{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,17]],"date-time":"2025-12-17T13:07:40Z","timestamp":1765976860897,"version":"build-2065373602"},"reference-count":28,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2025,6,14]],"date-time":"2025-06-14T00:00:00Z","timestamp":1749859200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Key R&amp;D Program Intelligent Robot Key Special Project \u201cRobot Joint Drive Control Integrated Chip\u201d","award":["2023YFB4704000","62125307","U22A2046"],"award-info":[{"award-number":["2023YFB4704000","62125307","U22A2046"]}]},{"name":"National Natural Science Foundation of China","award":["2023YFB4704000","62125307","U22A2046"],"award-info":[{"award-number":["2023YFB4704000","62125307","U22A2046"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>This paper investigates a multi-sensor system for the state estimation of a maneuvering target, wherein the process noise of the target dynamics and the measurement noise of the sensor network are mutually correlated, and the measurement noises across different sensors are also cross-correlated. Under such conditions, we propose a globally optimal sequential least squares fusion estimation algorithm within the framework of linear minimum mean square error (LMMSE) estimation. This method is specifically designed to preserve structural symmetry and to accommodate the time-ordered arrival of sensor observations transmitted over a network. Rigorous theoretical analysis establishes the performance equivalence between the proposed sequential fusion estimator and the centralized Kalman filter. Numerical simulations further demonstrate the algorithm\u2019s superior estimation accuracy and stability under symmetry constraints, particularly when the noise statistics exhibit spatial or temporal symmetry.<\/jats:p>","DOI":"10.3390\/sym17060948","type":"journal-article","created":{"date-parts":[[2025,6,17]],"date-time":"2025-06-17T04:20:23Z","timestamp":1750134023000},"page":"948","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Sequential Fusion Least Squares Method for State Estimation of Multi-Sensor Linear Systems Under Noise Cross-Correlation"],"prefix":"10.3390","volume":"17","author":[{"given":"Xu","family":"Liang","sequence":"first","affiliation":[{"name":"School of Automation, Guangdong University of Petrochemical Technology, Maoming 525000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Chenglin","family":"Wen","sequence":"additional","affiliation":[{"name":"School of Automation, Guangdong University of Petrochemical Technology, Maoming 525000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2025,6,14]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"3885","DOI":"10.1109\/TIM.2009.2021212","article-title":"Particle filtering for state estimation in nonlinear industrial systems","volume":"58","author":"Rigatos","year":"2009","journal-title":"IEEE Trans. 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