{"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":"

\n <\/path> \n<\/svg> <\/p>\n

\u4e00\u3001\u5f15\u5165<\/h3>\n

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

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

\u4e8c\u3001GraphSLAM\u6a21\u578b<\/h3>\n

1. \u6700\u5927\u4f3c\u7136\u4f30\u8ba1<\/h4>\n

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

\uff081\uff09\u7279\u5f81\u91cf\u6d4b\u793a\u4f8b<\/h5>\n

\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

\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

\u673a\u5668\u4eba\u6d4b\u91cf\u4e00\u4e2a\u7279\u5f81\uff0c m 1 m_1 <\/span><\/span>m<\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\uff0c\u8fd4\u56de\u8ddd\u79bb\u4e3a1.8\u7c73\u3002<\/p>\n

\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

\u8fd9\u79cd\u6d4b\u91cf\u7684\u6982\u7387\u5206\u5e03\u53ef\u4ee5\u5b9a\u4e49\u4e3a\uff0c
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>p<\/span>(<\/span>x<\/span>)<\/span><\/span>=<\/span><\/span><\/span><\/span><\/span><\/span>\u03c3<\/span><\/span>2<\/span>\u03c0<\/span><\/span><\/span><\/span>
\n \n <\/path> \n <\/svg><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>e<\/span><\/span>\u2212<\/span><\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u03c3<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>z<\/span><\/span>1<\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2212<\/span>(<\/span>x<\/span><\/span>0<\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span>1<\/span>.<\/span>8<\/span>)<\/span>)<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

\u7b80\u5355\u5730\u8bf4\uff0c\u5f53 z 1 z_1 <\/span><\/span>z<\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u548c x 0 x_0 <\/span><\/span>x<\/span><\/span>0<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u76f8\u8ddd1.8\u7c73\u65f6\uff0c\u6982\u7387\u5206\u5e03\u6700\u9ad8\u3002
\"autostore\u673a\u5668\u4eba\u7a0b\u5e8f_\u673a\u5668\u4eba\u5de5\u7a0b\u5e08\u662f\u505a\u4ec0\u4e48\u7684<\/p>\n

\u7136\u800c\uff0c\u7531\u4e8e\u4f4d\u7f6e\u7684\u7b2c\u4e00\u4e2a\u59ff\u52bf\uff0c x 0 x_0 <\/span><\/span>x<\/span><\/span>0<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/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
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>p<\/span>(<\/span>x<\/span>)<\/span><\/span>=<\/span><\/span><\/span><\/span><\/span><\/span>\u03c3<\/span><\/span>2<\/span>\u03c0<\/span><\/span><\/span><\/span>
\n \n <\/path> \n <\/svg><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>e<\/span><\/span>\u2212<\/span><\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u03c3<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>z<\/span><\/span>1<\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2212<\/span>1<\/span>.<\/span>8<\/span>)<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>
\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

\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
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>p<\/span>(<\/span>x<\/span>)<\/span><\/span>=<\/span><\/span><\/span><\/span><\/span><\/span>\u03c3<\/span><\/span>2<\/span>\u03c0<\/span><\/span><\/span><\/span>
\n \n <\/path> \n <\/svg><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>e<\/span><\/span>\u2212<\/span><\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u03c3<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>z<\/span><\/span>1<\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2212<\/span>1<\/span>.<\/span>8<\/span>)<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u00d7<\/span><\/span><\/span><\/span><\/span><\/span>\u03c3<\/span><\/span>2<\/span>\u03c0<\/span><\/span><\/span><\/span>
\n \n <\/path> \n <\/svg><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>e<\/span><\/span>\u2212<\/span><\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u03c3<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>z<\/span><\/span>1<\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2212<\/span>2<\/span>.<\/span>2<\/span>)<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

\u5728\u8fd9\u4e2a\u7b80\u5355\u7684\u793a\u4f8b\u4e2d\uff0c\u6240\u4ee5\u6211\u4eec\u53ef\u4ee5\u731c\u6d4b z 1 z_1 <\/span><\/span>z<\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/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

