OPTIMAL STATE ESTIMATION FOR STOCHASTIC-SYSTEMS - AN INFORMATION-THEORETIC APPROACH

In this paper, we examine the problem of optimal state estimation or f iltering in stochastic systems using an approach based on information theoretic measures, In this setting, the traditional minimum mean-squa re measure is compared with information theoretic measures, Kalman fil tering theory is reexamined, and some new interpretations are offered. We show that for a linear Gaussian system, the Kalman fitter is the o ptimal filter not only for the mean-square error measure, but for seve ral information theoretic measures which ate introduced in this work, For nonlinear systems, these same measures generally are in conflict w ith each other, and the feedback control policy has a dual role with r egard to regulation and estimation, For linear stochastic systems with general noise processes, a lower bound on the achievable mutual infor mation between the estimation error and the observation are derived, T he properties of an optimal (probing) control law and the associated o ptimal filter, which achieve this lower bound, and their relationships are investigated. It is shown that for a linear stochastic system wit h an affine linear filter for the homogeneous system, under some reach ability and observability conditions, zero mutual information between estimation error and observations can be achieved only when the system is Gaussian.