{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,28]],"date-time":"2026-02-28T18:02:11Z","timestamp":1772301731762,"version":"3.50.1"},"reference-count":25,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2016,5,9]],"date-time":"2016-05-09T00:00:00Z","timestamp":1462752000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"the National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["51377172; 51577191"],"award-info":[{"award-number":["51377172; 51577191"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>The direction of arrival (DOA) tracking problem based on an angle sensor is an important topic in many fields. In this paper, a nonlinear filter named the feedback M-estimation based robust cubature Kalman filter (FMR-CKF) is proposed to deal with measurement outliers from the angle sensor. The filter designs a new equivalent weight function with the Mahalanobis distance to combine the cubature Kalman filter (CKF) with the M-estimation method. Moreover, by embedding a feedback strategy which consists of a splitting and merging procedure, the proper sub-filter (the standard CKF or the robust CKF) can be chosen in each time index. Hence, the probability of the outliers\u2019 misjudgment can be reduced. Numerical experiments show that the FMR-CKF performs better than the CKF and conventional robust filters in terms of accuracy and robustness with good computational efficiency. Additionally, the filter can be extended to the nonlinear applications using other types of sensors.<\/jats:p>","DOI":"10.3390\/s16050629","type":"journal-article","created":{"date-parts":[[2016,5,9]],"date-time":"2016-05-09T10:05:24Z","timestamp":1462788324000},"page":"629","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":13,"title":["Feedback Robust Cubature Kalman Filter for Target Tracking Using an Angle Sensor"],"prefix":"10.3390","volume":"16","author":[{"given":"Hao","family":"Wu","sequence":"first","affiliation":[{"name":"Information and Navigation College Air Force Engineering University, Fenghao east road No.1, Xi\u2019an 710077, China"}]},{"given":"Shuxin","family":"Chen","sequence":"additional","affiliation":[{"name":"Information and Navigation College Air Force Engineering University, Fenghao east road No.1, Xi\u2019an 710077, China"}]},{"given":"Binfeng","family":"Yang","sequence":"additional","affiliation":[{"name":"Information and Navigation College Air Force Engineering University, Fenghao east road No.1, Xi\u2019an 710077, China"}]},{"given":"Kun","family":"Chen","sequence":"additional","affiliation":[{"name":"Information and Navigation College Air Force Engineering University, Fenghao east road No.1, Xi\u2019an 710077, China"}]}],"member":"1968","published-online":{"date-parts":[[2016,5,9]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"24381","DOI":"10.3390\/s141224381","article-title":"Moving Target Tracking through Distributed Clustering in Directional Sensor Networks","volume":"14","author":"Enayet","year":"2014","journal-title":"Sensors"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1161","DOI":"10.1109\/TAES.2013.6494405","article-title":"A Gaussian-Sum Based Cubature Kalman Filter for Bearings-Only Tracking","volume":"49","author":"Leong","year":"2013","journal-title":"IEEE Trans. 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