{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,7]],"date-time":"2025-11-07T13:33:10Z","timestamp":1762522390451,"version":"3.38.0"},"reference-count":27,"publisher":"SAGE Publications","issue":"10","license":[{"start":{"date-parts":[[2020,2,10]],"date-time":"2020-02-10T00:00:00Z","timestamp":1581292800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"content-domain":{"domain":["journals.sagepub.com"],"crossmark-restriction":true},"short-container-title":["Transactions of the Institute of Measurement and Control"],"published-print":{"date-parts":[[2020,6]]},"abstract":"<jats:p> Bilinear stochastic differential equations have found applications to model turbulence in autonomous systems as well as switching uncertainty in non-linear dynamic circuits. In signal processing and control literature, bilinear stochastic differential equations are ubiquitous, since they capture non-linear qualitative characteristics of dynamic systems as well as offer closed-form solutions. The novelties of the paper are two: we weave bilinear filtering for the Stratonovich stochasticity. Then this paper unfolds the usefulness of bilinear filtering for switched dynamic systems. First, the Stratonovich stochasticity is embedded into a vector \u2018bilinear\u2019 time-varying stochastic differential equations. Then, coupled non-linear filtering equations are achieved. Finally, the non-linear filtering results are applied to an appealing bilinear stochastic \u0106uk converter circuit. This paper also encompasses a system of coupled bilinear filtering equations for the vector input Brownian motion case. This paper brings the notions of systems theory, that is, bilinearity, Stratonovich stochasticity, non-linear filtering techniques and switched electrical networks together. Numerical simulation results are presented to demonstrate that the proposed bilinear filter can achieve much better and accurate filtering performance than the conventional Extended Kalman Filter (EKF). <\/jats:p>","DOI":"10.1177\/0142331219895711","type":"journal-article","created":{"date-parts":[[2020,2,10]],"date-time":"2020-02-10T08:54:43Z","timestamp":1581324883000},"page":"1755-1768","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":4,"title":["Non-linear filtering for bilinear stochastic differential systems: A Stratonovich perspective"],"prefix":"10.1177","volume":"42","author":[{"given":"Sandhya","family":"Rathore","sequence":"first","affiliation":[{"name":"Electrical Engineering Department, Sardar Vallabhbhai National Institute of Technology, India"}]},{"given":"Shambhu N","family":"Sharma","sequence":"additional","affiliation":[{"name":"Electrical Engineering Department, Sardar Vallabhbhai National Institute of Technology, India"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4083-6422","authenticated-orcid":false,"given":"Dhruvi","family":"Bhatt","sequence":"additional","affiliation":[{"name":"Electrical Engineering Department, Sardar Vallabhbhai National Institute of Technology, India"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9867-8167","authenticated-orcid":false,"given":"Shaival","family":"Nagarsheth","sequence":"additional","affiliation":[{"name":"Electrical Engineering Department, Sardar Vallabhbhai National Institute of Technology, India"}]}],"member":"179","published-online":{"date-parts":[[2020,2,10]]},"reference":[{"key":"bibr1-0142331219895711","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.2002.803546"},{"key":"bibr2-0142331219895711","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.2007.908347"},{"key":"bibr3-0142331219895711","first-page":"2157","volume-title":"Proceedings of the 19th International Symposium on Mathematical Theory of Networks and Systems 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