{"id":150,"date":"2022-10-29T12:34:52","date_gmt":"2022-10-29T04:34:52","guid":{"rendered":"https:\/\/wp.ytdx.cc\/?p=150"},"modified":"2022-10-29T17:23:13","modified_gmt":"2022-10-29T09:23:13","slug":"%e5%8d%a1%e5%b0%94%e6%9b%bc%e6%bb%a4%e6%b3%a2%e7%ae%97%e6%b3%95","status":"publish","type":"post","link":"https:\/\/wp.ytdx.cc\/index.php\/2022\/10\/29\/%e5%8d%a1%e5%b0%94%e6%9b%bc%e6%bb%a4%e6%b3%a2%e7%ae%97%e6%b3%95\/","title":{"rendered":"\u5361\u5c14\u66fc\u6ee4\u6ce2\u7b97\u6cd5"},"content":{"rendered":"\r\n<p class=\"wp-block-paragraph\">1. \u5361\u5c14\u66fc\u6ee4\u6ce2\u5668\u7684\u4ecb\u7ecd<\/p>\r\n\r\n\r\n\r\n<p class=\"wp-block-paragraph\">\u4e3a\u4e86\u53ef\u4ee5\u66f4\u52a0\u5bb9\u6613\u7684\u7406\u89e3\u5361\u5c14\u66fc\u6ee4\u6ce2\u5668\uff0c\u8fd9\u91cc\u4f1a\u5e94\u7528\u5f62\u8c61\u7684\u63cf\u8ff0\u65b9\u6cd5\u6765\u8bb2\u89e3\uff0c\u800c\u4e0d\u662f\u50cf\u5927\u591a\u6570\u53c2\u8003\u4e66\u90a3\u6837\u7f57\u5217\u4e00\u5927\u5806\u7684\u6570\u5b66\u516c\u5f0f\u548c\u6570\u5b66\u7b26\u53f7\u3002\u4f46\u662f\uff0c\u4ed6\u76845\u6761\u516c\u5f0f\u662f\u5176\u6838\u5fc3\u5185\u5bb9\u3002\u7ed3\u5408\u73b0\u4ee3\u7684\u8ba1\u7b97\u673a\uff0c\u5176\u5b9e\u5361\u5c14\u66fc\u7684\u7a0b\u5e8f\u76f8\u5f53\u7684\u7b80\u5355\uff0c\u53ea\u8981\u4f60\u7406\u89e3\u4e86\u4ed6\u7684\u90a35\u6761\u516c\u5f0f\u3002<\/p>\r\n\r\n\r\n\r\n<p class=\"wp-block-paragraph\">\u5728\u4ecb\u7ecd\u4ed6\u76845\u6761\u516c\u5f0f\u4e4b\u524d\uff0c\u5148\u8ba9\u6211\u4eec\u6765\u6839\u636e\u4e0b\u9762\u7684\u4f8b\u5b50\u4e00\u6b65\u4e00\u6b65\u7684\u63a2\u7d22\u3002<\/p>\r\n\r\n\r\n\r\n<p class=\"wp-block-paragraph\">\u5047\u8bbe\u6211\u4eec\u8981\u7814\u7a76\u7684\u5bf9\u8c61\u662f\u4e00\u4e2a\u623f\u95f4\u7684\u6e29\u5ea6\u3002\u6839\u636e\u4f60\u7684\u7ecf\u9a8c\u5224\u65ad\uff0c\u8fd9\u4e2a\u623f\u95f4\u7684\u6e29\u5ea6\u662f\u6052\u5b9a\u7684\uff0c\u4e5f\u5c31\u662f\u4e0b\u4e00\u5206\u949f\u7684\u6e29\u5ea6\u7b49\u4e8e\u73b0\u5728\u8fd9\u4e00\u5206\u949f\u7684\u6e29\u5ea6\uff08\u5047\u8bbe\u6211\u4eec\u7528\u4e00\u5206\u949f\u6765\u505a\u65f6\u95f4\u5355\u4f4d\uff09\u3002\u5047\u8bbe\u4f60\u5bf9\u4f60\u7684\u7ecf\u9a8c\u4e0d\u662f100%\u7684\u76f8\u4fe1\uff0c\u53ef\u80fd\u4f1a\u6709\u4e0a\u4e0b\u504f\u5dee\u51e0\u5ea6\u3002\u6211\u4eec\u628a\u8fd9\u4e9b\u504f\u5dee\u770b\u6210\u662f\u9ad8\u65af\u767d\u566a\u58f0\uff08White Gaussian Noise\uff09\uff0c\u4e5f\u5c31\u662f\u8fd9\u4e9b\u504f\u5dee\u8ddf\u524d\u540e\u65f6\u95f4\u662f\u6ca1\u6709\u5173\u7cfb\u7684\u800c\u4e14\u7b26\u5408\u9ad8\u65af\u5206\u914d\uff08Gaussian