{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T07:47:58Z","timestamp":1777448878560,"version":"3.51.4"},"reference-count":0,"publisher":"SAGE Publications","issue":"3-4","license":[{"start":{"date-parts":[[2010,12,1]],"date-time":"2010-12-01T00:00:00Z","timestamp":1291161600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Asymptotic Analysis"],"published-print":{"date-parts":[[2010,12]]},"abstract":"<jats:p>We consider nonlinear filtering applications to target tracking based on a vector of multi-scaled models where some of the processes are rapidly mean reverting to their local equilibria. We focus attention on target tracking problems because multiple scaled models with fast mean-reversion (FMR) are a simple way to model latency in the response of tracking systems. The main results of this paper show that nonlinear filtering algorithms for multi-scale models with FMR states can be simplified significantly by exploiting the FMR structures, which leads to a simplified Baum\u2013Welch recursion that is of reduced dimension. We implement the simplified algorithms with numerical simulations and discuss their efficiency and robustness.<\/jats:p>","DOI":"10.3233\/asy-2010-1011","type":"journal-article","created":{"date-parts":[[2019,11,29]],"date-time":"2019-11-29T19:14:19Z","timestamp":1575054859000},"page":"155-176","source":"Crossref","is-referenced-by-count":3,"title":["Filtering for fast mean-reverting processes"],"prefix":"10.1177","volume":"70","author":[{"given":"Andrew","family":"Papanicolaou","sequence":"first","affiliation":[{"name":"Sherrerd Hall, Charlton Street, Princeton, NJ 08544, USA. E-mail: apapanic@princeton.edu"}]}],"member":"179","published-online":{"date-parts":[[2010,12,1]]},"container-title":["Asymptotic Analysis"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/ASY-2010-1011","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/ASY-2010-1011","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,28]],"date-time":"2026-04-28T12:39:15Z","timestamp":1777379955000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/10.3233\/ASY-2010-1011"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010,12]]},"references-count":0,"journal-issue":{"issue":"3-4","published-print":{"date-parts":[[2010,12]]}},"alternative-id":["10.3233\/ASY-2010-1011"],"URL":"https:\/\/doi.org\/10.3233\/asy-2010-1011","relation":{},"ISSN":["0921-7134","1875-8576"],"issn-type":[{"value":"0921-7134","type":"print"},{"value":"1875-8576","type":"electronic"}],"subject":[],"published":{"date-parts":[[2010,12]]}}}