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The switching in the state equation is performed between two different nonlinear functions according to a sequence of independent Bernoulli random variables that take the quantities of zero and one. The mean-square filtering solution is obtained for a general nonlinear discrete-time polynomial system and a finite-dimensional system of filtering equations is then obtained for a second degree polynomial system as a particular case. The mean-square estimates of polynomial state terms are expressed as functions of the estimate and covariance matrix. Finally, some numerical simulations are carried out to reconstruct the variable states given a vector output measurement for a linear system, a second degree polynomial system, and an induction motor model to show effectiveness of the proposed algorithm. The proposed method is compared with an extended Kalman filter-based algorithm for discrete-time switched nonlinear systems.<\/jats:p>","DOI":"10.1177\/0142331221998856","type":"journal-article","created":{"date-parts":[[2021,3,24]],"date-time":"2021-03-24T09:00:48Z","timestamp":1616576448000},"page":"3031-3043","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":0,"title":["Discrete-time estimation of switched stochastic polynomial systems and its application to reconstruction of induction motor variables"],"prefix":"10.1177","volume":"43","author":[{"given":"Miguel","family":"Hernandez\u2013Gonzalez","sequence":"first","affiliation":[{"name":"Facultad de Ciencias F\u00edsico\u2013Matem\u00e1ticas, Universidad Aut\u00f3noma de Nuevo Le\u00f3n, M\u00e9xico"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7274-4303","authenticated-orcid":false,"given":"Michael","family":"Basin","sequence":"additional","affiliation":[{"name":"Facultad de Ciencias F\u00edsico\u2013Matem\u00e1ticas, Universidad Aut\u00f3noma de Nuevo Le\u00f3n, M\u00e9xico"},{"name":"Department of Control Systems and Robotics, ITMO University, Russia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Oleg","family":"Stepanov","sequence":"additional","affiliation":[{"name":"Department of Control Systems and Robotics, ITMO University, Russia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","published-online":{"date-parts":[[2021,3,24]]},"reference":[{"key":"bibr1-0142331221998856","doi-asserted-by":"publisher","DOI":"10.1016\/j.sigpro.2017.01.001"},{"key":"bibr2-0142331221998856","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.2005.858684"},{"key":"bibr3-0142331221998856","volume-title":"Optimal Filtering","author":"Anderson BDO","year":"1979"},{"key":"bibr4-0142331221998856","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.2009.2019800"},{"key":"bibr5-0142331221998856","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.1967.1098732"},{"key":"bibr6-0142331221998856","doi-asserted-by":"publisher","DOI":"10.1016\/j.nahs.2017.12.004"},{"key":"bibr7-0142331221998856","volume-title":"New Trends in Optimal Filtering and Control for Polynomial and Time-delay Systems","author":"Basin MV","year":"2008"},{"key":"bibr8-0142331221998856","volume-title":"The Induction Machine Handbook","author":"Boldea I","year":"2002"},{"key":"bibr9-0142331221998856","doi-asserted-by":"publisher","DOI":"10.1109\/PROC.1970.7792"},{"key":"bibr10-0142331221998856","doi-asserted-by":"publisher","DOI":"10.1016\/j.neucom.2016.10.006"},{"key":"bibr11-0142331221998856","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-319-10795-0","volume-title":"Hybrid Dynamical Systems. 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