{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,11]],"date-time":"2026-02-11T20:47:24Z","timestamp":1770842844874,"version":"3.50.1"},"reference-count":30,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2020,9,3]],"date-time":"2020-09-03T00:00:00Z","timestamp":1599091200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100012166","name":"National Key Research and Development Program of China","doi-asserted-by":"publisher","award":["2016YFB0501801"],"award-info":[{"award-number":["2016YFB0501801"]}],"id":[{"id":"10.13039\/501100012166","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>R\u00e9nyi entropy as a generalization of the Shannon entropy allows for different averaging of probabilities of a control parameter \u03b1. This paper gives a new perspective of the Kalman filter from the R\u00e9nyi entropy. Firstly, the R\u00e9nyi entropy is employed to measure the uncertainty of the multivariate Gaussian probability density function. Then, we calculate the temporal derivative of the R\u00e9nyi entropy of the Kalman filter\u2019s mean square error matrix, which will be minimized to obtain the Kalman filter\u2019s gain. Moreover, the continuous Kalman filter approaches a steady state when the temporal derivative of the R\u00e9nyi entropy is equal to zero, which means that the R\u00e9nyi entropy will keep stable. As the temporal derivative of the R\u00e9nyi entropy is independent of parameter \u03b1 and is the same as the temporal derivative of the Shannon entropy, the result is the same as for Shannon entropy. Finally, an example of an experiment of falling body tracking by radar using an unscented Kalman filter (UKF) in noisy conditions and a loosely coupled navigation experiment are performed to demonstrate the effectiveness of the conclusion.<\/jats:p>","DOI":"10.3390\/e22090982","type":"journal-article","created":{"date-parts":[[2020,9,3]],"date-time":"2020-09-03T08:40:26Z","timestamp":1599122426000},"page":"982","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["A Novel Perspective of the Kalman Filter from the R\u00e9nyi Entropy"],"prefix":"10.3390","volume":"22","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6840-4800","authenticated-orcid":false,"given":"Yarong","family":"Luo","sequence":"first","affiliation":[{"name":"Global Navigation Satellite System Research Center, Wuhan University, Wuhan 430079, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Chi","family":"Guo","sequence":"additional","affiliation":[{"name":"Global Navigation Satellite System Research Center, Wuhan University, Wuhan 430079, China"},{"name":"Artificial Intelligence Institute, Wuhan University, Wuhan 430079, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shengyong","family":"You","sequence":"additional","affiliation":[{"name":"Global Navigation Satellite System Research Center, Wuhan University, Wuhan 430079, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jingnan","family":"Liu","sequence":"additional","affiliation":[{"name":"Global Navigation Satellite System Research Center, Wuhan University, Wuhan 430079, China"},{"name":"Artificial Intelligence Institute, Wuhan University, Wuhan 430079, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2020,9,3]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"379","DOI":"10.1002\/j.1538-7305.1948.tb01338.x","article-title":"A mathematical theory of communication","volume":"27","author":"Shannon","year":"1948","journal-title":"Bell Syst. 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