> m j m_j <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.716668em; vertical-align: -0.286108em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">m<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.311664em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.05724em;\">j<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.286108em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u4e4b\u95f4\u5efa\u7acb\u4e86\u89c2\u6d4b\u8fb9\u3002 \u8fd9\u4e9b\u8fb9\u7684\u5b58\u5728\uff0c\u4f7f\u5f97\u6211\u4eec\u4e0d\u80fd\u901a\u8fc7\u7b80\u5355\u7684\u7ebf\u6027\u53d8\u6362\u5f97\u5230\u5e26\u5bf9\u89d2\u9635\uff0c\u56e0\u6b64\u6c42\u89e3\u5730\u56fe\u8fc7\u7a0b\u66f4\u590d\u6742\u3002\u5b9e\u9645\u4e0a\uff0c\u56e0\u4e3a<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> \u03a9 \\Omega <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.68333em; vertical-align: 0em;\"><\/span><span class=\"mord\">\u03a9<\/span><\/span><\/span><\/span><\/span>\u7684\u9006\u4e0e\u4e00\u4e2a\u5411\u91cf\u76f8\u4e58\uff0c\u6240\u4ee5\u5176\u7ed3\u679c\u53ef\u4ee5\u901a\u8fc7\u8bf8\u5982\u5171\u8f6d\u68af\u5ea6\u8fd9\u6837\u7684\u4f18\u5316\u7b97\u6cd5\u5f97\u5230\uff0c \u800c\u4e0d\u9700\u8981\u663e\u793a\u7684\u8ba1\u7b97\u4e00\u4e2a\u77e9\u9635\u7684\u9006\u3002\u56e0\u4e3a\u5b9e\u9645\u7684\u5b9e\u9645\u603b\u662f\u6709\u7740\u5404\u79cd\u5404\u6837\u7684\u73af\uff0c\u6240\u4ee5\u8fd9\u4e00\u8fc7\u7a0b\u5c31\u66f4\u6709\u610f\u4e49\u4e86\u3002<\/p>\n<p>GraphSLAM\u4f7f\u7528\u4e86\u4e00\u79cd\u79f0\u4e3a<strong>\u56e0\u5f0f\u5206\u89e3<\/strong>\uff08factorization trick\uff09\u7684\u624b\u6bb5\uff0c\u6211\u4eec\u53ef\u4ee5\u5c06\u4e4b\u770b\u4f5c\u662f\u901a\u8fc7\u4fe1\u606f\u77e9\u9635\u4f20\u64ad\u7684\u4fe1\u606f\uff0c\u5b9e\u9645\u4e0a\u5b83\u662f\u8457\u540d\u7684\u6c42\u89e3\u77e9\u9635\u9006\u7684\u6d88\u5143\u6cd5\u7684\u4e00\u79cd\u63a8\u5e7f\u5f62\u5f0f\u3002 \u5047\u8bbe\u6211\u4eec\u60f3\u8981\u4ece\u4fe1\u606f\u77e9\u9635<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> \u03a9 \\Omega <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.68333em; vertical-align: 0em;\"><\/span><span class=\"mord\">\u03a9<\/span><\/span><\/span><\/span><\/span>\u548c\u4fe1\u606f\u72b6\u6001<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> \u03be \\xi <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.88888em; vertical-align: -0.19444em;\"><\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.04601em;\">\u03be<\/span><\/span><\/span><\/span><\/span>\u4e2d\u79fb\u9664\u4e00\u4e2a\u7279\u5f81<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> m j m_j <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.716668em; vertical-align: -0.286108em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">m<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.311664em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.05724em;\">j<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.286108em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u3002\u5728\u5f39\u7c27\u8d28\u5757\u7684\u6a21\u578b\u4e2d\uff0c\u8fd9\u5c31\u76f8\u5f53\u4e8e\u79fb\u9664\u4e00\u4e2a\u8282\u70b9\u548c\u8fde\u63a5\u5728\u8be5\u8282\u70b9\u4e0a\u7684\u6240\u6709\u8fb9\u3002 \u540e\u9762\u6211\u4eec\u4f1a\u770b\u5230\uff0c\u8fd9\u53ef\u4ee5\u901a\u8fc7\u4e00\u4e2a\u5341\u5206\u7b80\u5355\u7684\u64cd\u4f5c\u6765\u5b9e\u73b0\uff0c\u6211\u4eec\u53ef\u4ee5\u901a\u8fc7\u5728\u4efb\u4f55\u5171\u6709<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> m j m_j <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.716668em; vertical-align: -0.286108em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">m<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.311664em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.05724em;\">j<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.286108em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u7684\u4e24\u4e2a\u4f4d\u59ff\u8282\u70b9\u4e4b\u95f4\u6dfb\u52a0\u4e00\u6761\u8fb9\uff0c\u6765\u79fb\u9664\u6240\u6709<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> m j m_j <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.716668em; vertical-align: -0.286108em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">m<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.311664em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.05724em;\">j<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.286108em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u548c\u89c2\u6d4b\u5230<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> m j m_j <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.716668em; vertical-align: -0.286108em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">m<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.311664em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.05724em;\">j<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.286108em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u7684\u4f4d\u59ff\u8282\u70b9\u4e4b\u95f4\u7684\u8fb9\u3002<\/p>\n<p>\u8fd9\u4e00\u8fc7\u7a0b\u5982\u56fe3.1.2\u6240\u793a\uff0c\u79fb\u9664\u4e86\u4e24\u4e2a\u5730\u56fe\u7279\u5f81<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> m 1 m_1 <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.58056em; vertical-align: -0.15em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">m<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.301108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u548c<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> m 3 m_3 <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.58056em; vertical-align: -0.15em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">m<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.301108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">3<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\uff0c\u5bf9\u4e8e\u8fd9\u4e2a\u5730\u56fe\u800c\u8a00\u79fb\u9664<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> m 2 m_2 <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.58056em; vertical-align: -0.15em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">m<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.301108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u548c<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> m 4 m_4 <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.58056em; vertical-align: -0.15em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">m<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.301108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">4<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u65e0\u8db3\u8f7b\u91cd\u3002\u7279\u5f81\u7684\u79fb\u9664\u4fee\u6539\u4e86\u89c2\u6d4b\u5230\u7279\u5f81\u7684\u4f4d\u59ff\u5bf9\u4e4b\u95f4\u7684\u8fb9\u3002 \u5982\u56fe3.1.2b\u6240\u793a\uff0c\u8fd9\u4e00\u64cd\u4f5c\u53ef\u80fd\u4f1a\u5728\u56fe\u4e2d\u65b0\u589e\u8fb9\uff0c\u7279\u5f81<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> m 3 m_3 <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.58056em; vertical-align: -0.15em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">m<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.301108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">3<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u7684\u79fb\u9664\u5728\u4f4d\u59ff<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> x 2 x_2 <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.58056em; vertical-align: -0.15em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.301108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u548c<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> x 4 x_4 <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.58056em; vertical-align: -0.15em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.301108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">4<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u4e4b\u95f4\u65b0\u589e\u4e86\u4e00\u6761\u8fb9\u3002<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/img-blog.csdnimg.cn\/20200523215516729.png\" =\"\" =\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" alt=\"autostore\u673a\u5668\u4eba\u7a0b\u5e8f_\u673a\u5668\u4eba\u5de5\u7a0b\u5e08\u662f\u505a\u4ec0\u4e48\u7684 (https:\/\/mushiming.com\/) \u7b2c9\u5f20\" title=\"autostore\u673a\u5668\u4eba\u7a0b\u5e8f_\u673a\u5668\u4eba\u5de5\u7a0b\u5e08\u662f\u505a\u4ec0\u4e48\u7684 \u7b2c9\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" ><br \/> \u56fe3.2. GraphSLAM\u7b97\u6cd5\u4e2d\u7684\u56fe\u5316\u7b80\u3002\u79fb\u9664\u7279\u5f81\u76f8\u5173\u7684\u8fb9\uff0c\u53ea\u7559\u4e0b\u4e86\u4f4d\u59ff\u72b6\u6001\u4e4b\u95f4\u7684\u8fb9\u3002<\/p>\n<p>\u6b63\u5f0f\u5730\uff0c\u4ee4<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> \u03c4 ( j ) \\tau(j) <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em; vertical-align: -0.25em;\"><\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.1132em;\">\u03c4<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.05724em;\">j<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span>\u4e3a\u89c2\u6d4b\u5230<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> m j m_j <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.716668em; vertical-align: -0.286108em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">m<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.311664em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.05724em;\">j<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.286108em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u7684\u4f4d\u59ff\u96c6\u5408\uff08\u5373<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> x t \u2208 \u03c4 ( j ) \u27fa \u2203 i : c t i = j x_t \\in \\tau(j) \\Longleftrightarrow \\exists i : c_t^i = j <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6891em; vertical-align: -0.15em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.280556em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">t<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><span class=\"mrel\">\u2208<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em; vertical-align: -0.25em;\"><\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.1132em;\">\u03c4<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.05724em;\">j<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><span class=\"mrel\">\u27fa<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.69444em; vertical-align: 0em;\"><\/span><span class=\"mord\">\u2203<\/span><span class=\"mord mathdefault\">i<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><span class=\"mrel\">:<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1.07166em; vertical-align: -0.247em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">c<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.824664em;\"><span class=\"\" style=\"top: -2.453em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">t<\/span><\/span><\/span><span class=\"\" style=\"top: -3.063em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">i<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.247em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.85396em; vertical-align: -0.19444em;\"><\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.05724em;\">j<\/span><\/span><\/span><\/span><\/span>\uff09\u3002\u90a3\u4e48\u6211\u4eec\u5c31\u77e5\u9053\u7279\u5f81<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> m j m_j <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.716668em; vertical-align: -0.286108em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">m<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.311664em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.05724em;\">j<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.286108em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u53ea\u4e0e\u96c6\u5408<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> \u03c4 ( j ) \\tau(j) <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em; vertical-align: -0.25em;\"><\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.1132em;\">\u03c4<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.05724em;\">j<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span>\u4e2d\u7684\u4f4d\u59ff\u6709\u5173\u8054\u3002 \u5728\u6784\u5efa\u8fc7\u7a0b\u4e2d\uff0c<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> m j m_j <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.716668em; vertical-align: -0.286108em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">m<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.311664em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.05724em;\">j<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.286108em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u4e0d\u518d\u4e0e\u5176\u5b83\u4efb\u4f55\u4f4d\u59ff\u6216\u8005\u7279\u5f81\u8282\u70b9\u6709\u5173\u8054\u3002\u73b0\u5728\u6211\u4eec\u53ef\u4ee5\u5c06\u6240\u6709<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> m j m_j <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.716668em; vertical-align: -0.286108em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">m<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.311664em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.05724em;\">j<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.286108em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u4e0e<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> \u03c4 ( j ) \\tau(j) <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em; vertical-align: -0.25em;\"><\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.1132em;\">\u03c4<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.05724em;\">j<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span>\u4e4b\u95f4\u7684\u8fb9\u90fd\u8bbe\u5b9a\u4e3a0\uff0c\u5e76\u5728\u4efb\u4f55\u4e24\u4e2a\u8282\u70b9<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> x t , x t \u2032 \u2208 \u03c4 ( j ) x_t, x_{t'} \\in \\tau(j) <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.73354em; vertical-align: -0.19444em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.280556em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">t<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.32798em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">t<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.682829em;\"><span class=\"\" style=\"top: -2.786em; margin-right: 0.0714286em;\"><span class=\"pstrut\" style=\"height: 2.5em;\"><\/span><span class=\"sizing reset-size3 size1 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">\u2032<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><span class=\"mrel\">\u2208<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em; vertical-align: -0.25em;\"><\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.1132em;\">\u03c4<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.05724em;\">j<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span>\u4e4b\u95f4\u5f15\u5165\u4e00\u6761\u65b0\u8fb9\u3002 \u7c7b\u4f3c\u7684\uff0c\u8fd8\u8981\u66f4\u65b0\u4fe1\u606f\u5411\u91cf\u4e2d\u6240\u6709\u5bf9\u5e94\u4e8e\u4f4d\u59ff<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> \u03c4 j \\tau{j} <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.85396em; vertical-align: -0.19444em;\"><\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.1132em;\">\u03c4<\/span><span class=\"mord\"><span class=\"mord mathdefault\" style=\"margin-right: 0.05724em;\">j<\/span><\/span><\/span><\/span><\/span><\/span>\u7684\u503c\u3002\u8fd9\u4e00\u64cd\u4f5c\u7684\u91cd\u8981\u7279\u70b9\u5c31\u662f\uff0c\u5b83\u662f\u5c40\u90e8\u7684\uff0c\u53ea\u6d89\u53ca\u5230\u4e00\u5c0f\u90e8\u5206\u7ea6\u675f\u3002\u5f53\u79fb\u9664\u4e86\u6240\u6709\u5230<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> m j m_j <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.716668em; vertical-align: -0.286108em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">m<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.311664em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.05724em;\">j<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.286108em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u7684\u8fb9\u4e4b\u540e\uff0c\u6211\u4eec\u5c31\u53ef\u4ee5\u5b89\u5168\u7684\u5c06<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> m j m_j <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.716668em; vertical-align: -0.286108em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">m<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.311664em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.05724em;\">j<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.286108em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u4ece\u4fe1\u606f\u77e9\u9635\u548c\u4fe1\u606f\u5411\u91cf\u4e2d\u79fb\u9664\u3002 \u5f97\u5230\u7684\u4fe1\u606f\u77e9\u9635\u5c31\u66f4\u5c0f\u4e86\uff0c\u56e0\u4e3a\u5b83\u7f3a\u5c11\u4e86\u5143\u7d20<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> m j m_j <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.716668em; vertical-align: -0.286108em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">m<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.311664em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.05724em;\">j<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.286108em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u3002\u4f46\u662f\uff0c\u8be5\u4fe1\u606f\u77e9\u9635\u7684\u540e\u9a8c\u6982\u7387\u5728\u6570\u5b66\u5f62\u5f0f\u4e0a\uff0c\u4e0e\u79fb\u9664<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> m j m_j <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.716668em; vertical-align: -0.286108em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">m<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.311664em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.05724em;\">j<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.286108em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u4e4b\u524d\u7684\u540e\u9a8c\u6982\u7387\u7b49\u4ef7\u3002\u8fd9\u4e2a\u7b49\u4ef7\u5173\u7cfb\u662f\u7b26\u5408\u76f4\u89c9\u7684\uff0c \u6211\u4eec\u7528\u4e00\u7cfb\u5217\u76f4\u63a5\u4e0e\u4f4d\u59ff\u8282\u70b9\u76f8\u8fde\u7684\u8fb9\u66ff\u4ee3\u4e86\u8fde\u63a5\u5728<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> m j m_j <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.716668em; vertical-align: -0.286108em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">m<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.311664em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.05724em;\">j<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.286108em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u7684\u8fb9\u3002\u8fd9\u4e9b\u8fb9\u6240\u6784\u6210\u7684\u5408\u529b\u662f\u4e00\u6837\u7684\uff0c\u53ea\u662f<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> m j m_j <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.716668em; vertical-align: -0.286108em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">m<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.311664em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.05724em;\">j<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.286108em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u6ca1\u6709\u8fde\u63a5\u3002<\/p>\n<p>\u8fd9\u4e00\u524a\u51cf\u8fc7\u7a0b\u7684\u4f18\u70b9\u5c31\u662f\uff0c\u6211\u4eec\u53ef\u4ee5\u9010\u6e10\u7684\u5c06\u63a8\u7406\u95ee\u9898\u8f6c\u6362\u4e3a\u4e00\u4e2a\u66f4\u5c0f\u7684\u95ee\u9898\u3002\u901a\u8fc7\u89e3\u51b3<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> \u03a9 \\Omega <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.68333em; vertical-align: 0em;\"><\/span><span class=\"mord\">\u03a9<\/span><\/span><\/span><\/span><\/span>\u548c<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> \u03be \\xi <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.88888em; vertical-align: -0.19444em;\"><\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.04601em;\">\u03be<\/span><\/span><\/span><\/span><\/span>\u4e2d\u7684\u6bcf\u4e00\u4e2a\u7279\u5f81<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> m j m_j <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.716668em; vertical-align: -0.286108em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">m<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.311664em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.05724em;\">j<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.286108em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\uff0c \u6700\u7ec8\u6211\u4eec\u4f1a\u5f97\u5230\u4e00\u4e2a\u53ea\u5b9a\u4e49\u5728\u673a\u5668\u4eba\u8def\u5f84\u4e0a\u7684\u66f4\u5c0f\u7684\u4fe1\u606f\u77e9\u9635<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> \u03a9 ~ \\tilde{\\Omega} <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.92019em; vertical-align: 0em;\"><\/span><span class=\"mord accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.92019em;\"><span class=\"\" style=\"top: -3em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"mord\"><span class=\"mord\">\u03a9<\/span><\/span><\/span><span class=\"\" style=\"top: -3.60233em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"accent-body\" style=\"left: -0.25em;\">~<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u548c\u4fe1\u606f\u5411\u91cf<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> \u03be ~ \\tilde{\\xi} <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.12574em; vertical-align: -0.19444em;\"><\/span><span class=\"mord accent\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.9313em;\"><span class=\"\" style=\"top: -3em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\" style=\"margin-right: 0.04601em;\">\u03be<\/span><\/span><\/span><span class=\"\" style=\"top: -3.61344em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"accent-body\" style=\"left: -0.13889em;\">~<\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.19444em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u3002\u8fd9\u4e00\u7ea6\u7b80\u8fc7\u7a0b\u53ef\u4ee5\u4ee5\u5730\u56fe\u5c3a\u5bf8\u7684\u7ebf\u6027\u65f6\u95f4\u8fdb\u884c\uff0c\u5b9e\u9645\u4e0a\u5b83\u5c31\u662f\u4e00\u79cd\u4fe1\u606f\u5f62\u5f0f\u7684\u6d88\u5143\u6c42\u77e9\u9635\u9006\u7684\u65b9\u6cd5\uff0c \u5728\u8fd9\u79cd\u65b9\u6cd5\u4e2d\u6211\u4eec\u8fd8\u7ef4\u62a4\u4e86\u4e00\u4e2a\u4fe1\u606f\u72b6\u6001\u3002\u5173\u4e8e\u673a\u5668\u4eba\u8def\u5f84\u7684\u540e\u9a8c\u6982\u7387\u73b0\u5728\u5c31\u53ef\u4ee5\u5199\u4f5c<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> \u03a3 ~ = \u03a9 ~ \u2212 1 \\tilde{\\Sigma} = \\tilde{\\Omega}^{-1} <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.92019em; vertical-align: 0em;\"><\/span><span class=\"mord accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.92019em;\"><span class=\"\" style=\"top: -3em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"mord\"><span class=\"mord\">\u03a3<\/span><\/span><\/span><span class=\"\" style=\"top: -3.60233em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"accent-body\" style=\"left: -0.25em;\">~<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.92019em; vertical-align: 0em;\"><\/span><span class=\"mord\"><span class=\"mord accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.92019em;\"><span class=\"\" style=\"top: -3em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"mord\"><span class=\"mord\">\u03a9<\/span><\/span><\/span><span class=\"\" style=\"top: -3.60233em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"accent-body\" style=\"left: -0.25em;\">~<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.814108em;\"><span class=\"\" style=\"top: -3.063em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">\u2212<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u548c<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> \u03bc ~ = \u03a3 ~ \u03be \\tilde{\u03bc} = \\tilde{\\Sigma}\\xi <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8623em; vertical-align: -0.19444em;\"><\/span><span class=\"mord accent\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.66786em;\"><span class=\"\" style=\"top: -3em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">\u03bc<\/span><\/span><\/span><span class=\"\" style=\"top: -3.35em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"accent-body\" style=\"left: -0.22222em;\">~<\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.19444em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1.11463em; vertical-align: -0.19444em;\"><\/span><span class=\"mord accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.92019em;\"><span class=\"\" style=\"top: -3em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"mord\"><span class=\"mord\">\u03a3<\/span><\/span><\/span><span class=\"\" style=\"top: -3.60233em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"accent-body\" style=\"left: -0.25em;\">~<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.04601em;\">\u03be<\/span><\/span><\/span><\/span><\/span>\u3002 \u4e0d\u5e78\u7684\u662f\uff0c\u6211\u4eec\u7684\u6d88\u5143\u6cd5\u5e76\u4e0d\u80fd\u6d88\u9664\u540e\u9a8c\u6982\u7387\u4e2d\u7684\u73af\uff0c\u5269\u4f59\u7684\u63a8\u7406\u8fc7\u7a0b\u53ef\u80fd\u4e0d\u6b62\u9700\u8981\u7ebf\u6027\u7684\u65f6\u95f4\u3002<\/p>\n<p>\u6700\u540e\u4e00\u6b65\uff0cGraphSLAM\u7b97\u6cd5\u6062\u590d\u4e86\u7279\u5f81\u7684\u4f4d\u7f6e\u3002\u6982\u5ff5\u4e0a\uff0c\u5c31\u662f\u5bf9\u6bcf\u4e00\u4e2a<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> m j m_j <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.716668em; vertical-align: -0.286108em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">m<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.311664em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.05724em;\">j<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.286108em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u6784\u5efa\u4e00\u4e2a\u65b0\u7684\u4fe1\u606f\u77e9\u9635<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> \u03a9 j \\Omega_j <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.969438em; vertical-align: -0.286108em;\"><\/span><span class=\"mord\"><span class=\"mord\">\u03a9<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.311664em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.05724em;\">j<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.286108em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u548c\u4fe1\u606f\u5411\u91cf<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> \u03be j \\xi_j <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.980548em; vertical-align: -0.286108em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\" style=\"margin-right: 0.04601em;\">\u03be<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.311664em;\"><span class=\"\" style=\"top: -2.55em; margin-left: -0.04601em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.05724em;\">j<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.286108em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u3002\u5b83\u4eec\u90fd\u662f\u5b9a\u4e49\u5728\u7279\u5f81<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> m j m_j <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.716668em; vertical-align: -0.286108em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">m<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.311664em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.05724em;\">j<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.286108em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u548c\u89c2\u6d4b\u5230\u8be5\u7279\u5f81\u7684\u4f4d\u59ff\u96c6\u5408<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> \u03c4 ( j ) \\tau(j) <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em; vertical-align: -0.25em;\"><\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.1132em;\">\u03c4<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.05724em;\">j<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span>\u4e0a\u7684\u3002 \u5b83\u5305\u542b\u4e86<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> m j m_j <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.716668em; vertical-align: -0.286108em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">m<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.311664em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.05724em;\">j<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.286108em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u5230<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> \u03c4 ( j ) \\tau(j) <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em; vertical-align: -0.25em;\"><\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.1132em;\">\u03c4<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.05724em;\">j<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span>\u4e4b\u95f4\u7684\u539f\u59cb\u8fde\u63a5\uff0c\u4ee5\u53ca\u53d6\u503c\u4e3a<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> \u03bc ~ \\tilde{\u03bc} <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8623em; vertical-align: -0.19444em;\"><\/span><span class=\"mord accent\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.66786em;\"><span class=\"\" style=\"top: -3em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">\u03bc<\/span><\/span><\/span><span class=\"\" style=\"top: -3.35em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"accent-body\" style=\"left: -0.22222em;\">~<\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.19444em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u7684\u6ca1\u6709\u4e0d\u786e\u5b9a\u5ea6\u7684\u4f4d\u59ff<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> \u03c4 ( j ) \\tau(j) <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em; vertical-align: -0.25em;\"><\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.1132em;\">\u03c4<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.05724em;\">j<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span>\u3002\u4ece\u8fd9\u4e00\u4fe1\u606f\u5f62\u5f0f\u4e2d\uff0c\u4f7f\u7528\u901a\u5e38\u7684\u7684\u77e9\u9635\u6c42\u9006\u7684\u65b9\u6cd5\uff0c\u5c31\u53ef\u4ee5\u5f88\u5bb9\u6613\u7684\u8ba1\u7b97\u51fa<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> m j m_j <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.716668em; vertical-align: -0.286108em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">m<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.311664em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.05724em;\">j<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.286108em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u7684\u4f4d\u7f6e\u3002 \u663e\u7136\uff0c<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> \u03a9 j \\Omega_j <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.969438em; vertical-align: -0.286108em;\"><\/span><span class=\"mord\"><span class=\"mord\">\u03a9<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.311664em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.05724em;\">j<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.286108em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u53ea\u5305\u542b\u4e86\u90a3\u4e9b\u5173\u8054\u5728<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> m j m_j <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.716668em; vertical-align: -0.286108em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">m<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.311664em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.05724em;\">j<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.286108em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u4e0a\u7684\u5143\u7d20\uff0c\u56e0\u6b64\u77e9\u9635\u7684\u9006\u8fd0\u7b97\u53ef\u4ee5\u4ee5\u96c6\u5408<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> \u03c4 ( j ) \\tau(j) <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em; vertical-align: -0.25em;\"><\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.1132em;\">\u03c4<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.05724em;\">j<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span>\u4e2d\u4f4d\u59ff\u6570\u91cf\u7684\u7ebf\u6027\u65f6\u95f4\u6765\u5b8c\u6210\u3002<\/p>\n<p>\u4e3a\u4ec0\u4e48\u56fe\u5f62\u7684\u8868\u8fbe\u65b9\u5f0f\u662f\u5982\u6b64\u81ea\u7136\u7684\u65b9\u5f0f\u5c31\u5f88\u660e\u663e\u4e86\u3002\u5b8c\u5168SLAM\u95ee\u9898\u53ef\u4ee5\u901a\u8fc7\u5c40\u90e8\u5730\u5c06\u4fe1\u606f\u6dfb\u52a0\u5230\u4e00\u4e2a\u5927\u4fe1\u606f\u56fe\u4e2d\u6765\u89e3\u51b3\uff0c\u56fe\u4e2d\u7684\u6bcf\u4e00\u6761\u8fb9\u5bf9\u5e94\u7740\u4e00\u6b21\u6d4b\u91cf\u503c<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> z t i z_t^i <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.07166em; vertical-align: -0.247em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\" style=\"margin-right: 0.04398em;\">z<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.824664em;\"><span class=\"\" style=\"top: -2.453em; margin-left: -0.04398em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">t<\/span><\/span><\/span><span class=\"\" style=\"top: -3.063em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">i<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.247em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u548c\u63a7\u5236\u91cf<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> u t u_t <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.58056em; vertical-align: -0.15em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">u<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.280556em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">t<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u3002 \u4e3a\u4e86\u5c06\u8fd9\u4e9b\u4fe1\u606f\u8f6c\u6362\u4e3a\u5730\u56fe\u548c\u8def\u5f84\u7684\u4f30\u8ba1\uff0c\u9996\u5148\u8fdb\u884c\u7ebf\u6027\u5316\uff0c\u7136\u540e\u5c06\u4f4d\u59ff\u548c\u7279\u5f81\u4e4b\u95f4\u7684\u5173\u7cfb\u9010\u6e10\u7684\u8f6c\u6362\u4e3a\u4f4d\u59ff\u5bf9\u4e4b\u95f4\u7684\u5173\u7cfb\u3002\u5982\u6b64\u5f97\u5230\u53ea\u7ea6\u675f\u4e86\u673a\u5668\u4eba\u4f4d\u59ff\u7684\u7ed3\u6784\uff0c\u53ef\u4ee5\u901a\u8fc7\u77e9\u9635\u6c42\u9006\u89e3\u5f97\u3002 \u4e00\u65e6\u6062\u590d\u4e86\u4f4d\u59ff\uff0c\u7279\u5f81\u7684\u4f4d\u7f6e\u5c31\u53ef\u4ee5\u6839\u636e\u521d\u59cb\u7684\u7279\u5f81\u4f4d\u59ff\u4fe1\u606f\u9010\u4e2a\u89e3\u51fa\u3002<\/p>\n<h4>2. GraphSLAM\u7b97\u6cd5<\/h4>\n<p>\u4e0b\u9762\u6211\u4eec\u5c06\u66f4\u7cbe\u7ec6\u51c6\u786e\u7684\u8bf4\u660eGraphSLAM\u7b97\u6cd5\u7684\u5404\u4e2a\u8ba1\u7b97\u6b65\u9aa4\u3002\u5b8c\u5168GraphSLAM\u7b97\u6cd5fully GraphSLAM algorithm\u5c06\u88ab\u63cf\u8ff0\u4e3a\u51e0\u4e2a\u6b65\u9aa4\u3002\u5b9e\u73b0\u7684\u4e3b\u8981\u96be\u5ea6\u5728\u4e8e\u7b80\u5355\u7684\u589e\u52a0\u4fe1\u606f\u7684\u7b97\u6cd5\uff0c \u8574\u542b\u4e86\u5c06\u5f62\u5f0f\u4e3a<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> p ( z t i \u2223 x t , m ) p(z_t^i | x_t, m) <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.07466em; vertical-align: -0.25em;\"><\/span><span class=\"mord mathdefault\">p<\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathdefault\" style=\"margin-right: 0.04398em;\">z<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.824664em;\"><span class=\"\" style=\"top: -2.453em; margin-left: -0.04398em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">t<\/span><\/span><\/span><span class=\"\" style=\"top: -3.063em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">i<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.247em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\">\u2223<\/span><span class=\"mord\"><span class=\"mord mathdefault\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.280556em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">t<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord mathdefault\">m<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span>\u548c<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> p ( x t \u2223 u t , x t \u2212 1 ) p(x_t | u_t, x_{t-1}) <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em; vertical-align: -0.25em;\"><\/span><span class=\"mord mathdefault\">p<\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathdefault\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.280556em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">t<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\">\u2223<\/span><span class=\"mord\"><span class=\"mord mathdefault\">u<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.280556em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">t<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.301108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">t<\/span><span class=\"mbin mtight\">\u2212<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.208331em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span>\u7684\u6761\u4ef6\u6982\u7387\u8f6c\u6362\u4e3a\u4fe1\u606f\u77e9\u9635\u4e2d\u7684\u4e00\u4e2a\u8fb9\u3002\u4fe1\u606f\u77e9\u9635\u5143\u7d20\u90fd\u662f\u7ebf\u6027\u7684\uff0c\u56e0\u6b64\u8fd9\u4e00\u6b65\u4e5f\u6d89\u53ca\u5230\u4e86\u7ebf\u6027\u5316<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> p ( z t i \u2223 x t , m ) p(z_t^i | x_t, m) <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.07466em; vertical-align: -0.25em;\"><\/span><span class=\"mord mathdefault\">p<\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathdefault\" style=\"margin-right: 0.04398em;\">z<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.824664em;\"><span class=\"\" style=\"top: -2.453em; margin-left: -0.04398em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">t<\/span><\/span><\/span><span class=\"\" style=\"top: -3.063em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">i<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.247em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\">\u2223<\/span><span class=\"mord\"><span class=\"mord mathdefault\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.280556em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">t<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord mathdefault\">m<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span>\u548c<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> p ( x t \u2223 u t , x t \u2212 1 ) p(x_t | u_t, x_{t-1}) <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em; vertical-align: -0.25em;\"><\/span><span class=\"mord mathdefault\">p<\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathdefault\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.280556em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">t<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\">\u2223<\/span><span class=\"mord\"><span class=\"mord mathdefault\">u<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.280556em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">t<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.301108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">t<\/span><span class=\"mbin mtight\">\u2212<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.208331em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span>\u3002 \u5728EKF SLAM\u4e2d\uff0c\u7ebf\u6027\u5316\u662f\u901a\u8fc7\u8ba1\u7b97\u5728\u5e73\u5747\u4f4d\u59ff<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> \u03bc 0 : t \u03bc_{0:t} <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.625em; vertical-align: -0.19444em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">\u03bc<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.301108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">0<\/span><span class=\"mrel mtight\">:<\/span><span class=\"mord mathdefault mtight\">t<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u5904\u7684\u96c5\u53ef\u6bd4\u77e9\u9635\u5f97\u5230\u7684\u3002\u4e3a\u4e86\u6784\u5efa\u6211\u4eec\u7684\u521d\u59cb\u4fe1\u606f\u77e9\u9635<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> \u03a9 \\Omega <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.68333em; vertical-align: 0em;\"><\/span><span class=\"mord\">\u03a9<\/span><\/span><\/span><\/span><\/span>\u548c\u5411\u91cf<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> \u03be \\xi <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.88888em; vertical-align: -0.19444em;\"><\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.04601em;\">\u03be<\/span><\/span><\/span><\/span><\/span>\uff0c\u6211\u4eec\u9700\u8981\u4e00\u4e2a\u5bf9\u4e8e\u6240\u6709\u4f4d\u59ff<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> x 0 : t x_{0:t} <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.58056em; vertical-align: -0.15em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.301108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">0<\/span><span class=\"mrel mtight\">:<\/span><span class=\"mord mathdefault mtight\">t<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u7684\u521d\u59cb\u4f30\u8ba1<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> \u03bc 0 : t \u03bc_{0:t} <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.625em; vertical-align: -0.19444em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">\u03bc<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.301108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">0<\/span><span class=\"mrel mtight\">:<\/span><span class=\"mord mathdefault mtight\">t<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u3002<\/p>\n<p>\u6709\u5f88\u591a\u79cd\u65b9\u6cd5\u53ef\u4ee5\u627e\u5230\u9002\u7528\u4e8e\u7ebf\u6027\u5316\u7684\u521d\u59cb\u5747\u503c<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> \u03bc \u03bc <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.625em; vertical-align: -0.19444em;\"><\/span><span class=\"mord mathdefault\">\u03bc<\/span><\/span><\/span><\/span><\/span>\u3002\u6bd4\u5982\u8bf4\uff0c\u6211\u4eec\u53ef\u4ee5\u8fd0\u884c\u4e00\u904dEKF SLAM\u7b97\u6cd5\u5e76\u7528\u5b83\u7684\u4f30\u8ba1\u503c\u6765\u8fdb\u884c\u7ebf\u6027\u5316\u3002\u672c\u7ae0\u4e2d\uff0c\u6211\u4eec\u5c06\u4f7f\u7528\u4e00\u79cd\u66f4\u7b80\u5355\u7684\u6280\u672f\uff0c \u53ea\u662f\u5c06\u8fd0\u52a8\u6a21\u578b<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> p ( x t \u2223 u t , x t \u2212 1 ) p(x_t|u_t, x_{t-1}) <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em; vertical-align: -0.25em;\"><\/span><span class=\"mord mathdefault\">p<\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathdefault\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.280556em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">t<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\">\u2223<\/span><span class=\"mord\"><span class=\"mord mathdefault\">u<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.280556em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">t<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.301108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">t<\/span><span class=\"mbin mtight\">\u2212<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.208331em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span>\u7b80\u5355\u5730\u94fe\u63a5\u8d77\u6765\u6784\u6210\u521d\u59cb\u4f30\u8ba1\u3002\u8be5\u7b97\u6cd5\u5982\u56fe3.1\u6240\u793a\uff0c\u79f0\u4e3aGraphSLAM_initialize\u3002 \u8be5\u7b97\u6cd5\u4ee5\u63a7\u5236\u91cf<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> u 1 : t u_{1:t} <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.58056em; vertical-align: -0.15em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">u<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.301108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">1<\/span><span class=\"mrel mtight\">:<\/span><span class=\"mord mathdefault mtight\">t<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u4e3a\u8f93\u5165\uff0c\u8f93\u51fa\u662f\u4f4d\u59ff\u4f30\u8ba1\u5e8f\u5217<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> \u03bc 0 : t \u03bc_{0:t} <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.625em; vertical-align: -0.19444em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">\u03bc<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.301108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">0<\/span><span class=\"mrel mtight\">:<\/span><span class=\"mord mathdefault mtight\">t<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u3002\u5b83\u5c06\u521d\u59cb\u4f4d\u59ff\u5b9a\u4e49\u4e3a0\uff0c\u7136\u540e\u7528\u901f\u5ea6\u8fd0\u52a8\u6a21\u578b\u4f9d\u6b21\u4f30\u8ba1\u540e\u7eed\u4f4d\u59ff\u3002\u56e0\u4e3a\u6211\u4eec\u53ea\u5173\u6ce8\u5e73\u5747\u4f4d\u59ff\u5411\u91cf<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> \u03bc 0 : t \u03bc_{0:t} <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.625em; vertical-align: -0.19444em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">\u03bc<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.301108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">0<\/span><span class=\"mrel mtight\">:<\/span><span class=\"mord mathdefault mtight\">t<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\uff0c GraphSLAM_initialize\u53ea\u5e94\u7528\u4e86\u8fd0\u52a8\u6a21\u578b\u4e2d\u7684\u786e\u5b9a\u6027\u90e8\u5206\uff0c\u800c\u4e14\u4e5f\u6ca1\u6709\u8003\u8651\u4efb\u4f55\u6d4b\u91cf\u503c\u3002<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/img-blog.csdnimg.cn\/20200523221151532.png\" =\"\" =\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" alt=\"autostore\u673a\u5668\u4eba\u7a0b\u5e8f_\u673a\u5668\u4eba\u5de5\u7a0b\u5e08\u662f\u505a\u4ec0\u4e48\u7684 (https:\/\/mushiming.com\/) \u7b2c10\u5f20\" title=\"autostore\u673a\u5668\u4eba\u7a0b\u5e8f_\u673a\u5668\u4eba\u5de5\u7a0b\u5e08\u662f\u505a\u4ec0\u4e48\u7684 \u7b2c10\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" ><br \/> \u56fe3.1. GraphSLAM\u7b97\u6cd5\u4e2d\u521d\u59cb\u5316\u5e73\u5747\u4f4d\u59ff\u5411\u91cf<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> \u03bc 1 : t \u03bc_{1:t} <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.625em; vertical-align: -0.19444em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">\u03bc<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.301108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">1<\/span><span class=\"mrel mtight\">:<\/span><span class=\"mord mathdefault mtight\">t<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u3002<\/p>\n<p>\u4e00\u65e6\u6709\u4e86\u521d\u59cb\u7684\u4f30\u8ba1<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> \u03bc 0 : t \u03bc_{0:t} <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.625em; vertical-align: -0.19444em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">\u03bc<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.301108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">0<\/span><span class=\"mrel mtight\">:<\/span><span class=\"mord mathdefault mtight\">t<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\uff0cGraphSLAM\u7b97\u6cd5\u5c31\u53ef\u4ee5\u6784\u5efa\u5b8c\u5168SLAM\u4fe1\u606f\u77e9\u9635<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> \u03a9 \\Omega <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.68333em; vertical-align: 0em;\"><\/span><span class=\"mord\">\u03a9<\/span><\/span><\/span><\/span><\/span>\u548c\u5173\u8054\u7684\u4fe1\u606f\u5411\u91cf<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> \u03be \\xi <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.88888em; vertical-align: -0.19444em;\"><\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.04601em;\">\u03be<\/span><\/span><\/span><\/span><\/span>\u3002\u5b83\u662f\u901a\u8fc7\u5bf9\u56fe\u4e2d\u7684\u8fb9\u7ebf\u6027\u5316\u5f97\u5230\u7684\uff0c \u56fe3.2\u4e2d\u63cf\u8ff0\u4e86GraphSLAM_linearize\u7b97\u6cd5\u3002<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/img-blog.csdnimg.cn\/20200523221617932.png\" =\"\" =\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" alt=\"autostore\u673a\u5668\u4eba\u7a0b\u5e8f_\u673a\u5668\u4eba\u5de5\u7a0b\u5e08\u662f\u505a\u4ec0\u4e48\u7684 (https:\/\/mushiming.com\/) \u7b2c11\u5f20\" title=\"autostore\u673a\u5668\u4eba\u7a0b\u5e8f_\u673a\u5668\u4eba\u5de5\u7a0b\u5e08\u662f\u505a\u4ec0\u4e48\u7684 \u7b2c11\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" ><br \/> \u56fe3.2.GraphSLAM_linearize\u7b97\u6cd5\u3002<\/p>\n<p>\u8be5\u7b97\u6cd5\u4e2d\u7528\u5230\u4e86\u5f88\u591a\u6570\u5b66\u7b26\u53f7\uff0c\u5b83\u4eec\u7684\u610f\u4e49\u5c06\u5728\u540e\u9762\u63a8\u5bfc\u8be5\u7b97\u6cd5\u7684\u65f6\u5019\u5f97\u5230\u660e\u786e\u3002GraphSLAM_linearize\u4ee5\u63a7\u5236\u91cf<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> u 1 : t u_{1:t} <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.58056em; vertical-align: -0.15em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">u<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.301108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">1<\/span><span class=\"mrel mtight\">:<\/span><span class=\"mord mathdefault mtight\">t<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u3001\u6d4b\u91cf\u503c<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> z 1 : t z_{1:t} <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.58056em; vertical-align: -0.15em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\" style=\"margin-right: 0.04398em;\">z<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.301108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: -0.04398em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">1<\/span><span class=\"mrel mtight\">:<\/span><span class=\"mord mathdefault mtight\">t<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u3001\u5173\u8054\u5ea6\u53d8\u91cf<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> c 1 : t c_{1:t} <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.58056em; vertical-align: -0.15em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">c<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.301108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">1<\/span><span class=\"mrel mtight\">:<\/span><span class=\"mord mathdefault mtight\">t<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u3001 \u4ee5\u53ca\u5e73\u5747\u4f4d\u59ff\u4f30\u8ba1<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> \u03bc 0 : t \u03bc_{0:t} <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.625em; vertical-align: -0.19444em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">\u03bc<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.301108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">0<\/span><span class=\"mrel mtight\">:<\/span><span class=\"mord mathdefault mtight\">t<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u505a\u4e3a\u8f93\u5165\uff0c\u7136\u540e\u901a\u8fc7\u7ebf\u6027\u5316\u64cd\u4f5c\u9010\u6e10\u7684\u6784\u5efa\u4fe1\u606f\u77e9\u9635<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> \u03a9 \\Omega <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.68333em; vertical-align: 0em;\"><\/span><span class=\"mord\">\u03a9<\/span><\/span><\/span><\/span><\/span>\u548c\u4fe1\u606f\u5411\u91cf<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> \u03be \\xi <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.88888em; vertical-align: -0.19444em;\"><\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.04601em;\">\u03be<\/span><\/span><\/span><\/span><\/span>\uff0c\u4e0d\u65ad\u5730\u4ee5\u5b50\u77e9\u9635\u7684\u5f62\u5f0f\u6dfb\u52a0\u6bcf\u4e2a\u6d4b\u91cf\u503c\u548c\u63a7\u5236\u91cf\u7684\u4fe1\u606f\u3002<\/p>\n<p><strong>\u5177\u4f53\u6765\u8bf4\uff0c GraphSLAM_linearize \u7b97\u6cd5\u7b2c2 \u884c\u521d\u59cb\u5316\u4e86\u4fe1\u606f\u5143\u7d20\u3002<\/strong> \u5728\u7b2c3\u884c\u4e2d\uff0c\u4f7f\u7528\"\u65e0\u7a77\"\u4fe1\u606f\u5143\u7d20\u5c06\u521d\u59cb\u4f4d\u59ff<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> x 0 x_0 <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.58056em; vertical-align: -0.15em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.301108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">0<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u4fee\u6b63\u4e3a<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> ( 0 0 0 ) T \\begin{pmatrix} 0 & 0 & 0 \\end{pmatrix}^T <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.43124em; vertical-align: -0.35001em;\"><\/span><span class=\"minner\"><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top: 0em;\"><span class=\"delimsizing size1\">(<\/span><\/span><span class=\"mord\"><span class=\"mtable\"><span class=\"col-align-c\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.85em;\"><span class=\"\" style=\"top: -3.01em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"mord\"><span class=\"mord\">0<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.35em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"arraycolsep\" style=\"width: 0.5em;\"><\/span><span class=\"arraycolsep\" style=\"width: 0.5em;\"><\/span><span class=\"col-align-c\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.85em;\"><span class=\"\" style=\"top: -3.01em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"mord\"><span class=\"mord\">0<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.35em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"arraycolsep\" style=\"width: 0.5em;\"><\/span><span class=\"arraycolsep\" style=\"width: 0.5em;\"><\/span><span class=\"col-align-c\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.85em;\"><span class=\"\" style=\"top: -3.01em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"mord\"><span class=\"mord\">0<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.35em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose delimcenter\" style=\"top: 0em;\"><span class=\"delimsizing size1\">)<\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.08123em;\"><span class=\"\" style=\"top: -3.3029em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.13889em;\">T<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u3002 \u8fd9\u4e00\u8fc7\u7a0b\u662f\u5fc5\u987b\u7684\uff0c\u5426\u5219\u7684\u8bdd\u6700\u540e\u5f97\u5230\u7684\u77e9\u9635\u53ef\u80fd\u662f\u5947\u5f02\u7684\u3002\u8fd9\u4e5f\u8bf4\u660e\u4e00\u4e2a\u4e8b\u5b9e\uff0c\u53ea\u901a\u8fc7\u76f8\u5bf9\u4fe1\u606f\u6211\u4eec\u662f\u4e0d\u80fd\u5f97\u5230\u7edd\u5bf9\u4f30\u8ba1\u7684\u3002<\/p>\n<p><strong>\u63a7\u5236\u5728GraphSLAM_linearize \u7b97\u6cd5\u7684\u7b2c4 -9 \u884c\u88ab\u7efc\u5408\u3002<\/strong> \u5728\u5176\u4e2d\u7684\u7b2c5\u884c\u548c\u7b2c6\u884c\u4e2d\u8ba1\u7b97\u7684\u4f4d\u59ff<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> x ^ \\hat{x} <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.69444em; vertical-align: 0em;\"><\/span><span class=\"mord accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.69444em;\"><span class=\"\" style=\"top: -3em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">x<\/span><\/span><\/span><span class=\"\" style=\"top: -3em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"accent-body\" style=\"left: -0.22222em;\">^<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u548c\u96c5\u53ef\u6bd4\u77e9\u9635<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> G t G_t <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.83333em; vertical-align: -0.15em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">G<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.280556em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">t<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u662f\u5bf9\u975e\u7ebf\u6027\u63a7\u5236\u51fd\u6570<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> g g <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.625em; vertical-align: -0.19444em;\"><\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.03588em;\">g<\/span><\/span><\/span><\/span><\/span>\u7684\u7ebf\u6027\u5316\u8fd1\u4f3c\u3002 \u5982\u8fd9\u4e9b\u516c\u5f0f\u6240\u793a\uff0c\u7ebf\u6027\u5316\u8fc7\u7a0b\u6240\u7528\u7684\u6b63\u662f\u4f4d\u59ff\u4f30\u8ba1<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> \u03bc 0 : t \u2212 1 \u03bc_{0:t-1} <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.638891em; vertical-align: -0.208331em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">\u03bc<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.301108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">0<\/span><span class=\"mrel mtight\">:<\/span><span class=\"mord mathdefault mtight\">t<\/span><span class=\"mbin mtight\">\u2212<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.208331em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u5176\u4e2d<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> \u03bc 0 = ( 0 0 0 ) T \u03bc_0 = \\begin{pmatrix} 0 & 0 & 0 \\end{pmatrix}^T <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.625em; vertical-align: -0.19444em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">\u03bc<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.301108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">0<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1.43124em; vertical-align: -0.35001em;\"><\/span><span class=\"minner\"><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top: 0em;\"><span class=\"delimsizing size1\">(<\/span><\/span><span class=\"mord\"><span class=\"mtable\"><span class=\"col-align-c\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.85em;\"><span class=\"\" style=\"top: -3.01em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"mord\"><span class=\"mord\">0<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.35em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"arraycolsep\" style=\"width: 0.5em;\"><\/span><span class=\"arraycolsep\" style=\"width: 0.5em;\"><\/span><span class=\"col-align-c\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.85em;\"><span class=\"\" style=\"top: -3.01em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"mord\"><span class=\"mord\">0<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.35em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"arraycolsep\" style=\"width: 0.5em;\"><\/span><span class=\"arraycolsep\" style=\"width: 0.5em;\"><\/span><span class=\"col-align-c\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.85em;\"><span class=\"\" style=\"top: -3.01em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"mord\"><span class=\"mord\">0<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.35em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose delimcenter\" style=\"top: 0em;\"><span class=\"delimsizing size1\">)<\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.08123em;\"><span class=\"\" style=\"top: -3.3029em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.13889em;\">T<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u3002\u8fd9\u5c06\u5bfc\u81f4\u7b2c7\u884c\u548c\u7b2c8\u884c\u5206\u522b\u66f4\u65b0<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> \u03a9 \\Omega <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.68333em; vertical-align: 0em;\"><\/span><span class=\"mord\">\u03a9<\/span><\/span><\/span><\/span><\/span>\u548c<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> \u03be \\xi <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.88888em; vertical-align: -0.19444em;\"><\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.04601em;\">\u03be<\/span><\/span><\/span><\/span><\/span>\u3002 \u8fd9\u4e9b\u5143\u7d20\u5c06\u5206\u522b\u6dfb\u52a0\u5230<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> \u03a9 \\Omega <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.68333em; vertical-align: 0em;\"><\/span><span class=\"mord\">\u03a9<\/span><\/span><\/span><\/span><\/span>\u548c<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> \u03be \\xi <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.88888em; vertical-align: -0.19444em;\"><\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.04601em;\">\u03be<\/span><\/span><\/span><\/span><\/span>\u5bf9\u5e94\u7684\u884c\u548c\u5217\u4e2d\u3002\u8fd9\u4e00\u6dfb\u52a0\u64cd\u4f5c\u6b63\u662f\u8981\u5c06\u65b0\u7684\u7ea6\u675f\u5305\u542b\u8fdbSLAM\u7684\u540e\u9a8c\u6982\u7387\u4e2d\uff0c\u8fd9\u6b63\u662f\u4e0a\u4e00\u8282\u4e2d\u8ba8\u8bba\u7684\u7b97\u6cd5\u601d\u60f3\u7684\u5b9e\u8df5\u3002<\/p>\n<p><strong>\u6d4b\u91cf\u503c\u662f\u5728GraphSLAM_linearize\u7684\u7b2c10\u523021\u884c\u4e2d\u6574\u5408\u7684\u3002<\/strong> \u7b2c11\u884c\u4e2d\u7684\u77e9\u9635<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> Q t Q_t <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.87777em; vertical-align: -0.19444em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">Q<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.280556em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">t<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u6b63\u662f\u6211\u4eec\u6240\u719f\u6089\u7684\u6d4b\u91cf\u566a\u58f0\u534f\u65b9\u5dee\u3002\u7b2c13\u523017\u884c\uff0c\u5bf9\u6d4b\u91cf\u51fd\u6570\u8fdb\u884c\u4e86\u6cf0\u52d2\u5c55\u5f00\u3002 \u8fd9\u91cc\u4f7f\u7528\u7684\u662f6.6\u8282\u4e2d\u5b9a\u4e49\u7684\u57fa\u4e8e\u7279\u5f81\u7684\u6a21\u578b\u3002\u6211\u4eec\u9700\u8981\u7279\u522b\u5173\u6ce8\u7b2c16\u884c\u7684\u5b9e\u73b0\uff0c\u56e0\u4e3a\u89d2\u5ea6\u7684\u8868\u8fbe\u65b9\u5f0f\u53ef\u4ee5\u901a\u8fc7<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> 2 \u03c0 2\\pi <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.64444em; vertical-align: 0em;\"><\/span><span class=\"mord\">2<\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.03588em;\">\u03c0<\/span><\/span><\/span><\/span><\/span> \u8f6c\u6362\u3002\u8fd9\u4e00\u8ba1\u7b97\u8fc7\u7a0b\u5728\u7b2c18\u548c19\u884c\u4e2d\u8fdb\u884c\u6d4b\u91cf\u66f4\u65b0\u65f6\u7ec8\u6b62\u3002\u5728\u7b2c18\u884c\u4e2d\u6dfb\u52a0\u5230<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> \u03a9 \\Omega <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.68333em; vertical-align: 0em;\"><\/span><span class=\"mord\">\u03a9<\/span><\/span><\/span><\/span><\/span>\u7684\u77e9\u9635\u5c3a\u5bf8\u662f<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> 6 \u00d7 6 6 \u00d7 6 <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.72777em; vertical-align: -0.08333em;\"><\/span><span class=\"mord\">6<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><span class=\"mbin\">\u00d7<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.64444em; vertical-align: 0em;\"><\/span><span class=\"mord\">6<\/span><\/span><\/span><\/span><\/span>\u3002\u6211\u4eec\u5c06\u5b83\u5206\u89e3\u4e3a\u4e00\u4e2a\u63cf\u8ff0\u4f4d\u59ff<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> x t x_t <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.58056em; vertical-align: -0.15em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.280556em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">t<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u7684<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> 