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