{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T01:47:32Z","timestamp":1760233652725,"version":"build-2065373602"},"reference-count":25,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2021,2,5]],"date-time":"2021-02-05T00:00:00Z","timestamp":1612483200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Yong Jin","award":["61771006"],"award-info":[{"award-number":["61771006"]}]},{"name":"Zhentao Hu","award":["61976080"],"award-info":[{"award-number":["61976080"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Assuming that the measurement and process noise covariances are known, the probability hypothesis density (PHD) filter is effective in real-time multi-target tracking; however, noise covariance is often unknown and time-varying for an actual scene. To solve this problem, a strong tracking PHD filter based on Variational Bayes (VB) approximation is proposed in this paper. The measurement noise covariance is described in the linear system by the inverse Wishart (IW) distribution. Then, the fading factor in the strong tracking principle uses the optimal measurement noise covariance at the previous moment to control the state prediction covariance in real-time. The Gaussian IW (GIW) joint distribution adopts the VB approximation to jointly return the measurement noise covariance and the target state covariance. The simulation results show that, compared with the traditional Gaussian mixture PHD (GM-PHD) and the VB-adaptive PHD, the proposed algorithm has higher tracking accuracy and stronger robustness in a more reasonable calculation time.<\/jats:p>","DOI":"10.3390\/s21041126","type":"journal-article","created":{"date-parts":[[2021,2,7]],"date-time":"2021-02-07T14:04:13Z","timestamp":1612706653000},"page":"1126","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Strong Tracking PHD Filter Based on Variational Bayesian with Inaccurate Process and Measurement Noise Covariance"],"prefix":"10.3390","volume":"21","author":[{"given":"Zhentao","family":"Hu","sequence":"first","affiliation":[{"name":"School of Artificial Intelligence, Henan University, Kaifeng 475004, China"},{"name":"School of Computer and Information Engineering, Henan University, Kaifeng 475004, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Linlin","family":"Yang","sequence":"additional","affiliation":[{"name":"School of Computer and Information Engineering, Henan University, Kaifeng 475004, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9325-5966","authenticated-orcid":false,"given":"Yong","family":"Jin","sequence":"additional","affiliation":[{"name":"School of Artificial Intelligence, Henan University, Kaifeng 475004, China"},{"name":"School of Computer and Information Engineering, Henan University, Kaifeng 475004, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Han","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Computer and Information Engineering, Henan University, Kaifeng 475004, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shibo","family":"Yang","sequence":"additional","affiliation":[{"name":"School of Computer and Information Engineering, Henan University, Kaifeng 475004, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,2,5]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"63","DOI":"10.1109\/TII.2020.2979690","article-title":"An Indoor Localization Algorithm based on Modified Joint Probabilistic Data Association for Wireless Sensor Network","volume":"17","author":"Cheng","year":"2020","journal-title":"IEEE Trans. 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