Optimizing Estimation of a Statistically Undefined System

Abstract

Consideration was given to the optimal choice of the parameters for the best estimation of the phase state of a linear system fallible to the action of the Gaussian perturbation with undefined covariances of increments. The matrices at system perturbation and those in the measurement equation are the parameters to be selected for the choice of the observer player. The undefined increment matrices are selected by the opponent player. Both parameters are limited by compact sets. The problem comes to a differential game for the Riccati equation with a performance criterion in the form of a matrix trace. In a special case, consideration was given to the problem with constant matrices. Used were the methods of minimax optimization, optimal control theory, and the theory of differential games. Examples were considered.