Optimal filtering for crypto-deterministic systems with application to delay systems with unknown initial data

A result of Friedland for efficient filtering in the presence of a static bias is extended to the case where the bias signals are given by the response of persistent autonomous systems with random initial conditions. It is shown that the optimal filter decouples into a bias free and a bias error correction filter. We apply the results to filtering of a system with delay when the initial data is missing. Theses results have potential applications in secure communication, synchronization and networked control.