{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,1]],"date-time":"2026-05-01T02:57:20Z","timestamp":1777604240296,"version":"3.51.4"},"reference-count":39,"publisher":"MDPI AG","issue":"16","license":[{"start":{"date-parts":[[2022,8,10]],"date-time":"2022-08-10T00:00:00Z","timestamp":1660089600000},"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":["61973280"],"award-info":[{"award-number":["61973280"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["62003316"],"award-info":[{"award-number":["62003316"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["202003D111007"],"award-info":[{"award-number":["202003D111007"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Shanxi Province Key R&amp;D Program","award":["61973280"],"award-info":[{"award-number":["61973280"]}]},{"name":"Shanxi Province Key R&amp;D Program","award":["62003316"],"award-info":[{"award-number":["62003316"]}]},{"name":"Shanxi Province Key R&amp;D Program","award":["202003D111007"],"award-info":[{"award-number":["202003D111007"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>The accurate noise parameter is essential for the Kalman filter to obtain optimal estimates. However, problems such as variations in the noise environment and measurement anomalies can cause degradation of estimation accuracy or even divergence. The adaptive Kalman filter can simultaneously estimate state and noise parameters, while its performance will also be degraded in complex noise. To address the problem of estimation accuracy degradation and result divergence of the integrated navigation system in a complex time-varying noise environment, an improved multiple-model adaptive estimation (MMAE) that combines the Sage\u2013Husa adaptive unscented Kalman filter with the MMAE is proposed in this paper. The forgetting factor is included as an unknown parameter of MMAE so that the algorithm can adjust the value of the forgetting factor according to different system states. In addition, we improve the hypothesis testing algorithm of classical MMAE to deal with the competition problem of undesirable models that severely impacts the performance of variable-parameter MMAE and enhance the algorithm\u2019s parameter identification capability. Simulation results show that this method enhances the system\u2019s robustness to noises of different statistical properties and improves the estimation accuracy of the filter in time-varying noise environments.<\/jats:p>","DOI":"10.3390\/s22165976","type":"journal-article","created":{"date-parts":[[2022,8,10]],"date-time":"2022-08-10T09:42:56Z","timestamp":1660124576000},"page":"5976","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":10,"title":["Improved Multiple-Model Adaptive Estimation Method for Integrated Navigation with Time-Varying Noise"],"prefix":"10.3390","volume":"22","author":[{"given":"Jinhao","family":"Song","sequence":"first","affiliation":[{"name":"National Key Laboratory for Electronic Measurement Technology, North University of China, Taiyuan 030051, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jie","family":"Li","sequence":"additional","affiliation":[{"name":"National Key Laboratory for Electronic Measurement Technology, North University of China, Taiyuan 030051, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xiaokai","family":"Wei","sequence":"additional","affiliation":[{"name":"National Key Laboratory for Electronic Measurement Technology, North University of China, Taiyuan 030051, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Chenjun","family":"Hu","sequence":"additional","affiliation":[{"name":"National Key Laboratory for Electronic Measurement Technology, North University of China, Taiyuan 030051, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zeyu","family":"Zhang","sequence":"additional","affiliation":[{"name":"Aerospace System Engineering Shanghai, Shanghai 201108, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Lening","family":"Zhao","sequence":"additional","affiliation":[{"name":"National Key Laboratory for Electronic Measurement Technology, North University of China, Taiyuan 030051, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yubing","family":"Jiao","sequence":"additional","affiliation":[{"name":"National Key Laboratory for Electronic Measurement Technology, North University of China, Taiyuan 030051, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,8,10]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1151","DOI":"10.1007\/s00006-012-0326-8","article-title":"Strapdown Inertial Navigation System Algorithms Based on Geometric Algebra","volume":"22","author":"Wu","year":"2012","journal-title":"Adv. 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