Open AccessMean‐square filtering for polynomial discrete‐time systems with Poisson noises
Author(s) -
HernandezGonzalez Miguel,
Basin Michael V.,
Jose Maldonado Juan
Publication year - 2016
Publication title -
iet control theory and applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.059
H-Index - 108
eISSN - 1751-8652
pISSN - 1751-8644
DOI - 10.1049/iet-cta.2015.1000
Subject(s) - polynomial , kalman filter , mathematics , white noise , matrix polynomial , control theory (sociology) , filter (signal processing) , polynomial matrix , covariance , reciprocal polynomial , homogeneous polynomial , computer science , mathematical analysis , statistics , control (management) , artificial intelligence , computer vision
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.