Distribution\uff09\u3002\u53e6\u5916\uff0c\u6211\u4eec\u5728\u623f\u95f4\u91cc\u653e\u4e00\u4e2a\u6e29\u5ea6\u8ba1\uff0c\u4f46\u662f\u8fd9\u4e2a\u6e29\u5ea6\u8ba1\u4e5f\u4e0d\u51c6\u786e\u7684\uff0c\u6d4b\u91cf\u503c\u4f1a\u6bd4\u5b9e\u9645\u503c\u504f\u5dee\u3002\u6211\u4eec\u4e5f\u628a\u8fd9\u4e9b\u504f\u5dee\u770b\u6210\u662f\u9ad8\u65af\u767d\u566a\u58f0\u3002<\/p>\r\n\r\n\r\n\r\n<p class=\"wp-block-paragraph\">\u597d\u4e86\uff0c\u73b0\u5728\u5bf9\u4e8e\u67d0\u4e00\u5206\u949f\u6211\u4eec\u6709\u4e24\u4e2a\u6709\u5173\u4e8e\u8be5\u623f\u95f4\u7684\u6e29\u5ea6\u503c\uff1a\u4f60\u6839\u636e\u7ecf\u9a8c\u7684\u9884\u6d4b\u503c\uff08\u7cfb\u7edf\u7684\u9884\u6d4b\u503c\uff09\u548c\u6e29\u5ea6\u8ba1\u7684\u503c\uff08\u6d4b\u91cf\u503c\uff09\u3002\u4e0b\u9762\u6211\u4eec\u8981\u7528\u8fd9\u4e24\u4e2a\u503c\u7ed3\u5408\u4ed6\u4eec\u5404\u81ea\u7684\u566a\u58f0\u6765\u4f30\u7b97\u51fa\u623f\u95f4\u7684\u5b9e\u9645\u6e29\u5ea6\u503c\u3002<\/p>\r\n\r\n\r\n\r\n<p class=\"wp-block-paragraph\">\u5047\u5982\u6211\u4eec\u8981\u4f30\u7b97k\u65f6\u523b\u7684\u662f\u5b9e\u9645\u6e29\u5ea6\u503c\u3002\u9996\u5148\u4f60\u8981\u6839\u636ek-1\u65f6\u523b\u7684\u6e29\u5ea6\u503c\uff0c\u6765\u9884\u6d4bk\u65f6\u523b\u7684\u6e29\u5ea6\u3002\u56e0\u4e3a\u4f60\u76f8\u4fe1\u6e29\u5ea6\u662f\u6052\u5b9a\u7684\uff0c\u6240\u4ee5\u4f60\u4f1a\u5f97\u5230k\u65f6\u523b\u7684\u6e29\u5ea6\u9884\u6d4b\u503c\u662f\u8ddfk-1\u65f6\u523b\u4e00\u6837\u7684\uff0c\u5047\u8bbe\u662f23\u5ea6\uff0c\u540c\u65f6\u8be5\u503c\u7684\u9ad8\u65af\u566a\u58f0\u7684\u504f\u5dee\u662f5\u5ea6\uff085\u662f\u8fd9\u6837\u5f97\u5230\u7684\uff1a\u5982\u679ck-1\u65f6\u523b\u4f30\u7b97\u51fa\u7684\u6700\u4f18\u6e29\u5ea6\u503c\u7684\u504f\u5dee\u662f3\uff0c\u4f60\u5bf9\u81ea\u5df1\u9884\u6d4b\u7684\u4e0d\u786e\u5b9a\u5ea6\u662f4\u5ea6\uff0c\u4ed6\u4eec\u5e73\u65b9\u76f8\u52a0\u518d\u5f00\u65b9\uff0c\u5c31\u662f5\uff09\u3002\u7136\u540e\uff0c\u4f60\u4ece\u6e29\u5ea6\u8ba1\u90a3\u91cc\u5f97\u5230\u4e86k\u65f6\u523b\u7684\u6e29\u5ea6\u503c\uff0c\u5047\u8bbe\u662f25\u5ea6\uff0c\u540c\u65f6\u8be5\u503c\u7684\u504f\u5dee\u662f4\u5ea6\u3002<\/p>\r\n\r\n\r\n\r\n<p