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We integrate the inverse Kalman filter with the conjugate gradient algorithm, which substantially accelerates the computation of matrix inversion for a general form of covariance matrix, where other approximation approaches may not be directly applicable. We demonstrate the scalability and efficiency of the proposed approach through applications in nonparametric estimation of particle interaction functions, using both simulations and cell trajectories from microscopy data.<\/jats:p>","DOI":"10.1093\/biomet\/asaf054","type":"journal-article","created":{"date-parts":[[2025,7,17]],"date-time":"2025-07-17T10:11:53Z","timestamp":1752747113000},"source":"Crossref","is-referenced-by-count":2,"title":["The inverse Kalman filter"],"prefix":"10.1093","volume":"112","author":[{"given":"Xinyi","family":"Fang","sequence":"first","affiliation":[{"name":"Department of Statistics and Applied Probability, University of California , Santa Barbara , Santa Barbara, California 93106,","place":["USA"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3959-8965","authenticated-orcid":false,"given":"Mengyang","family":"Gu","sequence":"additional","affiliation":[{"name":"Department of Statistics and Applied Probability, University of California , Santa Barbara , Santa Barbara, California 93106,","place":["USA"]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2025,7,21]]},"reference":[{"key":"2026032607104970000_asaf054-B1","doi-asserted-by":"crossref","first-page":"451","DOI":"10.1140\/epjb\/e2008-00275-9","article-title":"Modeling collective motion: variations on the Vicsek model","volume":"64","author":"Chat\u00e9","year":"2008","journal-title":"Eur. 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