Robust filtering for systems with stochastic nonlinearities and deterministic uncertainties

In this paper, we consider the robust finite-horizon filter design problem for a class of discrete time varying systems with both stochastic nonlinearities and deterministic uncertainties. The description of the stochastic nonlinearities is quite general, which comprises the state-multiplicative noises and the random sequences whose powers depend on either the sector-bound nonlinear function of the state or the sign of a nonlinear function of the state. The norm bounded parameter uncertainties are allowed to enter both the system and the output matrices. We aim to design a robust filter that guarantees an optimized upper bound on the state estimation error variance, for all stochastic nonlinearities and admissible deterministic uncertainties. The existence conditions for the desired robust filters are first derived, and the filter parameters are then determined in terms of the solutions to two recursive Riccati-like difference equations. A numerical example is presented to show the applicability of the proposed method.