Design of Multivariable Cautious Discrete-time Wiener Filters:
A Probabilistic Approach
PhD Thesis, Uppsala University,
248pp, ISBN 91-506-1157-7, May 1996.
Chapter 1 of the Thesis available in Postscript :
Paper copies of the whole thesis can be obtained from
Signals and Systems Group, Uppsala University,
Box 534, SE-75121 Uppsala, Sweden.
Can uncertain dynamic models be used for linear filter design in a
systematic way? The answer is yes, if appropriate descriptions of the
model uncertainty are available.
The thesis develops a design method based on probabilistic
descriptions of the uncertainty, and on the minimization of averaged
mean square error criteria.
A new approach to robust filtering, prediction,
smoothing and open-loop control 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 time-invariant 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, averaged with respect
to the assumed model errors. A polynomial matrix solution,
based on an averaged spectral factorization and a Diophantine
equation, is derived. The robust filters are referred to as
cautious filters. The filters turn out to be not more
complicated to design than the ordinary filters.
The main effort is put into the design of cautious
multivariable Wiener filters. However, also robust open-loop
control, such as the design of robust multivariable
feedforward regulators, decoupling and model matching
filters is considered. Furthermore, robust Kalman filters,
predictors and smoothers for state estimation are
designed in the same spirit, using time-invariant
probabilistic error models.
These state estimators can be used as adaptation algorithms
for tracking the parameters of linear regression models.
A systematic way is thus obtained for utilizing uncertain
a priori information in the design of Kalman-based
- 1. Summary and Introduction
- 2. Probabilistic Error Models
- 3. Obtaining Error Models
- 4. Robust Multivariable H2 Estimation
- 5. Robust Multivariable H2 Feedforward Control
- 6. Robust State Estimation
- 7. A Concluding Example
- 8. Conclusions
- Related publications:
Paper in IEEE Trans. AC 1995,
describing the multivariable Wiener solution.
and comparison to minimax H-2, European Control Conf. 1995.
filtering, feedforward control
and uncertainty modelling, Automatica 1993.
Robust decision feedback equalizers ,
PhD thesis by Lars Lindbom
on model-based design of adaptive filters.