ean-Square Filtering for Polynomial System States Confused with Poisson Noises over Polynomial Observations

In this paper, the mean-square filtering problem for polynomial system states confused with white Poisson noises over polynomial observations is studied proceeding from the general expression for the stochastic Ito differentials of the mean-square estimate and the error variance.In contrast to the previously obtained results, the paper deals with the general case of nonlinear polynomial states and observations with white Poisson noises.As a result, the Ito differentials for the mean-square estimate and error variance corresponding to the stated filtering problem are first derived.The procedure for obtaining an approximate closed-form finite-dimensional system of the filtering equations for any polynomial state over observations with any polynomial drift is then established.In the example, the obtained closed-form filter is applied to solve the third order sensor filtering problem for a quadratic state, assuming a conditionally Poisson initial condition for the extended third order state vector.The simulation results show that the designed filter yields a reliable and rapidly converging estimate.