Mean‐square filtering for polynomial discrete‐time systems with Poisson noises. Issue 8 (1st May 2016)

• Record Type: Journal Article
• Authors: Hernandez‐Gonzalez, Miguel; Basin, Michael V.; Jose Maldonado, Juan
• Is Part Of: IET control theory & applications. Volume 10:Issue 8(2016)
• Page Start: 911
• Page End: 918
• Publication Date: 2016-05-01
• Subjects: discrete time systems -- covariance matrices -- stochastic systems -- nonlinear control systems -- mean square error methods -- polynomial matrices -- AWGN -- Kalman filters -- nonlinear filters; mean‐square filtering -- polynomial discrete‐time systems -- Poisson noises -- discrete‐time state estimation problem -- stochastic nonlinear polynomial systems -- linear observations -- filtering problem -- measurement‐update equations -- time‐update equations -- state estimate -- error covariance matrix -- conditional expectations -- finite‐dimensional filtering equations -- third degree polynomial system -- additive white Gaussian noises -- extended Kalman filter; Control theory -- Periodicals; Automatic control -- Periodicals; 629.8312
• DOI: 10.1049/iet-cta.2015.1000
• Languages: English
• ISSNs: 1751-8644

Abstract

Abstract : The discrete‐time state estimation problem for a class of stochastic non‐linear polynomial systems confused with Poisson noises over linear observations is presented in this study. The filtering problem is solved computing the time‐update and measurement‐update equations for the state estimate and error covariance matrix. A finite number of filtering equations can be obtained by expressing the conditional expectations of polynomial terms as functions of the estimate and error covariance. The finite‐dimensional filtering equations are explicitly derived in a closed form for third degree polynomial systems. Numerical simulations are performed for a third degree polynomial system and the performance of the designed filter is compared to the performances of the filter designed for polynomial systems confused with additive white Gaussian noises and the extended Kalman filter.