3 \u00d7 3 3\u00d73 <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.72777em; vertical-align: -0.08333em;\"><\/span><span class=\"mord\">3<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><span class=\"mbin\">\u00d7<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.64444em; vertical-align: 0em;\"><\/span><span class=\"mord\">3<\/span><\/span><\/span><\/span><\/span>\u7684\u77e9\u9635\u3001\u4e00\u4e2a\u63cf\u8ff0\u7279\u5f81<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> m j m_j <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.716668em; vertical-align: -0.286108em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">m<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.311664em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.05724em;\">j<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.286108em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u7684<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> 3 \u00d7 3 3\u00d73 <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.72777em; vertical-align: -0.08333em;\"><\/span><span class=\"mord\">3<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><span class=\"mbin\">\u00d7<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.64444em; vertical-align: 0em;\"><\/span><span class=\"mord\">3<\/span><\/span><\/span><\/span><\/span>\u7684\u77e9\u9635\u3001 \u4ee5\u53ca\u4e24\u4e2a<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> 3 \u00d7 3 3\u00d73 <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.72777em; vertical-align: -0.08333em;\"><\/span><span class=\"mord\">3<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><span class=\"mbin\">\u00d7<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.64444em; vertical-align: 0em;\"><\/span><span class=\"mord\">3<\/span><\/span><\/span><\/span><\/span>\u7684\u77e9\u9635\u7528\u4e8e\u63cf\u8ff0<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> x t x_t <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.58056em; vertical-align: -0.15em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.280556em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">t<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u548c<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> m j m_j <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.716668em; vertical-align: -0.286108em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">m<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.311664em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.05724em;\">j<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.286108em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u4e4b\u95f4\u5173\u7cfb\u7684\u77e9\u9635\u3002\u5c06\u4e4b\u5bf9\u5e94\u5730\u6dfb\u52a0\u5230<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> \u03a9 \\Omega <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.68333em; vertical-align: 0em;\"><\/span><span class=\"mord\">\u03a9<\/span><\/span><\/span><\/span><\/span>\u7684\u884c\u548c\u5217\u4e2d\u3002\u7c7b\u4f3c\u7684\uff0c\u6dfb\u52a0\u5230\u4fe1\u606f\u5411\u91cf<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> \u03be \\xi <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.88888em; vertical-align: -0.19444em;\"><\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.04601em;\">\u03be<\/span><\/span><\/span><\/span><\/span>\u7684\u5411\u91cf\u7684\u5217\u7ef4\u5ea6\u662f5\u3002\u5b83\u88ab\u5206\u4e3a3\u7ef4\u548c2\u7ef4\u7684\u4e24\u4e2a\u5411\u91cf\uff0c\u5e76\u5206\u522b\u5c06\u5b83\u4eec\u6dfb\u52a0\u5230\u5bf9\u5e94<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> x t x_t <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.58056em; vertical-align: -0.15em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.280556em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">t<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u548c<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> m j m_j <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.716668em; vertical-align: -0.286108em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">m<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.311664em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.05724em;\">j<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.286108em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u7684\u5143\u7d20\u4e2d\u3002GraphSLAM_initialize\u7684\u7ed3\u679c\u5c31\u662f\u4fe1\u606f\u5411\u91cf<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> \u03be \\xi <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.88888em; vertical-align: -0.19444em;\"><\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.04601em;\">\u03be<\/span><\/span><\/span><\/span><\/span>\u548c\u77e9\u9635<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> \u03a9 \\Omega <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.68333em; vertical-align: 0em;\"><\/span><span class=\"mord\">\u03a9<\/span><\/span><\/span><\/span><\/span>\u3002\u6211\u4eec\u5df2\u7ecf\u6ce8\u610f\u5230<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> \u03a9 \\Omega <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.68333em; vertical-align: 0em;\"><\/span><span class=\"mord\">\u03a9<\/span><\/span><\/span><\/span><\/span>\u662f\u7a00\u758f\u7684\uff0c\u5b83\u53ea\u5728\u4e3b\u5bf9\u89d2\u7ebf\u3001\u76f8\u90bb\u4f4d\u59ff\u4e4b\u95f4\u3001\u4f4d\u59ff\u4e0e\u5730\u56fe\u7279\u5f81\u4e4b\u95f4\u5bf9\u5e94\u7684\u5b50\u77e9\u9635\u5904\u6709\u975e\u96f6\u503c\u3002 \u8be5\u7b97\u6cd5\u7684\u8fd0\u884c\u65f6\u95f4\u7ebf\u6027\u4e8e\u83b7\u5f97\u6570\u636e\u7684\u65f6\u95f4\u6b65\u6570<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> t t <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.61508em; vertical-align: 0em;\"><\/span><span class=\"mord mathdefault\">t<\/span><\/span><\/span><\/span><\/span>\u3002<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/img-blog.csdnimg.cn\/20200523221519405.png\" =\"\" =\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" alt=\"autostore\u673a\u5668\u4eba\u7a0b\u5e8f_\u673a\u5668\u4eba\u5de5\u7a0b\u5e08\u662f\u505a\u4ec0\u4e48\u7684 (https:\/\/mushiming.com\/) \u7b2c12\u5f20\" title=\"autostore\u673a\u5668\u4eba\u7a0b\u5e8f_\u673a\u5668\u4eba\u5de5\u7a0b\u5e08\u662f\u505a\u4ec0\u4e48\u7684 \u7b2c12\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" ><\/p>\n<p>\u56fe3.3. GraphSLAM\u7b97\u6cd5\u7ea6\u7b80\u4fe1\u606f\u77e9\u9635\u3002<\/p>\n<p><strong>GraphSLAM\u7b97\u6cd5\u7684\u4e0b\u4e00\u6b65\u5c31\u662f\u6d88\u51cf\u4fe1\u606f\u77e9\u9635\u548c\u5411\u91cf\u7684\u7ef4\u5ea6\u3002<\/strong> \u5b83\u662f\u901a\u8fc7\u56fe3.3\u4e2d\u63cf\u8ff0\u7684GraphSLAM_reduce\u6765\u5b9e\u73b0\u7684\u3002 \u8be5\u7b97\u6cd5\u4ee5\u5b9a\u4e49\u5728\u6574\u4e2a\u5730\u56fe\u7279\u5f81\u548c\u4f4d\u59ff\u7a7a\u95f4\u4e0b\u7684<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> \u03a9 \\Omega <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.68333em; vertical-align: 0em;\"><\/span><span class=\"mord\">\u03a9<\/span><\/span><\/span><\/span><\/span>\u548c<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> \u03be \\xi <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.88888em; vertical-align: -0.19444em;\"><\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.04601em;\">\u03be<\/span><\/span><\/span><\/span><\/span>\u505a\u4e3a\u7b97\u6cd5\u7684\u8f93\u5165\uff0c\u8f93\u51fa\u662f\u5b8c\u5168\u5b9a\u4e49\u5728\u4f4d\u59ff\u7a7a\u95f4\u4e0a\u7684\u524a\u51cf\u540e\u7684\u77e9\u9635<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> \u03a9 ~ \\tilde{\\Omega} <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.92019em; vertical-align: 0em;\"><\/span><span class=\"mord accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.92019em;\"><span class=\"\" style=\"top: -3em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"mord\"><span class=\"mord\">\u03a9<\/span><\/span><\/span><span class=\"\" style=\"top: -3.60233em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"accent-body\" style=\"left: -0.25em;\">~<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u548c\u5411\u91cf<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> \u03b5 ~ \\tilde{\\varepsilon} <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.66786em; vertical-align: 0em;\"><\/span><span class=\"mord accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.66786em;\"><span class=\"\" style=\"top: -3em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">\u03b5<\/span><\/span><\/span><span class=\"\" style=\"top: -3.35em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"accent-body\" style=\"left: -0.16666em;\">~<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\uff0c \u9700\u8981\u6ce8\u610f\u8be5\u77e9\u9635\u548c\u5411\u91cf\u4e0e\u5730\u56fe\u7279\u5f81\u6ca1\u6709\u5173\u7cfb\u3002\u524a\u51cf\u8fc7\u7a0b\u901a\u8fc7GraphSLAM_reduce\u7684\u7b2c4\u52309\u884c\uff0c\u9010\u4e2a\u79fb\u9664\u7279\u5f81<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> m j m_j <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.716668em; vertical-align: -0.286108em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">m<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.311664em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.05724em;\">j<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.286108em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u6765\u5b9e\u73b0\u3002\u8bb0\u5f55<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> \u03a9 ~ , \u03be ~ \\tilde{\\Omega}, \\tilde{\\xi} <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.12574em; vertical-align: -0.19444em;\"><\/span><span class=\"mord accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.92019em;\"><span class=\"\" style=\"top: -3em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"mord\"><span class=\"mord\">\u03a9<\/span><\/span><\/span><span class=\"\" style=\"top: -3.60233em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"accent-body\" style=\"left: -0.25em;\">~<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord accent\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.9313em;\"><span class=\"\" style=\"top: -3em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\" style=\"margin-right: 0.04601em;\">\u03be<\/span><\/span><\/span><span class=\"\" style=\"top: -3.61344em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"accent-body\" style=\"left: -0.13889em;\">~<\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.19444em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u4e2d\u6bcf\u4e2a\u5143\u7d20\u7684\u786e\u5207\u7d22\u5f15\u662f\u5f88\u7e41\u7410\u7684\uff0c \u56e0\u6b64\u56fe3.3\u4e2d\u53ea\u63d0\u4f9b\u4e86\u57fa\u672c\u7684\u601d\u60f3\u3002<\/p>\n<p>\u7b2c5\u884c\u4e2d\u8ba1\u7b97\u4e86\u673a\u5668\u4eba\u89c2\u6d4b\u5230\u7279\u5f81<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> j j <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.85396em; vertical-align: -0.19444em;\"><\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.05724em;\">j<\/span><\/span><\/span><\/span><\/span>\u7684\u4f4d\u59ff\u96c6\u5408<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> \u03c4 ( j ) \\tau(j) <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em; vertical-align: -0.25em;\"><\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.1132em;\">\u03c4<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.05724em;\">j<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span>\u3002\u63a5\u7740\u4ece\u5f53\u524d\u7684<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> \u03a9 ~ \\tilde{\\Omega} <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.92019em; vertical-align: 0em;\"><\/span><span class=\"mord accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.92019em;\"><span class=\"\" style=\"top: -3em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"mord\"><span class=\"mord\">\u03a9<\/span><\/span><\/span><span class=\"\" style=\"top: -3.60233em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"accent-body\" style=\"left: -0.25em;\">~<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u4e2d\u63d0\u53d6\u51fa\u4e24\u4e2a\u5b50\u77e9\u9635:<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> \u03a9 ~ j , j \\tilde{\\Omega}_{j,j} <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.2063em; vertical-align: -0.286108em;\"><\/span><span class=\"mord\"><span class=\"mord accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.92019em;\"><span