An approximate method of state estimation for non-linear dynamical systems with state-dependent noise†

Abstract

In this paper a method of stochastic linearization is demonstrated for the purpose of establishing an approximate approach to solve filtering problems of non-linear stochastic systems with state-dependent noise in a Markovian framework. The models of both the dynamical system and the observation process are described by non-linear stochastic differential equations of Itô type. The principal line of attack is to expand the non-linear drift term into a certain linear function with coefficients which are determined under the minimal squared error criterion. Two methods of linearization are developed for the non-linear diffusion term. The linearized models are thus characterized by expansion coefficients dependent on both the state estimate and the error covariance. A method is given for the simultaneous treatment of the approximate structure of state estimator dynamics and of the running evaluation of the error covariance, including quantitative aspects of sample path behaviours obtained by digital simulation studies.