Kybernetika 33 no. 4, 409-425, 1997

Approximation approach for nonlinear filtering problem with time dependent noises. I. Conditionally optimal filter in the minimum mean square sense

S. Hoang, T. L. Nguyen, R. Baraille and O. Talagrand

Abstract:

An approximation approach is proposed to design a nonlinear recursive filter which is conditionally optimal in the minimum mean square (MMS) sense for a nonlinear filtering problem with dependent noises. Definition of an MMS estimator in a given class of estimators is introduced and its uniqueness (with probability 1) is established in Theorem 1. Efficiency of a new optimal filter is illustrated in Theorems 2, 3. Some numerical examples are presented.

Classification:

93C55, 93E11, 93C99, 93C10, 93E25