Optimum Wiener bounding filters in the presence of uncertainties

Abstract

Wiener filtering assumes knowledge of the signal and noise autocorrelations or spectral densities. When this information is only approximately known, an optimum bounding filter can be designed for the Wiener problem. This paper describes the design of a filter in which the actual estimation error covariance is bounded by the covariance calculated by the estimator. Therefore, the estimator generates a bound on the unavailable actual error covariance and prevents its apparent divergence. The bounding filter can be designed to be of lower order than the Wiener filters associated with each possible set of signal and noise spectral density. Conditions for the design of the optimum (minimum mean-square-error) bounding filter within a permissible class of solutions are discussed. The same approach to the design of bounding filters can be applied to a K / B filter version of the Wiener problem. The design of a bounding filter is illustrated by an example.