Generalized bounding filters for linear time invariant systems

Weiner and Kalman-Bucy filtering problems assume that the models describing the signal and noise stochastic processes are exactly known a priori. In most practical situations this exact a priori knowledge is not possible and suboptimality results. Nahi and Weiss (1971, 1972) have addressed this problem of uncertainty and suboptimality, for linear time-invariant systems, in their work on bounding filters. A bounding filter is essentially a Wiener filter that is designed using bounding power spectral densities. In this paper, now-stationary disturbances are considered and a technique is developed for designing casual, linear, tlme-invariant filters that have a calculated error covariance which bounds their actual error covariance in an "average" sense. The new filters are termed generalized bounding filters (GBF). A GBF is a "type of" Wiener filter that is designed using bounding "average energy" spectra.