class=\"wp-block-paragraph\">\u7531\u4e8e\u6211\u4eec\u7528\u4e8e\u4f30\u7b97k\u65f6\u523b\u7684\u5b9e\u9645\u6e29\u5ea6\u6709\u4e24\u4e2a\u6e29\u5ea6\u503c\uff0c\u5206\u522b\u662f23\u5ea6\u548c25\u5ea6\u3002\u7a76\u7adf\u5b9e\u9645\u6e29\u5ea6\u662f\u591a\u5c11\u5462\uff1f\u76f8\u4fe1\u81ea\u5df1\u8fd8\u662f\u76f8\u4fe1\u6e29\u5ea6\u8ba1\u5462\uff1f\u7a76\u7adf\u76f8\u4fe1\u8c01\u591a\u4e00\u70b9\uff0c\u6211\u4eec\u53ef\u4ee5\u7528\u4ed6\u4eec\u7684covariance\u6765\u5224\u65ad\u3002\u56e0\u4e3aKg^2=5^2\/(5^2+4^2)\uff0c\u6240\u4ee5Kg=0.78\uff0c\u6211\u4eec\u53ef\u4ee5\u4f30\u7b97\u51fak\u65f6\u523b\u7684\u5b9e\u9645\u6e29\u5ea6\u503c\u662f\uff1a23+0.78*(25-23)=24.56\u5ea6\u3002\u53ef\u4ee5\u770b\u51fa\uff0c\u56e0\u4e3a\u6e29\u5ea6\u8ba1\u7684covariance\u6bd4\u8f83\u5c0f\uff08\u6bd4\u8f83\u76f8\u4fe1\u6e29\u5ea6\u8ba1\uff09\uff0c\u6240\u4ee5\u4f30\u7b97\u51fa\u7684\u6700\u4f18\u6e29\u5ea6\u503c\u504f\u5411\u6e29\u5ea6\u8ba1\u7684\u503c\u3002<\/p>\r\n\r\n\r\n\r\n<p class=\"wp-block-paragraph\">\u73b0\u5728\u6211\u4eec\u5df2\u7ecf\u5f97\u5230k\u65f6\u523b\u7684\u6700\u4f18\u6e29\u5ea6\u503c\u4e86\uff0c\u4e0b\u4e00\u6b65\u5c31\u662f\u8981\u8fdb\u5165k+1\u65f6\u523b\uff0c\u8fdb\u884c\u65b0\u7684\u6700\u4f18\u4f30\u7b97\u3002\u5230\u73b0\u5728\u4e3a\u6b62\uff0c\u597d\u50cf\u8fd8\u6ca1\u770b\u5230\u4ec0\u4e48\u81ea\u56de\u5f52\u7684\u4e1c\u897f\u51fa\u73b0\u3002\u5bf9\u4e86\uff0c\u5728\u8fdb\u5165k+1\u65f6\u523b\u4e4b\u524d\uff0c\u6211\u4eec\u8fd8\u8981\u7b97\u51fak\u65f6\u523b\u90a3\u4e2a\u6700\u4f18\u503c\uff0824.56\u5ea6\uff09\u7684\u504f\u5dee\u3002\u7b97\u6cd5\u5982\u4e0b\uff1a((1-Kg)*5^2)^0.5=2.35\u3002\u8fd9\u91cc\u76845\u5c31\u662f\u4e0a\u9762\u7684k\u65f6\u523b\u4f60\u9884\u6d4b\u7684\u90a3\u4e2a23\u5ea6\u6e29\u5ea6\u503c\u7684\u504f\u5dee\uff0c\u5f97\u51fa\u76842.35\u5c31\u662f\u8fdb\u5165k+1\u65f6\u523b\u4ee5\u540ek\u65f6\u523b\u4f30\u7b97\u51fa\u7684\u6700\u4f18\u6e29\u5ea6\u503c\u7684\u504f\u5dee\uff08\u5bf9\u5e94\u4e8e\u4e0a\u9762\u76843\uff09\u3002<\/p>\r\n\r\n\r\n\r\n<p class=\"wp-block-paragraph\">\u5c31\u662f\u8fd9\u6837\uff0c\u5361\u5c14\u66fc\u6ee4\u6ce2\u5668\u5c31\u4e0d\u65ad\u7684\u628acovariance\u9012\u5f52\uff0c\u4ece\u800c\u4f30\u7b97\u51fa\u6700\u4f18\u7684\u6e29\u5ea6\u503c\u3002\u4ed6\u8fd0\u884c\u7684\u5f88\u5feb\uff0c\u800c\u4e14\u5b83\u53ea\u4fdd\u7559\u4e86\u4e0a\u4e00\u65f6\u523b\u7684covariance\u3002\u4e0a\u9762\u7684Kg\uff0c\u5c31\u662f\u5361\u5c14\u66fc\u589e\u76ca\uff08Kalman Gain\uff09\u3002\u4ed6\u53ef\u4ee5\u968f\u4e0d\u540c\u7684\u65f6\u523b\u800c\u6539\u53d8\u4ed6\u81ea\u5df1\u7684\u503c\uff0c\u662f\u4e0d\u662f\u5f88\u795e\u5947\uff01<\/p>\r\n\r\n\r\n\r\n<p class=\"wp-block-paragraph\">\u4e0b\u9762\u5c31\u8981\u8a00\u5f52\u6b63\u4f20\uff0c\u8ba8\u8bba\u771f\u6b63\u5de5\u7a0b\u7cfb\u7edf\u4e0a\u7684\u5361\u5c14\u66fc\u3002<\/p>\r\n\r\n\r\n\r\n<p class=\"wp-block-paragraph\">2\uff0e \u5361\u5c14\u66fc\u6ee4\u6ce2\u5668\u7b97\u6cd5<br \/>\u5728\u8fd9\u4e00\u90e8\u5206\uff0c\u6211\u4eec\u5c31\u6765\u63cf\u8ff0\u6e90\u4e8eDr Kalman \u7684\u5361\u5c14\u66fc\u6ee4\u6ce2\u5668\u3002\u4e0b\u9762\u7684\u63cf\u8ff0\uff0c\u4f1a\u6d89\u53ca\u4e00\u4e9b\u57fa\u672c\u7684\u6982\u5ff5\u77e5\u8bc6\uff0c\u5305\u62ec\u6982\u7387\uff08Probability\uff09\uff0c\u968f\u5373\u53d8\u91cf\uff08Random Variable\uff09\uff0c\u9ad8\u65af\u6216\u6b63\u6001\u5206\u914d\uff08Gaussian Distribution\uff09\u8fd8\u6709State-space Model\u7b49\u7b49\u3002\u4f46\u5bf9\u4e8e\u5361\u5c14\u66fc\u6ee4\u6ce2\u5668\u7684\u8be6\u7ec6\u8bc1\u660e\uff0c\u8fd9\u91cc\u4e0d\u80fd\u4e00\u4e00\u63cf\u8ff0\u3002<\/p>\r\n\r\n\r\n\r\n<p class=\"wp-block-paragraph\">\u9996\u5148\uff0c\u6211\u4eec\u5148\u8981\u5f15\u5165\u4e00\u4e2a\u79bb\u6563\u63a7\u5236\u8fc7\u7a0b\u7684\u7cfb\u7edf\u3002\u8be5\u7cfb\u7edf\u53ef\u7528\u4e00\u4e2a\u7ebf\u6027\u968f\u673a\u5fae\u5206\u65b9\u7a0b\uff08Linear Stochastic Difference equation\uff09\u6765\u63cf\u8ff0\uff1a<br \/>X(k)=A X(k-1)+B U(k)+W(k)<br \/>\u518d\u52a0\u4e0a\u7cfb\u7edf\u7684\u6d4b\u91cf\u503c\uff1a<br \/>Z(k)=H X(k)+V(k)<br \/>\u4e0a\u4e24\u5f0f\u5b50\u4e2d\uff0cX(k)\u662fk\u65f6\u523b\u7684\u7cfb\u7edf\u72b6\u6001\uff0cU(k)\u662fk\u65f6\u523b\u5bf9\u7cfb\u7edf\u7684\u63a7\u5236\u91cf\u3002A\u548cB\u662f\u7cfb\u7edf\u53c2\u6570\uff0c\u5bf9\u4e8e\u591a\u6a21\u578b\u7cfb\u7edf\uff0c\u4ed6\u4eec\u4e3a\u77e9\u9635\u3002Z(k)\u662fk\u65f6\u523b\u7684\u6d4b\u91cf\u503c\uff0cH\u662f\u6d4b\u91cf\u7cfb\u7edf\u7684\u53c2\u6570\uff0c\u5bf9\u4e8e\u591a\u6d4b\u91cf\u7cfb\u7edf\uff0cH\u4e3a\u77e9\u9635\u3002W(k)\u548cV(k)\u5206\u522b\u8868\u793a\u8fc7\u7a0b\u548c\u6d4b\u91cf\u7684\u566a\u58f0\u3002\u4ed6\u4eec\u88ab\u5047\u8bbe\u6210\u9ad8\u65af\u767d\u566a\u58f0(White Gaussian Noise)\uff0c\u4ed6\u4eec\u7684covariance \u5206\u522b\u662fQ\uff0cR\uff08\u8fd9\u91cc\u6211\u4eec\u5047\u8bbe\u4ed6\u4eec\u4e0d\u968f\u7cfb\u7edf\u72b6\u6001\u53d8\u5316\u800c\u53d8\u5316\uff09\u3002<\/p>\r\n\r\n\r\n\r\n<p class=\"wp-block-paragraph\">\u5bf9\u4e8e\u6ee1\u8db3\u4e0a\u9762\u7684\u6761\u4ef6(\u7ebf\u6027\u968f\u673a\u5fae\u5206\u7cfb\u7edf\uff0c\u8fc7\u7a0b\u548c\u6d4b\u91cf\u90fd\u662f\u9ad8\u65af\u767d\u566a\u58f0)\uff0c\u5361\u5c14\u66fc\u6ee4\u6ce2\u5668\u662f\u6700\u4f18\u7684\u4fe1\u606f\u5904\u7406\u5668\u3002\u4e0b\u9762\u6211\u4eec\u6765\u7528\u4ed6\u4eec\u7ed3\u5408\u4ed6\u4eec\u7684covariances \u6765\u4f30\u7b97\u7cfb\u7edf\u7684\u6700\u4f18\u5316\u8f93\u51fa\uff08\u7c7b\u4f3c\u4e0a\u4e00\u8282\u90a3\u4e2a\u6e29\u5ea6\u7684\u4f8b\u5b50\uff09\u3002<\/p>\r\n\r\n\r\n\r\n<p