Robust Filtering and Feedforward Control based on
Probabilistic Descriptions of Model Errors
Automatica, vol 29, pp 661-679, May 1993.
© 1993 Pergamon Press.
Also: Internal Report UPTEC 91071R, Dept. of Technology,
Report, without figures, available in Postscript :
compressed(gz) 180K ,
In Pdf 1.4M.
Spectral uncertainty in signal models is a problem for
model-based design of filters, predictors and smoothers.
If model errors are represented by stochastic variables,
performance robustness can be optimized by using a polynomial
Simple closed-form solutions exist which minimize quadratic criteria,
averaged with respect to the model error distribution.
A new approach to robust estimation of signals, prediction of
time-series and robust feedforward control is considered.
Signal and system parameter deviations are represented
as random variables, with known covariances.
A robust design is obtained
by minimizing the squared estimation error, averaged both
with respect to model errors and the noise.
A polynomial equations approach, based on
averaged spectral factorizations and averaged Diophantine equations,
is derived. Mild solvability conditions guarantee the
existence of stable optimal filters and feedforward regulators.
The robust design turns out to be no more
complicated than the design of an ordinary Wiener filter or
The proposed approach avoids two drawbacks of
robust minimax design.
descriptions of model uncertainties may have
soft bounds .
These are more readily obtainable
in a noisy environment than the hard bounds required for
minimax design. Furthermore, not only
the range of uncertainties, but also their likelihood is
taken into account;
common model deviations will
have a greater impact on an estimator design than do
very rare ``worst cases''.
The conservativeness is thus reduced.
- Related publications:
in IEEE Trans AC 1995, which generalizes to the multivariable
by Kenth Öhrn, May 1996, with more details, examples
PhD Thesis by Erik Lindskog,
treating robustness in decision feedback equalizers.
and comparison to minimax H-2, European Control Conf. 1995.
in IEEE Trans. SP 1991 on the polynomial approach to
(nominal) Wiener filter design.
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