{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,18]],"date-time":"2026-08-18T05:07:57Z","timestamp":1787029677022,"version":"build-2736575974"},"reference-count":53,"publisher":"MDPI AG","issue":"24","license":[{"start":{"date-parts":[[2025,12,12]],"date-time":"2025-12-12T00:00:00Z","timestamp":1765497600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100006769","name":"Russian Science Foundation","doi-asserted-by":"publisher","award":["23-19-00626"],"award-info":[{"award-number":["23-19-00626"]}],"id":[{"id":"10.13039\/501100006769","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>A class of nonlinear filtering problems connected with data fusion from various navigation sensors and a navigation system is considered. A special feature of these problems is that the posterior probability density function (PDF) of the state vector being estimated changes its character from multi-extremal to single-extremal as measurements accumulate. The algorithms based on sequential Monte Carlo methods, which, in principle, provide the possibility of attaining potential accuracy, are computationally complicated, especially when implemented in real time. Traditional recursive algorithms, such as the extended Kalman filter and its iterative modification prove to be inoperable in this case. Two algorithms, devoid of the above drawbacks, are proposed to solve this class of nonlinear filtering problems. The first algorithm, a Recursive Iterative Batch Linearized Smoother (RI-BLS), is essentially a nonrecursive iterative algorithm; at each iteration, it processes all measurements accumulated by the current time of measurement. However, to do this, it uses a recursive procedure: first, the measurements are processed from the first to the current one in the linearized Kalman filter, and then the obtained estimates are processed recursively in reverse time. The second algorithm, a Recursive Iterative Batch Multiple Linearized Smoother (RI-BMLS), is based on the simultaneous use of a set of RI-BLS running in parallel. The application of the proposed algorithms and their advantages are illustrated by a methodological example and solution of the map-aided navigation problem. The calculation of the computational complexity factor has shown that the RI-BLS is more than 15-fold simpler than the particle filter in computational terms, and the RI-BMLS, more than 20-fold with comparable estimation accuracy.<\/jats:p>","DOI":"10.3390\/s25247566","type":"journal-article","created":{"date-parts":[[2025,12,12]],"date-time":"2025-12-12T16:19:02Z","timestamp":1765556342000},"page":"7566","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Recursive Batch Smoother with Multiple Linearization for One Class of Nonlinear Estimation Problems: Application for Multisensor Navigation Data Fusion"],"prefix":"10.3390","volume":"25","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3640-3760","authenticated-orcid":false,"given":"Oleg","family":"Stepanov","sequence":"first","affiliation":[{"name":"Faculty of Control Systems and Robotic, ITMO University, 197101 St. Petersburg, Russia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2111-0308","authenticated-orcid":false,"given":"Alexey","family":"Isaev","sequence":"additional","affiliation":[{"name":"Faculty of Control Systems and Robotic, ITMO University, 197101 St. Petersburg, Russia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2591-5816","authenticated-orcid":false,"given":"Elena","family":"Dranitsyna","sequence":"additional","affiliation":[{"name":"Faculty of Control Systems and Robotic, ITMO University, 197101 St. Petersburg, Russia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5438-2911","authenticated-orcid":false,"given":"Yulia","family":"Litvinenko","sequence":"additional","affiliation":[{"name":"Faculty of Control Systems and Robotic, ITMO University, 197101 St. Petersburg, Russia"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2025,12,12]]},"reference":[{"key":"ref_1","unstructured":"Stratonovich, R.L. 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