class=\"wp-block-paragraph\">\u9996\u5148\u6211\u4eec\u8981\u5229\u7528\u7cfb\u7edf\u7684\u8fc7\u7a0b\u6a21\u578b\uff0c\u6765\u9884\u6d4b\u4e0b\u4e00\u72b6\u6001\u7684\u7cfb\u7edf\u3002\u5047\u8bbe\u73b0\u5728\u7684\u7cfb\u7edf\u72b6\u6001\u662fk\uff0c\u6839\u636e\u7cfb\u7edf\u7684\u6a21\u578b\uff0c\u53ef\u4ee5\u57fa\u4e8e\u7cfb\u7edf\u7684\u4e0a\u4e00\u72b6\u6001\u800c\u9884\u6d4b\u51fa\u73b0\u5728\u72b6\u6001\uff1a<br \/>X(k|k-1)=A X(k-1|k-1)+B U(k) \u2026\u2026\u2026.. (1)<br \/>\u5f0f(1)\u4e2d\uff0cX(k|k-1)\u662f\u5229\u7528\u4e0a\u4e00\u72b6\u6001\u9884\u6d4b\u7684\u7ed3\u679c\uff0cX(k-1|k-1)\u662f\u4e0a\u4e00\u72b6\u6001\u6700\u4f18\u7684\u7ed3\u679c\uff0cU(k)\u4e3a\u73b0\u5728\u72b6\u6001\u7684\u63a7\u5236\u91cf\uff0c\u5982\u679c\u6ca1\u6709\u63a7\u5236\u91cf\uff0c\u5b83\u53ef\u4ee5\u4e3a0\u3002<\/p>\r\n\r\n\r\n\r\n<p class=\"wp-block-paragraph\">\u5230\u73b0\u5728\u4e3a\u6b62\uff0c\u6211\u4eec\u7684\u7cfb\u7edf\u7ed3\u679c\u5df2\u7ecf\u66f4\u65b0\u4e86\uff0c\u53ef\u662f\uff0c\u5bf9\u5e94\u4e8eX(k|k-1)\u7684covariance\u8fd8\u6ca1\u66f4\u65b0\u3002\u6211\u4eec\u7528P\u8868\u793acovariance\uff1a<br \/>P(k|k-1)=A P(k-1|k-1) A\u2019+Q \u2026\u2026\u2026 (2)<br \/>\u5f0f(2)\u4e2d\uff0cP(k|k-1)\u662fX(k|k-1)\u5bf9\u5e94\u7684covariance\uff0cP(k-1|k-1)\u662fX(k-1|k-1)\u5bf9\u5e94\u7684covariance\uff0cA\u2019\u8868\u793aA\u7684\u8f6c\u7f6e\u77e9\u9635\uff0cQ\u662f\u7cfb\u7edf\u8fc7\u7a0b\u7684covariance\u3002\u5f0f\u5b501\uff0c2\u5c31\u662f\u5361\u5c14\u66fc\u6ee4\u6ce2\u56685\u4e2a\u516c\u5f0f\u5f53\u4e2d\u7684\u524d\u4e24\u4e2a\uff0c\u4e5f\u5c31\u662f\u5bf9\u7cfb\u7edf\u7684\u9884\u6d4b\u3002<\/p>\r\n\r\n\r\n\r\n<p class=\"wp-block-paragraph\">\u73b0\u5728\u6211\u4eec\u6709\u4e86\u73b0\u5728\u72b6\u6001\u7684\u9884\u6d4b\u7ed3\u679c\uff0c\u7136\u540e\u6211\u4eec\u518d\u6536\u96c6\u73b0\u5728\u72b6\u6001\u7684\u6d4b\u91cf\u503c\u3002\u7ed3\u5408\u9884\u6d4b\u503c\u548c\u6d4b\u91cf\u503c\uff0c\u6211\u4eec\u53ef\u4ee5\u5f97\u5230\u73b0\u5728\u72b6\u6001(k)\u7684\u6700\u4f18\u5316\u4f30\u7b97\u503cX(k|k)\uff1a<br \/>X(k|k)= X(k|k-1)+Kg(k) (Z(k)-H X(k|k-1)) \u2026\u2026\u2026 (3)<br \/>\u5176\u4e2dKg\u4e3a\u5361\u5c14\u66fc\u589e\u76ca(Kalman Gain)\uff1a<br \/>Kg(k)= P(k|k-1) H\u2019 \/ (H P(k|k-1) H\u2019 + R) \u2026\u2026\u2026 (4)<\/p>\r\n\r\n\r\n\r\n<p