A Probabilistic Approach Tomultivariable Robust Filtering Andopen - Loop

A new approach to robust ltering, prediction and smoothing of discrete-time signal vectors is presented. Linear time-invariant lters are designed to be insensitive to spectral uncertainty in signal models. The goal is to obtain a simple design method, leading to lters which are not overly conservative. Modelling errors are described by sets of models, parameterized by random variables with known covariances. These covariances could either be estimated from data, or be used as robustness \tuning knobs". A robust design is obtained by minimizing the H 2-norm or, equivalently, the mean square 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 derived. The robust estimator is referred to as a cautious Wiener lter. It turns out to be only slightly more complicated to design than an ordinary Wiener lter. The methodology can be applied to any open loop ltering or control problem. In particular, we illustrate this for the design of robust multivariable feedforward regulators, decoupling and model matching lters.