State Estimation for Linear Discrete-Time Systems with State-Dependent Noise

Abstract

In this paper, the state estimation problem is considered for a class of linear systems with state-dependent noise. The optimal nonlinear estimator in the mean square sense is first derived on the basis of the Bayesian approach. Then a sub-optimal estimator is proposed, in which the estimate is still nonlinear in the observation data, and the covariances are obtained recursively using the observation data. The case where the state-dependent noise is white is treated specifically. Some simulations for this case are made in order to examine the practicability of the proposed sub-optimal estimator, and the result is compared with that of the linear estimator by McLane.