{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,18]],"date-time":"2026-03-18T02:29:35Z","timestamp":1773800975826,"version":"3.50.1"},"reference-count":39,"publisher":"MDPI AG","issue":"21","license":[{"start":{"date-parts":[[2020,10,24]],"date-time":"2020-10-24T00:00:00Z","timestamp":1603497600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100012166","name":"National Key Research and Development Program of China","doi-asserted-by":"publisher","award":["2017YFC0821102"],"award-info":[{"award-number":["2017YFC0821102"]}],"id":[{"id":"10.13039\/501100012166","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100012166","name":"National Key Research and Development Program of China","doi-asserted-by":"publisher","award":["2016YFB0502004"],"award-info":[{"award-number":["2016YFB0502004"]}],"id":[{"id":"10.13039\/501100012166","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>Adaptive Kalman filters (AKF) have been widely applied to the inertial navigation system (INS)\/global navigation satellite system (GNSS) integrated navigation system. However, the traditional AKF methods suffer from the problems of filtering instability or covariance underestimation, especially when the GNSS measurement disturbances occur. In this paper, an enhanced redundant measurement-based AKF is developed to improve the filtering performance. The scheme is based on the mutual difference sequence derived from the redundant measurement of INS. By using the mutual difference sequence, the measurement noise covariance can be estimated without being affected by the inaccuracy estimates, hence avoiding the risk of filtering divergence. In addition, the kernel density estimation is used to estimate the GNSS measurement noise\u2019s probability density to detect whether the Gaussian properties of the measurement noise are maintained. When the noise statistics are far from Gaussian distribution, the difference sequence will be modeled as an autoregressive process using the Burg\u2019s method. The real variance of the difference sequence can then be updated relying on the autoregressive model in order to avoid the covariance underestimation. A field experiment was carried out to evaluate the performance of the proposed method. The test results demonstrate that the proposed method can effectively mitigate the GNSS measurement disturbances and improve the accuracy of the navigation solution.<\/jats:p>","DOI":"10.3390\/rs12213500","type":"journal-article","created":{"date-parts":[[2020,10,26]],"date-time":"2020-10-26T03:51:47Z","timestamp":1603684307000},"page":"3500","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":10,"title":["Enhanced Redundant Measurement-Based Kalman Filter for Measurement Noise Covariance Estimation in INS\/GNSS Integration"],"prefix":"10.3390","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7570-3948","authenticated-orcid":false,"given":"Baoshuang","family":"Ge","sequence":"first","affiliation":[{"name":"School of Automation Science and Electrical Engineering, Beihang University, Beijing 100191, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hai","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Automation Science and Electrical Engineering, Beihang University, Beijing 100191, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Wenxing","family":"Fu","sequence":"additional","affiliation":[{"name":"Science and Technology on Complex System Control and Intelligent Agent Cooperation Laboratory, Beijing 100074, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jianbing","family":"Yang","sequence":"additional","affiliation":[{"name":"School of Automation Science and Electrical Engineering, Beihang University, Beijing 100191, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2020,10,24]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.cja.2014.12.001","article-title":"Navigation sensors and systems in GNSS degraded and denied environments","volume":"28","author":"Schmidt","year":"2015","journal-title":"Chin. 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