class=\"\" style=\"top: -3em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"mord\"><span class=\"mord\">\u03a9<\/span><\/span><\/span><span class=\"\" style=\"top: -3.60233em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"accent-body\" style=\"left: -0.25em;\">~<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.311664em;\"><span class=\"\" style=\"top: -2.55em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.05724em;\">j<\/span><span class=\"mpunct mtight\">,<\/span><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.05724em;\">j<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.286108em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u548c<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> \u03a9 ~ \u03c4 ( j ) , j \\tilde{\\Omega}_{\\tau(j), j} <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.27539em; vertical-align: -0.3552em;\"><\/span><span class=\"mord\"><span class=\"mord accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.92019em;\"><span class=\"\" style=\"top: -3em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"mord\"><span class=\"mord\">\u03a9<\/span><\/span><\/span><span class=\"\" style=\"top: -3.60233em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"accent-body\" style=\"left: -0.25em;\">~<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3448em;\"><span class=\"\" style=\"top: -2.5198em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.1132em;\">\u03c4<\/span><span class=\"mopen mtight\">(<\/span><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.05724em;\">j<\/span><span class=\"mclose mtight\">)<\/span><span class=\"mpunct mtight\">,<\/span><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.05724em;\">j<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3552em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u3002 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> \u03a9 ~ j , j \\tilde{\\Omega}_{j,j} <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.2063em; vertical-align: -0.286108em;\"><\/span><span class=\"mord\"><span class=\"mord accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.92019em;\"><span class=\"\" style=\"top: -3em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"mord\"><span class=\"mord\">\u03a9<\/span><\/span><\/span><span class=\"\" style=\"top: -3.60233em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"accent-body\" style=\"left: -0.25em;\">~<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.311664em;\"><span class=\"\" style=\"top: -2.55em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.05724em;\">j<\/span><span class=\"mpunct mtight\">,<\/span><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.05724em;\">j<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.286108em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u662f<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> m j m_j <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.716668em; vertical-align: -0.286108em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">m<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.311664em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.05724em;\">j<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.286108em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u548c<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> m j m_j <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.716668em; vertical-align: -0.286108em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">m<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.311664em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.05724em;\">j<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.286108em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u4e4b\u95f4\u7684\u4e8c\u6b21\u5b50\u77e9\u9635\uff0c<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> \u03a9 ~ \u03c4 ( j ) , j \\tilde{\\Omega}_{\\tau(j),j} <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.27539em; vertical-align: -0.3552em;\"><\/span><span class=\"mord\"><span class=\"mord accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.92019em;\"><span class=\"\" style=\"top: -3em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"mord\"><span class=\"mord\">\u03a9<\/span><\/span><\/span><span class=\"\" style=\"top: -3.60233em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"accent-body\" style=\"left: -0.25em;\">~<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3448em;\"><span class=\"\" style=\"top: -2.5198em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.1132em;\">\u03c4<\/span><span class=\"mopen mtight\">(<\/span><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.05724em;\">j<\/span><span class=\"mclose mtight\">)<\/span><span class=\"mpunct mtight\">,<\/span><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.05724em;\">j<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3552em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u5219\u662f<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> m j m_j <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.716668em; vertical-align: -0.286108em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">m<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.311664em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.05724em;\">j<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.286108em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u4e0e\u4f4d\u59ff\u53d8\u91cf<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> \u03c4 ( j ) \\tau(j) <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em; vertical-align: -0.25em;\"><\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.1132em;\">\u03c4<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.05724em;\">j<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span>\u4e4b\u95f4\u7684\u975e\u5bf9\u89d2\u5143\u3002\u5b83\u4e5f\u4ece\u4fe1\u606f\u72b6\u6001\u5411\u91cf<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> \u03be ~ \\tilde{\\xi} <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.12574em; vertical-align: -0.19444em;\"><\/span><span class=\"mord accent\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.9313em;\"><span class=\"\" style=\"top: -3em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\" style=\"margin-right: 0.04601em;\">\u03be<\/span><\/span><\/span><span class=\"\" style=\"top: -3.61344em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"accent-body\" style=\"left: -0.13889em;\">~<\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.19444em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u4e2d\u63d0\u53d6\u51fa\u5bf9\u5e94\u4e8e\u7b2c<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> j j <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.85396em; vertical-align: -0.19444em;\"><\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.05724em;\">j<\/span><\/span><\/span><\/span><\/span>\u4e2a\u7279\u5f81\u7684\u5143\u7d20\uff0c\u5e76\u6807\u8bb0\u4e3a<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> \u03b5 j \\varepsilon_j <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.716668em; vertical-align: -0.286108em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">\u03b5<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.311664em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.05724em;\">j<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.286108em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u3002\u63a5\u7740\u5728\u7b2c6\u884c\u548c7\u884c\u4e2d\u5c06\u5176\u5bf9\u5e94\u4fe1\u606f\u4ece<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> \u03a9 ~ \\tilde{\\Omega} <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.92019em; vertical-align: 0em;\"><\/span><span class=\"mord accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.92019em;\"><span class=\"\" style=\"top: -3em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"mord\"><span class=\"mord\">\u03a9<\/span><\/span><\/span><span class=\"\" style=\"top: -3.60233em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"accent-body\" style=\"left: -0.25em;\">~<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u548c<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> \u03b5 ~ \\tilde{\\varepsilon} <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.66786em; vertical-align: 0em;\"><\/span><span class=\"mord accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.66786em;\"><span class=\"\" style=\"top: -3em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">\u03b5<\/span><\/span><\/span><span class=\"\" style=\"top: -3.35em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"accent-body\" style=\"left: -0.16666em;\">~<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u51cf\u53bb\u3002\u5728\u8be5\u64cd\u4f5c\u4e4b\u540e\uff0c<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> m j m_j <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.716668em; vertical-align: -0.286108em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">m<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.311664em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.05724em;\">j<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.286108em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u6240\u5bf9\u5e94\u7684\u884c\u548c\u5217\u7684\u5143\u7d20\u90fd\u4e3a0\u3002\u63a5\u7740\u5c31\u628a\u8fd9\u4e9b\u884c\u5217\u79fb\u9664\uff0c\u5bf9\u5e94\u7684\u524a\u51cf\u4e86<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> \u03a9 ~ \\tilde{\\Omega} <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.92019em; vertical-align: 0em;\"><\/span><span class=\"mord accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.92019em;\"><span class=\"\" style=\"top: -3em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"mord\"><span class=\"mord\">\u03a9<\/span><\/span><\/span><span class=\"\" style=\"top: -3.60233em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"accent-body\" style=\"left: -0.25em;\">~<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u548c<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> \u03be ~ \\tilde{\\xi} <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.12574em; vertical-align: -0.19444em;\"><\/span><span class=\"mord accent\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.9313em;\"><span class=\"\" style=\"top: -3em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\" style=\"margin-right: 0.04601em;\">\u03be<\/span><\/span><\/span><span class=\"\" style=\"top: -3.61344em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"accent-body\" style=\"left: -0.13889em;\">~<\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.19444em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u7684\u7ef4\u5ea6\u3002\u5faa\u73af\u8fd9\u4e00\u64cd\u4f5c\u76f4\u5230\u6240\u6709\u7684\u7279\u5f81\u90fd\u88ab\u79fb\u9664\u4e86\uff0c <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> \u03a9 ~ \\tilde{\\Omega} <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.92019em; vertical-align: 0em;\"><\/span><span class=\"mord accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.92019em;\"><span class=\"\" style=\"top: -3em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"mord\"><span class=\"mord\">\u03a9<\/span><\/span><\/span><span class=\"\" style=\"top: -3.60233em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"accent-body\" style=\"left: -0.25em;\">~<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u548c<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> \u03be ~ \\tilde{\\xi} <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.12574em; vertical-align: -0.19444em;\"><\/span><span class=\"mord accent\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.9313em;\"><span class=\"\" style=\"top: -3em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\" style=\"margin-right: 0.04601em;\">\u03be<\/span><\/span><\/span><span class=\"\" style=\"top: -3.61344em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"accent-body\" style=\"left: -0.13889em;\">~<\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.19444em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u4e2d\u53ea\u4fdd\u7559\u4e86\u4f4d\u59ff\u53d8\u91cf\u3002GraphSLAM_reduce\u7b97\u6cd5\u7684\u590d\u6742\u5ea6\u4e5f\u662f\u7ebf\u6027\u4e8e\u65f6\u95f4\u6b65\u6570<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> t t <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.61508em; vertical-align: 0em;\"><\/span><span class=\"mord