{"id":8738,"date":"1960-12-20T10:00:35","date_gmt":"1960-12-20T01:00:35","guid":{"rendered":"http:\/\/jsapt.net\/ja\/?p=8738"},"modified":"2017-12-08T14:08:26","modified_gmt":"2017-12-08T05:08:26","slug":"16601220","status":"publish","type":"post","link":"https:\/\/jsapt.net\/ja\/post\/16601220","title":{"rendered":"A New Approach to Linear Filtering and Prediction Problems"},"content":{"rendered":"<p><a href=\"https:\/\/jsapt.net\/ja\/?s=R.E.Kalman\">R.E.Kalman<\/a><br \/>\n[ Link to ASME(UNC) ] <\/p>\n<p style=\"padding: 0 20px;\">Overview - The classical filtering and prediction problem is re-examined using the Bode-Shannon representation of random processes and the \u201cstate transition\u201d method of analysis of dynamic systems. New results are:<br \/>\n(1) The formulation and methods of solution of the problem apply without modification to stationary and nonstationary statistics and to growing-memory and infinitememory filters.<br \/>\n(2) A nonlinear difference (or differential) equation is derived for the covariance matrix of the optimal estimation error. From the solution of this equation the coefficients of the difference (or differential) equation of the optimal linear filter are obtained without further calculations.<br \/>\n(3) The filtering problem is shown to be the dual of the noise-free regulator problem. The new method developed here is applied to two well-known problems, confirming and extending earlier results.<br \/>\nThe discussion is largely self-contained and proceeds from first principles; basic concepts of the theory of random processes are reviewed in the Appendix.<\/p>\n<p><a href=\"https:\/\/www.cs.unc.edu\/~welch\/kalman\/media\/pdf\/Kalman1960.pdf\"><\/a><\/p>\n\n<div class=\"wp-block-button\">\n<a  data-e-Disable-Page-Transition=\"true\" class=\"dlm-download-link dlm-download-button wp-block-button__link wp-element-button\" title=\"\u30d0\u30fc\u30b8\u30e7\u30f3 \uff11\" href=\"https:\/\/jsapt.net\/ja\/download\/8736\/?tmstv=1791164226\" rel=\"nofollow\" id=\"download-link-8736\" data-redirect=\"false\" >\n\t&ldquo;A New Approach to Linear Filtering and Prediction Problems&rdquo; \u3092\u30c0\u30a6\u30f3\u30ed\u30fc\u30c9\t<span class=\"dlm-button-meta\">Kalman1960.pdf\t\t&ndash; 742 \u56de\u306e\u30c0\u30a6\u30f3\u30ed\u30fc\u30c9\t\t&ndash; 167.49 KB<\/span>\n<\/a>\n<\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>R.E.Kalman [ Link to ASME(UNC) ] Overview - The classical filtering and prediction problem is re-examined usin [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"sns_share_botton_hide":"","vkExUnit_sns_title":"","_vk_print_noindex":"","sitemap_hide":"","vkExUnit_EyeCatch_disable":"","_veu_custom_css":"","veu_display_promotion_alert":"","vkexunit_cta_each_option":"","footnotes":""},"categories":[2],"tags":[134,385],"class_list":["post-8738","post","type-post","status-publish","format-standard","hentry","category-algorism","tag-kalmanfilter","tag-optimal"],"veu_head_title_object":{"title":"","add_site_title":""},"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v28.1 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>A New Approach to Linear Filtering and Prediction Problems - \u6e2c\u4f4d\u6280\u8853\u632f\u8208\u4f1a<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/jsapt.net\/ja\/post\/16601220\" \/>\n<meta property=\"og:locale\" content=\"ja_JP\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"A New Approach to Linear Filtering and Prediction Problems - 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