{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,28]],"date-time":"2026-09-28T03:08:55Z","timestamp":1790564935174,"version":"4.1.0"},"reference-count":0,"publisher":"ASME International","issue":"1","content-domain":{"domain":["asmedigitalcollection.asme.org"],"crossmark-restriction":true},"short-container-title":[],"published-print":{"date-parts":[[1960,3,1]]},"abstract":"<jats:p>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: (1) The formulation and methods of solution of the problem apply without modification to stationary and nonstationary statistics and to growing-memory and infinite-memory filters. (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 co-efficients of the difference (or differential) equation of the optimal linear filter are obtained without further calculations. (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. The discussion is largely self-contained and proceeds from first principles; basic concepts of the theory of random processes are reviewed in the Appendix.<\/jats:p>","DOI":"10.1115\/1.3662552","type":"journal-article","created":{"date-parts":[[2011,11,8]],"date-time":"2011-11-08T16:15:52Z","timestamp":1320768952000},"page":"35-45","update-policy":"https:\/\/doi.org\/10.1115\/crossmarkpolicy-asme","source":"Crossref","is-referenced-by-count":23542,"title":["A New Approach to Linear Filtering and Prediction Problems"],"prefix":"10.1115","volume":"82","author":[{"given":"R. E.","family":"Kalman","sequence":"first","affiliation":[{"name":"Research Institute for Advanced Study, Baltimore, Md."}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"33","published-online":{"date-parts":[[1960,3,1]]},"container-title":["Journal of Basic Engineering"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/asmedigitalcollection.asme.org\/fluidsengineering\/article-pdf\/82\/1\/35\/5518977\/35_1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"http:\/\/asmedigitalcollection.asme.org\/fluidsengineering\/article-pdf\/82\/1\/35\/5518977\/35_1.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,11,7]],"date-time":"2019-11-07T09:49:48Z","timestamp":1573120188000},"score":1,"resource":{"primary":{"URL":"https:\/\/asmedigitalcollection.asme.org\/fluidsengineering\/article\/82\/1\/35\/397706\/A-New-Approach-to-Linear-Filtering-and-Prediction"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1960,3,1]]},"references-count":0,"journal-issue":{"issue":"1","published-print":{"date-parts":[[1960,3,1]]}},"URL":"https:\/\/doi.org\/10.1115\/1.3662552","relation":{},"ISSN":["0021-9223"],"issn-type":[{"value":"0021-9223","type":"print"}],"subject":[],"published":{"date-parts":[[1960,3,1]]}}}