A Probabilistic Approach to Multivariable Robust Filtering, Prediction and Smoothing

Kenth Öhrn , Anders Ahlén and Mikael Sternad

32nd IEEE Conference on Decision and Control, San Antonio, TX,
December 15-17, 1993, pp 1227-1232. © 1993 IEEE.

Paper In Pdf 461K.

Outline:

The performance of Wiener filters is degraded by the presence of model errors. The paper develops a method for robust design of multisignal estimators. It is based on probabilistic descriptions of the uncertainty and on the minimization of averaged mean square error criteria.

Abstract:

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-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.

Related publications:

PhD Thesis by Kenth Öhrn, May 1996, which considers also general matrix fraction descriptions.
Paper in IEEE Trans. AC 1995, including proofs and the dual feedforward control problem.
State-space design and comparison to minimax H-2, European Control Conf. 1995.
SISO filtering, feedforward control and uncertainty modelling, Automatica 1993.
Robust decision feedback equalizers, IEEE ICASSP'93.