{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,1]],"date-time":"2026-03-01T04:35:34Z","timestamp":1772339734356,"version":"3.50.1"},"reference-count":33,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2019,5,17]],"date-time":"2019-05-17T00:00:00Z","timestamp":1558051200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001659","name":"Deutsche Forschungsgemeinschaft","doi-asserted-by":"publisher","award":["SFB 1294 and SFB 1114"],"award-info":[{"award-number":["SFB 1294 and SFB 1114"]}],"id":[{"id":"10.13039\/501100001659","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>The success of the ensemble Kalman filter has triggered a strong interest in expanding its scope beyond classical state estimation problems. In this paper, we focus on continuous-time data assimilation where the model and measurement errors are correlated and both states and parameters need to be identified. Such scenarios arise from noisy and partial observations of Lagrangian particles which move under a stochastic velocity field involving unknown parameters. We take an appropriate class of McKean\u2013Vlasov equations as the starting point to derive ensemble Kalman\u2013Bucy filter algorithms for combined state and parameter estimation. We demonstrate their performance through a series of increasingly complex multi-scale model systems.<\/jats:p>","DOI":"10.3390\/e21050505","type":"journal-article","created":{"date-parts":[[2019,5,17]],"date-time":"2019-05-17T11:06:46Z","timestamp":1558091206000},"page":"505","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":12,"title":["State and Parameter Estimation from Observed Signal Increments"],"prefix":"10.3390","volume":"21","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5415-5284","authenticated-orcid":false,"given":"Nikolas","family":"N\u00fcsken","sequence":"first","affiliation":[{"name":"Institute of Mathematics, University of Potsdam, Karl-Liebknecht-Str. 24\/25, D-14476 Potsdam, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5336-8904","authenticated-orcid":false,"given":"Sebastian","family":"Reich","sequence":"additional","affiliation":[{"name":"Institute of Mathematics, University of Potsdam, Karl-Liebknecht-Str. 24\/25, D-14476 Potsdam, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7068-1740","authenticated-orcid":false,"given":"Paul J.","family":"Rozdeba","sequence":"additional","affiliation":[{"name":"Institute of Mathematics, University of Potsdam, Karl-Liebknecht-Str. 24\/25, D-14476 Potsdam, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2019,5,17]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Kutoyants, Y. 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