mathdefault\">t<\/span><\/span><\/span><\/span><\/span> \u7684\u3002<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/img-blog.csdnimg.cn\/20200523221501102.png\" =\"\" =\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" alt=\"autostore\u673a\u5668\u4eba\u7a0b\u5e8f_\u673a\u5668\u4eba\u5de5\u7a0b\u5e08\u662f\u505a\u4ec0\u4e48\u7684 (https:\/\/mushiming.com\/) \u7b2c13\u5f20\" title=\"autostore\u673a\u5668\u4eba\u7a0b\u5e8f_\u673a\u5668\u4eba\u5de5\u7a0b\u5e08\u662f\u505a\u4ec0\u4e48\u7684 \u7b2c13\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" ><\/p>\n<p>\u56fe3.4. \u66f4\u65b0\u540e\u9a8c\u6982\u7387<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> \u03bc \u03bc <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.625em; vertical-align: -0.19444em;\"><\/span><span class=\"mord mathdefault\">\u03bc<\/span><\/span><\/span><\/span><\/span>\u7684\u7b97\u6cd5\u3002<\/p>\n<p>GraphSLAM\u7b97\u6cd5\u7684\u6700\u540e\u4e00\u6b65\u5c31\u662f\u8ba1\u7b97\u673a\u5668\u4eba\u8def\u5f84\u4e0a\u6240\u6709\u4f4d\u59ff\u7684\u5747\u503c\u548c\u65b9\u5dee\uff0c\u4ee5\u53ca\u5730\u56fe\u4e2d\u6240\u6709\u7279\u5f81\u7684\u5e73\u5747\u4f4d\u7f6e\u4f30\u8ba1\u3002\u8fd9\u662f\u901a\u8fc7\u56fe3.4\u7684GraphSLAM_solve\u6765\u5b9e\u73b0\u7684\u3002 \u7b2c2\u884c\u548c\u7b2c3\u884c\u4e2d\u8ba1\u7b97\u8def\u5f84\u4f30\u8ba1<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> \u03bc 0 : t \u03bc_{0:t} <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.625em; vertical-align: -0.19444em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">\u03bc<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.301108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">0<\/span><span class=\"mrel mtight\">:<\/span><span class=\"mord mathdefault mtight\">t<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\uff0c\u901a\u8fc7\u5bf9\u7ea6\u7b80\u7684\u4fe1\u606f\u77e9\u9635<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> \u03a9 ~ \\tilde{\\Omega} <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.92019em; vertical-align: 0em;\"><\/span><span class=\"mord accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.92019em;\"><span class=\"\" style=\"top: -3em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"mord\"><span class=\"mord\">\u03a9<\/span><\/span><\/span><span class=\"\" style=\"top: -3.60233em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"accent-body\" style=\"left: -0.25em;\">~<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u6c42\u9006\uff0c\u5e76\u5c06\u5176\u7ed3\u679c\u4e0e\u4fe1\u606f\u5411\u91cf\u76f8\u4e58\u3002\u7d27\u63a5\u7740\uff0cGraphSLAM_solve\u5728\u7b2c4\u5230\u7b2c7\u884c\u4e2d\u4f9d\u6b21\u8ba1\u7b97\u6bcf\u4e2a\u7279\u5f81\u7684\u5730\u5740\u3002 \u8be5\u7b97\u6cd5\u8fd4\u56de\u7684\u662f\u673a\u5668\u4eba\u8def\u5f84\u548c\u6240\u6709\u5730\u56fe\u7279\u5f81\u7684\u5747\u503c\uff0c\u4ee5\u53ca\u673a\u5668\u4eba\u8def\u5f84\u7684\u534f\u65b9\u5dee\u3002\u6211\u4eec\u6ce8\u610f\u5230\u8fd8\u6709\u4e00\u79cd\u66f4\u9ad8\u6548\u7684\u8ba1\u7b97<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> \u03bc 0 : t \u03bc_{0:t} <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.625em; vertical-align: -0.19444em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">\u03bc<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.301108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">0<\/span><span class=\"mrel mtight\">:<\/span><span class=\"mord mathdefault mtight\">t<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u7684\u65b9\u6cd5\uff0c\u53ef\u4ee5\u7ed5\u8fc7\u5bf9\u77e9\u9635\u6c42\u9006\u3002<\/p>\n<p>GraphSLAM\u7b97\u6cd5\u7684\u89e3\u7684\u8d28\u91cf\u4f9d\u8d56\u4e8eGraphSLAM_initialize\u5bf9\u521d\u59cb\u5747\u503c\u4f30\u8ba1\u7684\u8d28\u91cf\u3002\u8fd9\u4e9b\u4f30\u8ba1\u7684<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> x x <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.43056em; vertical-align: 0em;\"><\/span><span class=\"mord mathdefault\">x<\/span><\/span><\/span><\/span><\/span>-<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> y y <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.625em; vertical-align: -0.19444em;\"><\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.03588em;\">y<\/span><\/span><\/span><\/span><\/span>\u8981\u7d20\uff0c\u4ee5\u4e00\u79cd\u7ebf\u6027\u7684\u5f62\u5f0f\u5f71\u54cd\u5bf9\u5e94\u7684\u6a21\u578b\uff0c\u56e0\u6b64\u7ebf\u6027\u5316\u5e76\u4e0d\u4f9d\u8d56\u4e8e\u8fd9\u4e9b\u503c\u3002 \u5bf9\u4e8e<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> \u03bc 0 : t \u03bc_{0:t} <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.625em; vertical-align: -0.19444em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">\u03bc<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.301108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">0<\/span><span class=\"mrel mtight\">:<\/span><span class=\"mord mathdefault mtight\">t<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u4e2d\u7684\u65b9\u5411\u53d8\u91cf\u5219\u4e0d\u662f\u8fd9\u6837\u3002\u8fd9\u4e9b\u53d8\u91cf\u7684\u521d\u59cb\u5316\u8bef\u5dee\u4f1a\u5f71\u54cd\u6cf0\u52d2\u8fd1\u4f3c\u7684\u51c6\u786e\u5ea6\uff0c\u6700\u7ec8\u4f1a\u5f71\u54cd\u5230\u7b97\u6cd5\u7684\u7ed3\u679c\u3002<\/p>\n<p>\u4e3a\u4e86\u964d\u4f4e\u7ebf\u6027\u5316\u8fc7\u7a0b\u4e2d\u4ee5\u5185\u6cf0\u52d2\u8fd1\u4f3c\u800c\u5e26\u6765\u7684\u8bef\u5dee\uff0c\u5e38\u4f1a\u5728\u540c\u4e00\u4e2a\u6570\u636e\u96c6\u4e0a\u8fd0\u884cGraphSLAM_linearize, GraphSLAM_reduce, GraphSLAM_solve\u591a\u6b21\u3002 \u6bcf\u6b21\u8fed\u4ee3\u90fd\u4ee5\u4e0a\u6b21\u8fed\u4ee3\u8f93\u51fa\u7684\u5747\u503c\u5411\u91cf<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> \u03bc 0 : t \u03bc_{0:t} <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.625em; vertical-align: -0.19444em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">\u03bc<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.301108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">0<\/span><span class=\"mrel mtight\">:<\/span><span class=\"mord mathdefault mtight\">t<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u4f5c\u4e3a\u8f93\u5165\uff0c\u5e76\u8f93\u51fa\u4e00\u4e2a\u65b0\u7684\uff0c\u6539\u8fdb\u540e\u7684\u4f30\u8ba1\u3002\u53ea\u6709\u5f53\u521d\u59cb\u4f4d\u59ff\u4f30\u8ba1\u5177\u6709\u5f88\u5927\u504f\u5dee\u7684\u65f6\u5019\uff0c\u624d\u9700\u8981\u5bf9GraphSLAM\u8fdb\u884c\u8fed\u4ee3\u4f18\u5316\u3002\u901a\u5e38\u8fed\u4ee3\u51e0\u6b21\u5c31\u53ef\u4ee5\u5f97\u5230\u6bd4\u8f83\u597d\u7684\u7ed3\u679c\u4e86\u3002<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/img-blog.csdnimg.cn\/20200523221435497.png\" =\"\" =\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" alt=\"autostore\u673a\u5668\u4eba\u7a0b\u5e8f_\u673a\u5668\u4eba\u5de5\u7a0b\u5e08\u662f\u505a\u4ec0\u4e48\u7684 (https:\/\/mushiming.com\/) \u7b2c14\u5f20\" title=\"autostore\u673a\u5668\u4eba\u7a0b\u5e8f_\u673a\u5668\u4eba\u5de5\u7a0b\u5e08\u662f\u505a\u4ec0\u4e48\u7684 \u7b2c14\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" ><\/p>\n<p>\u56fe3.5. \u7528\u4e8e\u5df2\u77e5\u5173\u8054\u5ea6\u7684\u5b8c\u5168SLAM\u95ee\u9898\u7684GraphSLAM\u7b97\u6cd5\u3002<\/p>\n<p>\u56fe3.5\u603b\u7ed3\u4e86\u6700\u7ec8\u7684\u7b97\u6cd5\u3002\u5b83\u521d\u59cb\u5316\u4e86\u5747\u503c\uff0c\u7136\u540e\u5c31\u91cd\u590d\u6784\u9020\u8fc7\u7a0b\u3001\u7ea6\u7b80\u8fc7\u7a0b\u3001\u548c\u6c42\u89e3\u8fc7\u7a0b\u3002\u901a\u5e38\u4e24\u4e09\u6b21\u8fed\u4ee3\u5c31\u80fd\u591f\u6536\u655b\u4e86\uff0c\u8f93\u51fa\u7684\u5747\u503c<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> \u03bc \u03bc <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.625em; vertical-align: -0.19444em;\"><\/span><span class=\"mord mathdefault\">\u03bc<\/span><\/span><\/span><\/span><\/span>\u5c31\u662f\u5bf9\u673a\u5668\u4eba\u8def\u5f84\u548c\u5730\u56fe\u7684\u6700\u597d\u7684\u4f30\u8ba1\u3002<\/p>\n<h3>\u56db\u3001RTAB-Map<\/h3>\n<p>\u66f4\u591a\u5173\u4e8eRTAB-Map\u7684\u4f7f\u7528\u5c06\u5728\u4e4b\u540e\u7684\u535a\u5ba2\u4e2d\u5c55\u793a\u3002<\/p>\n<blockquote>\n<p>\u66f4\u591a\u4fe1\u606f\u8bf7\u8bbf\u95ee\u6b64\u5904\u3002<\/p>\n<\/blockquote>\n<p><img decoding=\"async\" src=\"https:\/\/img-blog.csdnimg.cn\/20200523212759376.png\" =\"\" =\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" alt=\"autostore\u673a\u5668\u4eba\u7a0b\u5e8f_\u673a\u5668\u4eba\u5de5\u7a0b\u5e08\u662f\u505a\u4ec0\u4e48\u7684 (https:\/\/mushiming.com\/) \u7b2c15\u5f20\" title=\"autostore\u673a\u5668\u4eba\u7a0b\u5e8f_\u673a\u5668\u4eba\u5de5\u7a0b\u5e08\u662f\u505a\u4ec0\u4e48\u7684 \u7b2c15\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" ><\/p>\n<p>RTAB-Map\uff08\u57fa\u4e8e\u5b9e\u65f6\u5916\u89c2\u7684\u6620\u5c04\uff09\u662f\u4e00\u79cd\u57fa\u4e8e\u589e\u91cf\u57fa\u4e8e\u5916\u89c2\u7684\u95ed\u73af\u68c0\u6d4b\u5668\u7684RGB-D\uff0c\u57fa\u4e8e\u7acb\u4f53\u58f0\u548c\u6fc0\u5149\u96f7\u8fbe\u56fe\u7684SLAM\u65b9\u6cd5\u3002\u95ed\u73af\u68c0\u6d4b\u5668\u4f7f\u7528\u8bcd\u888b\u65b9\u6cd5\u6765\u786e\u5b9a\u65b0\u56fe\u50cf\u6765\u81ea\u5148\u524d\u4f4d\u7f6e\u6216\u65b0\u4f4d\u7f6e\u7684\u53ef\u80fd\u6027\u3002\u5f53\u63a5\u53d7\u5faa\u73af\u95ed\u5408\u5047\u8bbe\u65f6\uff0c\u65b0\u7ea6\u675f\u5c06\u6dfb\u52a0\u5230\u5730\u56fe\u7684\u56fe\u5f62\u4e2d\uff0c\u7136\u540e\u56fe\u5f62\u4f18\u5316\u5668\u5c06\u5730\u56fe\u4e2d\u7684\u9519\u8bef\u6700\u5c0f\u5316\u3002\u4f7f\u7528\u5185\u5b58\u7ba1\u7406\u65b9\u6cd5\u6765\u9650\u5236\u7528\u4e8e\u95ed\u73af\u68c0\u6d4b\u548c\u56fe\u5f62\u4f18\u5316\u7684\u4f4d\u7f6e\u6570\u91cf\uff0c\u4ee5\u4fbf\u59cb\u7ec8\u9075\u5b88\u5bf9\u5927\u578b\u73af\u5883\u7684\u5b9e\u65f6\u7ea6\u675f\u3002RTAB-Map\u53ef\u4ee5\u4e0e\u624b\u6301Kinect\uff0c\u7acb\u4f53\u76f8\u673a\u62163D\u6fc0\u5149\u96f7\u8fbe\u4e00\u8d77\u5355\u72ec\u4f7f\u7528\u4ee5\u8fdb\u884c6DoF\u6620\u5c04\uff0c\u4e5f\u53ef\u4ee5\u5728\u914d\u5907\u6709\u6fc0\u5149\u6d4b\u8ddd\u4eea\u7684\u673a\u5668\u4eba\u4e0a\u8fdb\u884c3DoF\u6620\u5c04\u3002<\/p>\n<p>RTAB-Map\u4f7f\u7528\u5185\u5b58\u7ba1\u7406\u6280\u672f\u6765\u9650\u5236\u5728\u95ed\u73af\u68c0\u6d4b\u671f\u95f4\u88ab\u89c6\u4e3a\u5019\u9009\u4f4d\u7f6e\u7684\u4f4d\u7f6e\u6570\u91cf\u3002\u6b64\u6280\u672f\u662fRTAB-Map\u7684\u4e00\u9879\u5173\u952e\u529f\u80fd\uff0c\u5b83\u5141\u8bb8\u5b9e\u65f6\u5173\u95ed\u5faa\u73af\u3002<\/p>\n<ul>\n<li>\n<p>\u603b\u4f53\u7b56\u7565\u662f\u5c06\u6700\u65b0\u7684\u548c\u7ecf\u5e38\u89c2\u5bdf\u5230\u7684\u4f4d\u7f6e\u4fdd\u7559\u5728\u673a\u5668\u4eba\u7684\u5de5\u4f5c\u5185\u5b58\uff08WM\uff09\u4e2d\uff0c\u5e76\u5c06\u5176\u4ed6\u4f4d\u7f6e\u8f6c\u79fb\u5230\u957f\u671f\u5185\u5b58\uff08LTM\uff09\u4e2d\u3002<\/p>\n<\/li>\n<li>\n<p>\u5f53\u83b7\u53d6\u65b0\u56fe\u50cf\u65f6\uff0c\u5728\u77ed\u671f\u5b58\u50a8\u5668\uff08STM\uff09\u4e2d\u521b\u5efa\u4e00\u4e2a\u65b0\u8282\u70b9\u3002<\/p>\n<\/li>\n<li>\n<p>\u521b\u5efa\u8282\u70b9\u65f6\uff0c\u8bf7\u8bb0\u4f4f\u63d0\u53d6\u7279\u5f81\u5e76\u5c06\u5176\u4e0e\u8bcd\u6c47\u8868\u8fdb\u884c\u6bd4\u8f83\uff0c\u4ee5\u627e\u5230\u56fe\u50cf\u4e2d\u7684\u6240\u6709\u5355\u8bcd\uff0c\u4ece\u800c\u4e3a\u6b64\u8282\u70b9\u521b\u5efa\u4e00\u4e2a\u8bcd\u888b\u3002<\/p>\n<\/li>\n<li>\n<p>\u5728STM\u4e2d\uff0c\u5c06\u6839\u636e\u673a\u5668\u4eba\u5728\u8be5\u4f4d\u7f6e\u82b1\u8d39\u7684\u65f6\u95f4\u4e3a\u8282\u70b9\u5206\u914d\u6743\u91cd-\u65f6\u95f4\u8d8a\u957f\uff0c\u6743\u91cd\u5c31\u8d8a\u9ad8\u3002<\/p>\n<\/li>\n<li>\n<p>STM\u5177\u6709\u56fa\u5b9a\u7684S\u5927\u5c0f\u3002\u5f53STM\u5230\u8fbeS\u4e2a\u8282\u70b9\u65f6\uff0c\u6700\u65e9\u7684\u8282\u70b9\u5c06\u79fb\u81f3WM\u4ee5\u8fdb\u884c\u73af\u8def\u95ed\u5408\u68c0\u6d4b\u3002<\/p>\n<\/li>\n<li>\n<p>\u5faa\u73af\u5173\u95ed\u53d1\u751f\u5728WM\u4e2d\u3002<\/p>\n<\/li>\n<li>\n<p>WM\u5927\u5c0f\u53d6\u51b3\u4e8e\u56fa\u5b9a\u7684\u65f6\u95f4\u9650\u5236T\u3002\u5f53\u5904\u7406\u65b0\u6570\u636e\u6240\u9700\u7684\u65f6\u95f4\u8fbe\u5230T\u65f6\uff0c\u56fe\u5f62\u7684\u67d0\u4e9b\u8282\u70b9\u4eceWM\u8f6c\u79fb\u5230LTM-\u7ed3\u679c\uff0cWM\u5927\u5c0f\u51e0\u4e4e\u4fdd\u6301\u6052\u5b9a\u3002<\/p>\n<\/li>\n<li>\n<p>WM\u4e2d\u6700\u65e9\u7684\uff0c\u6743\u91cd\u8f83\u5c0f\u7684\u8282\u70b9\u5148\u8f6c\u79fb\u5230LTM\uff0c\u56e0\u6b64WM\u7531\u8f83\u957f\u65f6\u95f4\u7684\u8282\u70b9\u7ec4\u6210\u3002<\/p>\n<\/li>\n<li>\n<p>LTM\u4e0d\u7528\u4e8e\u95ed\u73af\u68c0\u6d4b\u548c\u56fe\u5f62\u4f18\u5316\u3002<\/p>\n<\/li>\n<li>\n<p>\u5982\u679c\u68c0\u6d4b\u5230\u73af\u8def\u5173\u95ed\uff0c\u5219\u53ef\u4ee5\u5c06\u65e7\u8282\u70b9\u7684LTM\u4e2d\u7684\u90bb\u5c45\u8f6c\u79fb\u56deWM\uff08\u79f0\u4e3a\u68c0\u7d22\u7684\u8fc7\u7a0b\uff09\u3002<\/p>\n<\/li>\n<\/ul>\n<p><img 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