{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,17]],"date-time":"2026-03-17T17:53:25Z","timestamp":1773770005592,"version":"3.50.1"},"reference-count":33,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2023,10,3]],"date-time":"2023-10-03T00:00:00Z","timestamp":1696291200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Natural Science Foundations of Shaanxi Province","award":["2021 JM-251"],"award-info":[{"award-number":["2021 JM-251"]}]},{"name":"Natural Science Foundations of Shaanxi Province","award":["2020JM-355"],"award-info":[{"award-number":["2020JM-355"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>To improve the reliability of strapdown inertial navigation system (SINS)\/Doppler radar\/odometer integrated navigation system, the federated Kalman filter with two-stage fault detection structure is designed, and a fault-tolerant SINS\/Doppler radar\/odometer integrated navigation method is proposed. Firstly, the pre-fault detection module sets before the local filter, and the residual chi-square test in the carrier coordinate system is selected to detect the abrupt faults of Doppler radar and odometer. Then, the secondary-fault detection module emplaces between the local filter and the main filter, and the sequential probability ratio test (SPRT) is selected to further detect the ramp faults that are difficult to detect by the residual chi-square test. To address the limitation of the SPRT in accurately determining the end time of faults, an improved SPRT is proposed. The improved SPRT reduces the influence of historical fault on the fault statistics by introducing forgetting factors to improve its sensitivity to the fault end. The simulation experiment indicates that the proposed method can quickly detect and isolate abrupt and ramp faults, and promptly restore normal operation of the integrated navigation system after the fault ends, effectively improving the fault tolerance and reliability of the integrated navigation system.<\/jats:p>","DOI":"10.3390\/e25101412","type":"journal-article","created":{"date-parts":[[2023,10,3]],"date-time":"2023-10-03T07:28:29Z","timestamp":1696318109000},"page":"1412","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Fault-Tolerant SINS\/Doppler Radar\/Odometer Integrated Navigation Method Based on Two-Stage Fault Detection Structure"],"prefix":"10.3390","volume":"25","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-6327-3394","authenticated-orcid":false,"given":"Bo","family":"Yang","sequence":"first","affiliation":[{"name":"Department of Control Engineering, Xi\u2019an Research Institute of High Technology, Xi\u2019an 710025, China"}]},{"given":"Feng","family":"Liu","sequence":"additional","affiliation":[{"name":"Department of Control Engineering, Xi\u2019an Research Institute of High Technology, Xi\u2019an 710025, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0044-4598","authenticated-orcid":false,"given":"Liang","family":"Xue","sequence":"additional","affiliation":[{"name":"Department of Control Engineering, Xi\u2019an Research Institute of High Technology, Xi\u2019an 710025, China"}]},{"given":"Bin","family":"Shan","sequence":"additional","affiliation":[{"name":"Department of Control Engineering, Xi\u2019an Research Institute of High Technology, Xi\u2019an 710025, China"}]}],"member":"1968","published-online":{"date-parts":[[2023,10,3]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"111117","DOI":"10.1016\/j.measurement.2022.111117","article-title":"Temperature drift compensation of fiber strapdown inertial navigation system based on GSA-SVR","volume":"195","author":"Zhao","year":"2018","journal-title":"Measurement"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"8974","DOI":"10.1109\/JSEN.2022.3155166","article-title":"Deep learning-enabled fusion to bridge GPS outages for INS\/GPS integrated navigation","volume":"22","author":"Liu","year":"2022","journal-title":"IEEE Sens. 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