Optimal polynomial filter of degrees 3 and 4 and its application to an automotive system

Abstract

This paper presents the optimal nonlinear filter for a stochastic system state given by a polynomial equation of degree 3 or 4 and linear observations confused with white Gaussian noises. The obtained filtering equations are applied to solution of the state estimation problem for a nonlinear automotive system. Simulation results are compared for the optimal polynomial filter given in this paper and the linear Kalman-Bucy filter applied to the linearized system.