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Adv. Signal Process."],"abstract":"<jats:title>Abstract<\/jats:title><jats:p>The problem of designing a robustified Kalman filtering technique, insensitive to spiky observations, or outliers, contaminating the Gaussian observations has been presented in the paper. Firstly, a class of M-robustified dynamic stochastic approximation algorithms is derived by minimizing at each stage a specific time-varying M-robust performance index, that is, general for a family of algorithms to be considered. The gain matrix of a particular algorithm is calculated at each stage by minimizing an additional criterion of the approximate minimum variance type, with the aid of the statistical linearization method. By combining the proposed M-robust estimator with the one-stage optimal prediction, in the minimum mean-square error sense, a new statistically linearized M-robustified Kalman filtering technique has been derived. Two simple practical versions of the proposed M-robustified state estimator are derived by approximating the mean-square optimal statistical linearization coefficient with the fixed and the time-varying factors. The feasibility of the approaches has been analysed by the simulations, using a manoeuvring target radar tracking example, and the real data, related to an object video tracking using short-wave infrared camera.<\/jats:p>","DOI":"10.1186\/s13634-023-01030-1","type":"journal-article","created":{"date-parts":[[2023,6,21]],"date-time":"2023-06-21T04:19:20Z","timestamp":1687321160000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":10,"title":["Approximate Kalman filtering by both M-robustified dynamic stochastic approximation and statistical linearization methods"],"prefix":"10.1186","volume":"2023","author":[{"given":"Milo\u0161","family":"Pavlovi\u0107","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8195-8576","authenticated-orcid":false,"given":"Zoran","family":"Banjac","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Branko","family":"Kova\u010devi\u0107","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2023,6,21]]},"reference":[{"key":"1030_CR1","volume-title":"Applied optimal estimation, Analytic Sciences Corporation","year":"2010","unstructured":"A. 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