class=\"wp-block-paragraph\">\u5230\u73b0\u5728\u4e3a\u6b62\uff0c\u6211\u4eec\u5df2\u7ecf\u5f97\u5230\u4e86k\u72b6\u6001\u4e0b\u6700\u4f18\u7684\u4f30\u7b97\u503cX(k|k)\u3002\u4f46\u662f\u4e3a\u4e86\u8981\u53e6\u5361\u5c14\u66fc\u6ee4\u6ce2\u5668\u4e0d\u65ad\u7684\u8fd0\u884c\u4e0b\u53bb\u76f4\u5230\u7cfb\u7edf\u8fc7\u7a0b\u7ed3\u675f\uff0c\u6211\u4eec\u8fd8\u8981\u66f4\u65b0k\u72b6\u6001\u4e0bX(k|k)\u7684covariance\uff1a<br \/>P(k|k)=\uff08I-Kg(k) H\uff09P(k|k-1) \u2026\u2026\u2026 (5)<br \/>\u5176\u4e2dI \u4e3a1\u7684\u77e9\u9635\uff0c\u5bf9\u4e8e\u5355\u6a21\u578b\u5355\u6d4b\u91cf\uff0cI=1\u3002\u5f53\u7cfb\u7edf\u8fdb\u5165k+1\u72b6\u6001\u65f6\uff0cP(k|k)\u5c31\u662f\u5f0f\u5b50(2)\u7684P(k-1|k-1)\u3002\u8fd9\u6837\uff0c\u7b97\u6cd5\u5c31\u53ef\u4ee5\u81ea\u56de\u5f52\u7684\u8fd0\u7b97\u4e0b\u53bb\u3002<\/p>\r\n\r\n\r\n\r\n<p class=\"wp-block-paragraph\">\u5361\u5c14\u66fc\u6ee4\u6ce2\u5668\u7684\u539f\u7406\u57fa\u672c\u63cf\u8ff0\u4e86\uff0c\u5f0f\u5b501\uff0c2\uff0c3\uff0c4\u548c5\u5c31\u662f\u4ed6\u76845 \u4e2a\u57fa\u672c\u516c\u5f0f\u3002\u6839\u636e\u8fd95\u4e2a\u516c\u5f0f\uff0c\u53ef\u4ee5\u5f88\u5bb9\u6613\u7684\u5b9e\u73b0\u8ba1\u7b97\u673a\u7684\u7a0b\u5e8f\u3002<\/p>\r\n\r\n\r\n\r\n<p class=\"wp-block-paragraph\">\u4e0b\u9762\uff0c\u6211\u4f1a\u7528\u7a0b\u5e8f\u4e3e\u4e00\u4e2a\u5b9e\u9645\u8fd0\u884c\u7684\u4f8b\u5b50\u3002\u3002\u3002<\/p>\r\n\r\n\r\n\r\n<p class=\"wp-block-paragraph\">3\uff0e \u7b80\u5355\u4f8b\u5b50<\/p>\r\n\r\n\r\n\r\n<p class=\"wp-block-paragraph\">\u8fd9\u91cc\u6211\u4eec\u7ed3\u5408\u7b2c\u4e8c\u7b2c\u4e09\u8282\uff0c\u4e3e\u4e00\u4e2a\u975e\u5e38\u7b80\u5355\u7684\u4f8b\u5b50\u6765\u8bf4\u660e\u5361\u5c14\u66fc\u6ee4\u6ce2\u5668\u7684\u5de5\u4f5c\u8fc7\u7a0b\u3002\u6240\u4e3e\u7684\u4f8b\u5b50\u662f\u8fdb\u4e00\u6b65\u63cf\u8ff0\u7b2c\u4e8c\u8282\u7684\u4f8b\u5b50\uff0c\u800c\u4e14\u8fd8\u4f1a\u914d\u4ee5\u7a0b\u5e8f\u6a21\u62df\u7ed3\u679c\u3002<\/p>\r\n\r\n\r\n\r\n<p class=\"wp-block-paragraph\">\u6839\u636e\u7b2c\u4e8c\u8282\u7684\u63cf\u8ff0\uff0c\u628a\u623f\u95f4\u770b\u6210\u4e00\u4e2a\u7cfb\u7edf\uff0c\u7136\u540e\u5bf9\u8fd9\u4e2a\u7cfb\u7edf\u5efa\u6a21\u3002\u5f53\u7136\uff0c\u6211\u4eec\u89c1\u7684\u6a21\u578b\u4e0d\u9700\u8981\u975e\u5e38\u5730\u7cbe\u786e\u3002\u6211\u4eec\u6240\u77e5\u9053\u7684\u8fd9\u4e2a\u623f\u95f4\u7684\u6e29\u5ea6\u662f\u8ddf\u524d\u4e00\u65f6\u523b\u7684\u6e29\u5ea6\u76f8\u540c\u7684\uff0c\u6240\u4ee5A=1\u3002\u6ca1\u6709\u63a7\u5236\u91cf\uff0c\u6240\u4ee5U(k)=0\u3002\u56e0\u6b64\u5f97\u51fa\uff1a<br \/>X(k|k-1)=X(k-1|k-1) \u2026\u2026\u2026.. (6)<br \/>\u5f0f\u5b50\uff082\uff09\u53ef\u4ee5\u6539\u6210\uff1a<br \/>P(k|k-1)=P(k-1|k-1) +Q \u2026\u2026\u2026 (7)<\/p>\r\n\r\n\r\n\r\n<p class=\"wp-block-paragraph\">\u56e0\u4e3a\u6d4b\u91cf\u7684\u503c\u662f\u6e29\u5ea6\u8ba1\u7684\uff0c\u8ddf\u6e29\u5ea6\u76f4\u63a5\u5bf9\u5e94\uff0c\u6240\u4ee5H=1\u3002\u5f0f\u5b503\uff0c4\uff0c5\u53ef\u4ee5\u6539\u6210\u4ee5\u4e0b\uff1a<br \/>X(k|k)= X(k|k-1)+Kg(k) (Z(k)-X(k|k-1)) \u2026\u2026\u2026 (8)<br \/>Kg(k)= P(k|k-1) \/ (P(k|k-1) + R) \u2026\u2026\u2026 (9)<br \/>P(k|k)=\uff081-Kg(k)\uff09P(k|k-1) \u2026\u2026\u2026 (10)<\/p>\r\n\r\n\r\n\r\n<p class=\"wp-block-paragraph\">\u73b0\u5728\u6211\u4eec\u6a21\u62df\u4e00\u7ec4\u6d4b\u91cf\u503c\u4f5c\u4e3a\u8f93\u5165\u3002\u5047\u8bbe\u623f\u95f4\u7684\u771f\u5b9e\u6e29\u5ea6\u4e3a25\u5ea6\uff0c\u6211\u6a21\u62df\u4e86200\u4e2a\u6d4b\u91cf\u503c\uff0c\u8fd9\u4e9b\u6d4b\u91cf\u503c\u7684\u5e73\u5747\u503c\u4e3a25\u5ea6\uff0c\u4f46\u662f\u52a0\u5165\u4e86\u6807\u51c6\u504f\u5dee\u4e3a\u51e0\u5ea6\u7684\u9ad8\u65af\u767d\u566a\u58f0\uff08\u5728\u56fe\u4e2d\u4e3a\u84dd\u7ebf\uff09\u3002<\/p>\r\n\r\n\r\n\r\n<p class=\"wp-block-paragraph\">\u4e3a\u4e86\u4ee4\u5361\u5c14\u66fc\u6ee4\u6ce2\u5668\u5f00\u59cb\u5de5\u4f5c\uff0c\u6211\u4eec\u9700\u8981\u544a\u8bc9\u5361\u5c14\u66fc\u4e24\u4e2a\u96f6\u65f6\u523b\u7684\u521d\u59cb\u503c\uff0c\u662fX(0|0)\u548cP(0|0)\u3002\u4ed6\u4eec\u7684\u503c\u4e0d\u7528\u592a\u5728\u610f\uff0c\u968f\u4fbf\u7ed9\u4e00\u4e2a\u5c31\u53ef\u4ee5\u4e86\uff0c\u56e0\u4e3a\u968f\u7740\u5361\u5c14\u66fc\u7684\u5de5\u4f5c\uff0cX\u4f1a\u9010\u6e10\u7684\u6536\u655b\u3002\u4f46\u662f\u5bf9\u4e8eP\uff0c\u4e00\u822c\u4e0d\u8981\u53d60\uff0c\u56e0\u4e3a\u8fd9\u6837\u53ef\u80fd\u4f1a\u4ee4\u5361\u5c14\u66fc\u5b8c\u5168\u76f8\u4fe1\u4f60\u7ed9\u5b9a\u7684X(0|0)\u662f\u7cfb\u7edf\u6700\u4f18\u7684\uff0c\u4ece\u800c\u4f7f\u7b97\u6cd5\u4e0d\u80fd\u6536\u655b\u3002\u6211\u9009\u4e86X(0|0)=1\u5ea6\uff0cP(0|0)=10\u3002<\/p>\r\n\r\n\r\n\r\n<p class=\"wp-block-paragraph\">\u8be5\u7cfb\u7edf\u7684\u771f\u5b9e\u6e29\u5ea6\u4e3a25\u5ea6\uff0c\u56fe\u4e2d\u7528\u9ed1\u7ebf\u8868\u793a\u3002\u56fe\u4e2d\u7ea2\u7ebf\u662f\u5361\u5c14\u66fc\u6ee4\u6ce2\u5668\u8f93\u51fa\u7684\u6700\u4f18\u5316\u7ed3\u679c\uff08\u8be5\u7ed3\u679c\u5728\u7b97\u6cd5\u4e2d\u8bbe\u7f6e\u4e86Q=1e-6\uff0cR=1e-1\uff09\u3002<\/p>\r\n\r\n\r\n\r\n<ul class=\"wp-block-list\">\r\n<li>clear<\/li>\r\n<li>N=200;<\/li>\r\n<li>w(1)=0;<\/li>\r\n<li>w=randn(1,N)<\/li>\r\n<li>x(1)=0;<\/li>\r\n<li>a=1;<\/li>\r\n<li>for k=2:N;<\/li>\r\n<li>x(k)=a*x(k-1)+w(k-1);<\/li>\r\n<li>end<\/li>\r\n<li>\u00a0<\/li>\r\n<li>\u00a0<\/li>\r\n<li>V=randn(1,N);<\/li>\r\n<li>q1=std(V);<\/li>\r\n<li>Rvv=q1.