{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T02:30:28Z","timestamp":1760236228259,"version":"build-2065373602"},"reference-count":23,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2021,11,10]],"date-time":"2021-11-10T00:00:00Z","timestamp":1636502400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Nonlinear filtering is of great significance in industries. In this work, we develop a new linear regression Kalman filter for discrete nonlinear filtering problems. Under the framework of linear regression Kalman filter, the key step is minimizing the Kullback\u2013Leibler divergence between standard normal distribution and its Dirac mixture approximation formed by symmetric samples so that we can obtain a set of samples which can capture the information of reference density. The samples representing the conditional densities evolve in a deterministic way, and therefore we need less samples compared with particle filter, as there is less variance in our method. The numerical results show that the new algorithm is more efficient compared with the widely used extended Kalman filter, unscented Kalman filter and particle filter.<\/jats:p>","DOI":"10.3390\/sym13112139","type":"journal-article","created":{"date-parts":[[2021,11,11]],"date-time":"2021-11-11T23:07:21Z","timestamp":1636672041000},"page":"2139","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["A New Linear Regression Kalman Filter with Symmetric Samples"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3844-7177","authenticated-orcid":false,"given":"Xiuqiong","family":"Chen","sequence":"first","affiliation":[{"name":"School of Mathematics, Renmin University of China, Beijing 100872, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7784-6432","authenticated-orcid":false,"given":"Jiayi","family":"Kang","sequence":"additional","affiliation":[{"name":"Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China"}]},{"given":"Mina","family":"Teicher","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Gonda Brain Research Center, Bar-Ilan University, Ramat-Gan 52900, Israel"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7634-7981","authenticated-orcid":false,"given":"Stephen","family":"Yau","sequence":"additional","affiliation":[{"name":"Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China"},{"name":"Yanqi Lake Beijing Institute of Mathematical Sciences and Applications (BIMSA), Huairou, Beijing 101400, China"}]}],"member":"1968","published-online":{"date-parts":[[2021,11,10]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"35","DOI":"10.1115\/1.3662552","article-title":"A new approach to linear filtering and prediction problem","volume":"82","author":"Kalman","year":"1960","journal-title":"ASME Trans. 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