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.