^2;<\/li>\r\n<li>q2=std(x);<\/li>\r\n<li>Rxx=q2.^2;<\/li>\r\n<li>q3=std(w);<\/li>\r\n<li>Rww=q3.^2;<\/li>\r\n<li>c=0.2;<\/li>\r\n<li>Y=c*x+V;<\/li>\r\n<li>\u00a0<\/li>\r\n<li>p(1)=0;<\/li>\r\n<li>s(1)=0;<\/li>\r\n<li>for t=2:N;<\/li>\r\n<li>p1(t)=a.^2*p(t-1)+Rww;<\/li>\r\n<li>b(t)=c*p1(t)\/(c.^2*p1(t)+Rvv);<\/li>\r\n<li>s(t)=a*s(t-1)+b(t)*(Y(t)-a*c*s(t-1));<\/li>\r\n<li>p(t)=p1(t)-c*b(t)*p1(t);<\/li>\r\n<li>end<\/li>\r\n<li>\u00a0<\/li>\r\n<li>t=1:N;<\/li>\r\n<li>plot(t,s,&#8217;r&#8217;,t,Y,&#8217;g&#8217;,t,x,&#8217;b&#8217;);<\/li>\r\n<li>\u00a0<\/li>\r\n<\/ul>\r\n","protected":false},"excerpt":{"rendered":"<p>1. \u5361\u5c14\u66fc\u6ee4\u6ce2\u5668\u7684\u4ecb\u7ecd \u4e3a\u4e86\u53ef\u4ee5\u66f4\u52a0\u5bb9\u6613\u7684\u7406\u89e3\u5361\u5c14\u66fc\u6ee4\u6ce2\u5668\uff0c\u8fd9\u91cc\u4f1a\u5e94\u7528\u5f62\u8c61\u7684\u63cf\u8ff0\u65b9\u6cd5\u6765\u8bb2\u89e3\uff0c\u800c\u4e0d\u662f\u50cf\u5927\u591a\u6570\u53c2 &hellip; <\/p>\n<p class=\"link-more\"><a href=\"https:\/\/wp.ytdx.cc\/index.php\/2022\/10\/29\/%e5%8d%a1%e5%b0%94%e6%9b%bc%e6%bb%a4%e6%b3%a2%e7%ae%97%e6%b3%95\/\" class=\"more-link\">\u7ee7\u7eed\u9605\u8bfb<span class=\"screen-reader-text\">\u201c\u5361\u5c14\u66fc\u6ee4\u6ce2\u7b97\u6cd5\u201d<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[4],"tags":[],"class_list":["post-150","post","type-post","status-publish","format-standard","hentry","category-date","entry"],"jetpack_featured_media_url":"","jetpack-related-posts":[],"jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/wp.ytdx.cc\/index.php\/wp-json\/wp\/v2\/posts\/150","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/wp.ytdx.cc\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/wp.ytdx.cc\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/wp.ytdx.cc\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/wp.ytdx.cc\/index.php\/wp-json\/wp\/v2\/comments?post=150"}],"version-history":[{"count":2,"href":"https:\/\/wp.ytdx.cc\/index.php\/wp-json\/wp\/v2\/posts\/150\/revisions"}],"predecessor-version":[{"id":152,"href":"https:\/\/wp.ytdx.cc\/index.php\/wp-json\/wp\/v2\/posts\/150\/revisions\/152"}],"wp:attachment":[{"href":"https:\/\/wp.ytdx.cc\/index.php\/wp-json\/wp\/v2\/media?parent=150"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wp.ytdx.cc\/index.php\/wp-json\/wp\/v2\/categories?post=150"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wp.ytdx.cc\/index.php\/wp-json\/wp\/v2\/tags?post=150"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}