Robust H-2 Filtering for Structured Uncertainty:
The Performance of Probabilistic and Minimax Schemes.

Mikael Sternad, Kenth Öhrn and Anders Ahlén

1995 European Control Conference, Rome, Italy, September 1995, pp 87-92.
Also: Internal Report UPTEC 94090R, Dept. of Technology, Uppsala University.

Outline:

The performance of Kalman filters may be degraded in the presence of model errors. A method for robust design, based on the minimization of averaged mean square error criteria, is proposed here. Its properties are compared to those of an alternative minimax approach.

Abstract:

A probabilistic approach to the robustification of Kalman filters is presented. It results in a higher order model, in which the uncertainty can be taken into account by simply modifying the noise covariance matrices. The proposed method provides a systematic way of performing this transformation.

The performance of the robustified Kalman filter is compared to that of a recently proposed minimax H-2 scheme, based on two coupled Riccati equations and a one-dimensional numerical search. It is concluded that such methods should be used with care, since their guaranteed performance may be worse than that obtained by doing no filtering at all.

Related publications:

PhD Thesis by Kenth Öhrn May 1996, with details, examples and generalizations.
Paper in IEEE Trans. AC 1995, on the corresponding design of multivariable Wiener filters.
Paper in Automatica 1993, which includes an alternative way of robustifying state estimators.

Source:

In Postscript (without figures) : compressed(gz) 62K ; uncompressed 269K.
Pdf 285K.