Bounding filters in the presence of inexactly known parameters

Abstract

Kalman-Bucy (K/B) filtering assumes that the linear dynamic system and corresponding noise statistics are exactly known. When this information is only approximately known, an optimum bounding filter can be designed for specific versions (steady state time-invariant with scalar observations) of the K/B problem. A system is designed in which 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 the apparent divergence is prevented. The bounding filter can be designed to be of lower order than the original system, however, this results in a higher error covariance. Conditions for the design of the optimum (minimum mean square error) bounding filter within a permissible class are derived. Since the specific K/B problem is formulated as an equivalent Wiener filtering problem, therefore, all the results are applicable to the design of bounding filters for Wiener problems. The design of a bounding filter is illustrated by an example.