{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,18]],"date-time":"2025-12-18T14:17:08Z","timestamp":1766067428137,"version":"build-2065373602"},"reference-count":18,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2021,10,16]],"date-time":"2021-10-16T00:00:00Z","timestamp":1634342400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61573113"],"award-info":[{"award-number":["61573113"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>In this paper, a new variational Bayesian-based Kalman filter (KF) is presented to solve the filtering problem for a linear system with unknown time-varying measurement loss probability (UTVMLP) and non-stationary heavy-tailed measurement noise (NSHTMN). Firstly, the NSHTMN was modelled as a Gaussian-Student\u2019s t-mixture distribution via employing a Bernoulli random variable (BM). Secondly, by utilizing another Bernoulli random variable (BL), the form of the likelihood function consisting of two mixture distributions was converted from a weight sum to an exponential product and a new hierarchical Gaussian state-space model was therefore established. Finally, the system state vector, BM, BL, the intermediate random variables, the mixing probability, and the UTVMLP were jointly inferred by employing the variational Bayesian technique. Simulation results revealed that in the scenario of NSHTMN, the proposed filter had a better performance than current algorithms and further improved the estimation accuracy of UTVMLP.<\/jats:p>","DOI":"10.3390\/e23101351","type":"journal-article","created":{"date-parts":[[2021,10,17]],"date-time":"2021-10-17T23:13:32Z","timestamp":1634512412000},"page":"1351","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["A New Variational Bayesian-Based Kalman Filter with Unknown Time-Varying Measurement Loss Probability and Non-Stationary Heavy-Tailed Measurement Noise"],"prefix":"10.3390","volume":"23","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7301-7725","authenticated-orcid":false,"given":"Chenghao","family":"Shan","sequence":"first","affiliation":[{"name":"Department of Intelligent Systems Science and Engineering, Harbin Engineering University, Harbin 150001, China"}]},{"given":"Weidong","family":"Zhou","sequence":"additional","affiliation":[{"name":"Department of Intelligent Systems Science and Engineering, Harbin Engineering University, Harbin 150001, China"}]},{"given":"Yefeng","family":"Yang","sequence":"additional","affiliation":[{"name":"Center for Control Theory and Guidance Technology, Harbin Institute of Technology, Harbin 150001, China"}]},{"given":"Hanyu","family":"Shan","sequence":"additional","affiliation":[{"name":"Department of Information and Communication Engineering, Harbin Engineering University, Harbin 150001, China"}]}],"member":"1968","published-online":{"date-parts":[[2021,10,16]]},"reference":[{"key":"ref_1","unstructured":"Mohinder, S.G., and Angus, P.A. 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