Robust Wiener Filtering based on Probabilistic Descriptions of Model Errors

Mikael Sternad and Anders Ahlén

Kybernetika, (Prague) vol 29, pp 439-454, September 1993.

In Pdf

Outline:

In robust filter synthesis, the ever present model uncertainty, and the whole range of expected system behaviour, is taken into account. We here propose a novel approach to robust design for signal estimation. It is based on a stochastic description of model errors, related to the stochastic embedding concept of Goodwin and Salgado.

Abstract:

A new approach to robust estimation of signals and prediction of time-series is considered. Possible modelling errors are described by sets of systems, parametrized by random variables, with known covariances. A robust design is obtained by minimizing the squared estimation error, averaged both with respect to model errors and noise. A polynomial solution, based on averaged spectral factorizations and averaged Diophantine equations, is derived.

The robust estimator is called a cautious Wiener filter. It turns out to be no more complicated to design than an ordinary Wiener filter. The methodology can be applied to any open loop filtering or control problem.

Related publications:

Paper in Automatica 1993 discussing also error modelling, feedforward control and state estimation.
PhD Thesis by Kenth Öhrn, May 1996, with additional details, examples and generalizations.
Paper in IEEE Trans. AC 1995, describing the multivariable Wiener solution.
State-space design and comparison to minimax H-2, European Control Conf. 1995.