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Zbl 0544.93062
Poor, Vincent; Looze, Douglas P.
Minimax state estimation for linear stochastic systems with noise uncertainty. (English)
[J] IEEE Trans. Autom. Control 26, 902-906 (1981). ISSN 0018-9286

Summary: The problem of minimax linear state estimation for linear stochastic systems driven and observed in noises whose second-order properties are unknown is considered. Two general aspects of this problem are treated: the single-variable problem with uncertain noise spectra and the multivariable problem with uncertain componentwise noise correlation. General minimax results are presented for each of these situations involving characterizations of the minimax filters in terms of least favorable second-order properties. Explicit solutions are given for the spectral-band uncertainty model in the single-variable cases treated and for a matrix-norm neighborhood model in the multivariable case. Characterization of saddle-points in terms of the extremal properties of the noise uncertainty classes is also discussed.

MSC 2000:: *93E10 Estimation and detection in stochastic control
93C05 Linear control systems
93E11 Filtering in stochastic control
49J35 Minimax problems (existence)
60G35 Appl. of stochastic processes
62M20 Prediction, etc. (statistics)

Keywords: minimax linear state estimation; minimax filters; noise uncertainty

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Zentralblatt MATH Berlin [Germany]