An Approximate Method of State Estimation for Nonlinear Dynamical Systems

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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 in the Markovian framework. The principal line of attack is to expand the nonlinear function into a certain linear function with coefficients which are determined under the minimal squared error criterion. The linearized function is specified by the coefficients dependent on both the state estimate and the error covariance. Thus, a method is given for the simultaneous treatments of approximate structure of state estimator dynamics and of running evaluation of the error covariance through the linearized procedure. Comparative discussions on the other filter structures are also given, including quantitative aspects of sample path behaviors obtained by digital simulation studies.

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