Stochastic approximation type nonlinear filter using empirical distribution of residuals

Abstract

State estimation of dynamical systems is one of the most important problems in control systems engineering. This paper is concerned with a nonlinear filter of stochastic approximation type for state estimation of nonlinear dynamical systems and its modifications to improve the convergence property. First, the asymptotic variance of the estimation error is derived for the nonlinear filter of stochastic approximation type. Then it is shown that a suitable nonlinear transformation function minimizes the variance. Since the optimal transformation function requires the knowledge of probability distribution of observation noise, a construction method of the asymptotically optimal transformation function based on the sequence of residuals is also provided. Results of numerical simulation studies indicate the usefulness of the proposed idea.