A Procedure for Constructing Optimum Functional Filters for Linear Stationary Stochastic Systems

Abstract

Three problems closely related to the classical unbiased optimal filtration problem: an unbiased optimal filtration problem without a control in the system,a biased optimal filtration problem where the bias does not exceed a given value, and the joint problem of stabilization and optimal filtration. It is proposed these problems be reduced to ones of nonlinear optimization. For unbiased filtration with no control, conditions are provided that allow the one for classical unbiasedness to be weakened or excluded for the filter. A new estimate of the bias of the mean filtration error is proposed.