Mean-square filter design for nonlinear polynomial systems with Poisson noise

This paper presents the mean-square filtering problem for incompletely measured polynomial system states, confused with white Poisson noises, over linear observations. The problem is treated proceeding from the general expression for the stochastic Ito differential of the optimal estimate and the error variance. As a result, the Ito differentials for the optimal estimate and error variance corresponding to the stated filtering problem are first derived. The procedure for obtaining a closed system of the filtering equations for any polynomial system state with white Poisson noises over linear observations is then established, which yields the explicit closed form of the filtering equations in the particular case of a third-order state equation. In the example, performance of the designed optimal filter is verified against the conventional mean-square polynomial filter designed for systems with white Gaussian noises.