{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,16]],"date-time":"2026-03-16T21:40:56Z","timestamp":1773697256329,"version":"3.50.1"},"reference-count":37,"publisher":"MDPI AG","issue":"24","license":[{"start":{"date-parts":[[2024,12,17]],"date-time":"2024-12-17T00:00:00Z","timestamp":1734393600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"PhD Research Startup Foundation of Hubei University of Science and Technology","award":["BK201801"],"award-info":[{"award-number":["BK201801"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>Multi-source heterogeneous information fusion based on the Global Navigation Satellite System (GNSS)\/Inertial Navigation System (INS)\/odometer is an important technical means to solve the problem of navigation and positioning in complex environments. The measurement noise of the GNSS\/INS\/odometer integrated navigation system is complex and non-stationary; it approximates a Gaussian distribution in an open-sky environment, and it has heavy-tailed properties in the GNSS challenging environment. This work models the measurement noise and one-step prediction as the Gaussian and Student\u2019s t mixture distribution to adjust to different scenarios. The mixture distribution is formulated as the hierarchical Gaussian form by introducing Bernoulli random variables, and the corresponding hierarchical Gaussian state-space model is constructed. Then, the mixing probability of Gaussian and Student\u2019s t distributions could adjust adaptively according to the real-time kinematic solution state. Based on the novel distribution, a robust variational Bayesian Kalman filter is proposed. Finally, two vehicle test cases conducted in GNSS-friendly and challenging environments demonstrate that the proposed robust Kalman filter with the Gaussian\u2013Student\u2019s t mixture distribution can better model heavy-tailed non-Gaussian noise. In challenging environments, the proposed algorithm has position root mean square (RMS) errors of 0.80 m, 0.62 m, and 0.65 m in the north, east, and down directions, respectively. With the assistance of inertial sensors, the positioning gap caused by GNSS outages has been compensated. During seven periods of 60 s simulated GNSS data outages, the RMS position errors in the north, east, and down directions were 0.75 m, 0.30 m, and 0.20 m, respectively.<\/jats:p>","DOI":"10.3390\/rs16244716","type":"journal-article","created":{"date-parts":[[2024,12,17]],"date-time":"2024-12-17T10:54:02Z","timestamp":1734432842000},"page":"4716","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Gaussian\u2013Student\u2019s t Mixture Distribution-Based Robust Kalman Filter for Global Navigation Satellite System\/Inertial Navigation System\/Odometer Data Fusion"],"prefix":"10.3390","volume":"16","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8314-8419","authenticated-orcid":false,"given":"Jiaji","family":"Wu","sequence":"first","affiliation":[{"name":"GNSS Research Center, Wuhan University, Wuhan 430079, China"},{"name":"Electronic Information School, Wuhan University, Wuhan 430079, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0122-5514","authenticated-orcid":false,"given":"Jinguang","family":"Jiang","sequence":"additional","affiliation":[{"name":"GNSS Research Center, Wuhan University, Wuhan 430079, China"},{"name":"Electronic Information School, Wuhan University, Wuhan 430079, China"},{"name":"Hubei Luojia Laboratory, Wuhan University, Wuhan 430079, China"},{"name":"School of Microelectronics, Wuhan University, Wuhan 430079, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7345-5506","authenticated-orcid":false,"given":"Yanan","family":"Tang","sequence":"additional","affiliation":[{"name":"GNSS Research Center, Wuhan University, Wuhan 430079, China"},{"name":"Electronic Information School, Wuhan University, Wuhan 430079, China"}]},{"given":"Jianghua","family":"Liu","sequence":"additional","affiliation":[{"name":"School of Electronics and Information Engineering, Hubei University of Science and Technology, Xianning 437099, China"}]}],"member":"1968","published-online":{"date-parts":[[2024,12,17]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"21","DOI":"10.1186\/s43020-024-00141-w","article-title":"Multiple integer candidates ambiguity resolution: A unification ambiguity resolution algorithm","volume":"5","author":"Gu","year":"2024","journal-title":"Satell. 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