Mean‐square filtering for polynomial discrete‐time systems with Poisson noises

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.