Feedback estimation systems and the separation principle of stochastic control

Estimation systems with a feedback link have a structure similar to that encountered in the study of stochastic feedback control systems. A feedback estimation algorithm of a specific form is derived in this paper. This algorithm is shown to be superior to one based upon the separation principle of stochastic control and inferior to one employing a different feedback signal structure. The observed differences in performance of these algorithms give insight into a basic limitation on control policies derived from formal application of the separation principle.