{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T03:58:21Z","timestamp":1760241501136,"version":"build-2065373602"},"reference-count":14,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2018,5,3]],"date-time":"2018-05-03T00:00:00Z","timestamp":1525305600000},"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":["61304241"],"award-info":[{"award-number":["61304241"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Science and Technology Committee Fund","award":["2101034"],"award-info":[{"award-number":["2101034"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>In this paper, a sequential multiplicative extended Kalman filter (SMEKF) is proposed for attitude estimation using vector observations. In the proposed SMEKF, each of the vector observations is processed sequentially to update the attitude, which can make the measurement model linearization more accurate for the next vector observation. This is the main difference to Murrell\u2019s variation of the MEKF, which does not update the attitude estimate during the sequential procedure. Meanwhile, the covariance is updated after all the vector observations have been processed, which is used to account for the special characteristics of the reset operation necessary for the attitude update. This is the main difference to the traditional sequential EKF, which updates the state covariance at each step of the sequential procedure. The numerical simulation study demonstrates that the proposed SMEKF has more consistent and accurate performance in a wide range of initial estimate errors compared to the MEKF and its traditional sequential forms.<\/jats:p>","DOI":"10.3390\/s18051414","type":"journal-article","created":{"date-parts":[[2018,5,4]],"date-time":"2018-05-04T03:08:21Z","timestamp":1525403301000},"page":"1414","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":13,"title":["A Sequential Multiplicative Extended Kalman Filter for Attitude Estimation Using Vector Observations"],"prefix":"10.3390","volume":"18","author":[{"given":"Fangjun","family":"Qin","sequence":"first","affiliation":[{"name":"Department of Navigation Engineering, Naval University of Engineering, Wuhan 430000, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6705-3401","authenticated-orcid":false,"given":"Lubin","family":"Chang","sequence":"additional","affiliation":[{"name":"Department of Navigation Engineering, Naval University of Engineering, Wuhan 430000, China"}]},{"given":"Sai","family":"Jiang","sequence":"additional","affiliation":[{"name":"Office of Research and Development, Naval University of Engineering, Wuhan 430000, China"}]},{"given":"Feng","family":"Zha","sequence":"additional","affiliation":[{"name":"Department of Navigation Engineering, Naval University of Engineering, Wuhan 430000, China"}]}],"member":"1968","published-online":{"date-parts":[[2018,5,3]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Crassidis, J.L., and Junkins, J.L. 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Guid. Control Dyn."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"192","DOI":"10.1109\/TAES.1982.309226","article-title":"Nonlinear Estimation with Radar Observations","volume":"18","author":"Miller","year":"1982","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"1337","DOI":"10.1109\/7.722718","article-title":"Design of a Practical Tracking Algorithm with Radar Measurements","volume":"34","author":"Park","year":"1998","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"727","DOI":"10.1109\/7.937485","article-title":"Improved Kalman Filter Design for Three-Dimensional Radar Tracking","volume":"37","author":"Park","year":"2001","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"2053","DOI":"10.1109\/TAES.2016.150237","article-title":"Iterated Multiplicative Extended Kalman filter for Attitude Estimation using Vector Observations","volume":"52","author":"Chang","year":"2016","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_14","unstructured":"Auman, A.J. (2015). Geometric Attitude Estimation & Orbit Modelling,. [Ph.D. Thesis, Surrey Space Centre]."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/18\/5\/1414\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T15:03:06Z","timestamp":1760194986000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/18\/5\/1414"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,5,3]]},"references-count":14,"journal-issue":{"issue":"5","published-online":{"date-parts":[[2018,5]]}},"alternative-id":["s18051414"],"URL":"https:\/\/doi.org\/10.3390\/s18051414","relation":{},"ISSN":["1424-8220"],"issn-type":[{"type":"electronic","value":"1424-8220"}],"subject":[],"published":{"date-parts":[[2018,5,3]]}}}