Bounding filter: A simple solution to lack of exact a priori statistics

Abstract

Wiener and Kalman-Bucy estimation problems assume that models describing the signal and noise stochastic processes are exactly known. When this modeling information, i.e., the signal and noise spectral densities for Wiener filter and the signal and noise dynamic system and disturbing noise representations for Kalman-Bucy filtering, is inexactly known, then the filter's performance is suboptimal and may even exhibit apparent divergence. In this paper a system is designed whereby the actual estimation error covariance is bounded by the covariance calculated by the estimator. Therefore, the estimator obtains a bound on the actual error covariance which is not available, and also prevents its apparent divergence. The bounding filter can be of lower order than the original stochastic models; hence, a technique is devised of reducing the order of the filtering system and concurrently obtaining a figure of merit for its performance. For many cases, the design conditions devised for the steady state Wiener filter apply to transient K/B filter performance.