\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

\u5220\u9664\u6bd4\u4f8b\u7cfb\u6570<\/h6>\n

\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
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>p<\/span>(<\/span>x<\/span>)<\/span><\/span>=<\/span><\/span><\/span><\/span>e<\/span><\/span>\u2212<\/span><\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u03c3<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>z<\/span><\/span>1<\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2212<\/span>1<\/span>.<\/span>8<\/span>)<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u00d7<\/span><\/span><\/span><\/span>e<\/span><\/span>\u2212<\/span><\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u03c3<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>z<\/span><\/span>1<\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2212<\/span>2<\/span>.<\/span>2<\/span>)<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

\u5bf9\u6570\u4f3c\u7136\u51fd\u6570<\/h6>\n

\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
\u9996\u5148\uff0c\u6211\u4eec\u5fc5\u987b\u4f7f\u7528\u4e0b\u9762\u7684\u6027\u8d28\uff0c e a e b = e a + b e^ae^b=e^{a+b} <\/span><\/span>e<\/span><\/span>a<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>e<\/span><\/span>b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>e<\/span><\/span>a<\/span>+<\/span>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
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>e<\/span><\/span>\u2212<\/span><\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u03c3<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>z<\/span><\/span>1<\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2212<\/span>1<\/span>.<\/span>8<\/span>)<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u00d7<\/span><\/span><\/span><\/span>e<\/span><\/span>\u2212<\/span><\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u03c3<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>z<\/span><\/span>1<\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2212<\/span>2<\/span>.<\/span>2<\/span>)<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>e<\/span><\/span>\u2212<\/span><\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u03c3<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>z<\/span><\/span>1<\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2212<\/span>1<\/span>.<\/span>8<\/span>)<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2212<\/span><\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u03c3<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>z<\/span><\/span>1<\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2212<\/span>2<\/span>.<\/span>2<\/span>)<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

\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
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>ln<\/span>(<\/span>e<\/span><\/span>\u2212<\/span><\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u03c3<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>z<\/span><\/span>1<\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2212<\/span>1<\/span>.<\/span>8<\/span>)<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u00d7<\/span><\/span><\/span><\/span>e<\/span><\/span>\u2212<\/span><\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u03c3<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>z<\/span><\/span>1<\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2212<\/span>2<\/span>.<\/span>2<\/span>)<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span>=<\/span><\/span><\/span><\/span>\u2212<\/span><\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u03c3<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>z<\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2212<\/span>1<\/span>.<\/span>8<\/span>)<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2212<\/span><\/span><\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u03c3<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>z<\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2212<\/span>2<\/span>.<\/span>2<\/span>)<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>
\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

\"autostore\u673a\u5668\u4eba\u7a0b\u5e8f_\u673a\u5668\u4eba\u5de5\u7a0b\u5e08\u662f\u505a\u4ec0\u4e48\u7684<\/p>\n

\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

\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
( z 1 \u2212 1.8 ) 2 + ( z 1 \u2212 2.2 ) 2 (z_1 \u22121.8)^2 +(z_1\u22122.2) ^2 <\/span><\/span>(<\/span>z<\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2212<\/span>1<\/span>.<\/span>8<\/span>)<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span><\/span><\/span>(<\/span>z<\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2212<\/span>2<\/span>.<\/span>2<\/span>)<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

\u4f18\u5316<\/h6>\n

\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
2 z 1 2 \u2212 8 z 1 + 8.08 2z_1^2\u22128z_1+8.08 <\/span><\/span>2<\/span>z<\/span><\/span>1<\/span><\/span><\/span><\/span>2<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2212<\/span>8<\/span>z<\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span><\/span><\/span>8<\/span>.<\/span>0<\/span>8<\/span><\/span><\/span><\/span><\/span><\/span>
\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
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>4<\/span>z<\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2212<\/span>8<\/span><\/span>=<\/span><\/span><\/span><\/span>0<\/span><\/span><\/span><\/span>4<\/span>z<\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>8<\/span><\/span><\/span><\/span>z<\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

\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

\"autostore\u673a\u5668\u4eba\u7a0b\u5e8f_\u673a\u5668\u4eba\u5de5\u7a0b\u5e08\u662f\u505a\u4ec0\u4e48\u7684<\/p>\n

\u603b\u89c8<\/h6>\n

\u8fd9\u91cc\u6267\u884c\u7684\u8fc7\u7a0b\u662fMLE\u95ee\u9898\u7684\u89e3\u6790\u89e3\u3002\u5305\u62ec\u7684\u6b65\u9aa4\uff1a<\/p>\n