A probabilistic approach to multivariable robust filtering prediction and smoothing

A new approach to robust filtering, prediction and smoothing of discrete-time signal vectors is presented. Linear time-invariant filters are designed to be insensitive to spectral uncertainty in signal models. The goal is to obtain a simple design method, leading to filters which are not overly conservative. Modelling errors are described by sets of models, parametrized by random variables with known covariances. A robust design is obtained by minimizing the H/sub 2/-norm of the estimation error, averaged with respect to the assumed model errors. A polynomial solution, based on an averaged spectral factorization and a unilateral Diophantine equation, is presented. The robust estimator is referred to as a cautious Wiener filter. It turns out to be only slightly more complicated to design than an ordinary Wiener filter.