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Problemy Peredachi Informatsii, 2006, Volume 42, Issue 4, Pages 77–86
(Mi ppi62)
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Methods of Signal Processing
On-line Estimation of Smooth Signals with Partial
Observation
P.-L. Chowa, R. Z. Khas'minskiiba a Wayne State University
b Institute for Information Transmission Problems, Russian Academy of Sciences
Abstract:
The paper concerns the estimation of a smooth signal $S(t)$ and its derivatives
in the presence of a noise depending on a small parameter $\varepsilon$ based on a partial observation.
A nonlinear Kalman-type filter is proposed to perform on-line estimation. For the signal $S$
in a given class of smooth functions, the convergence rate for the estimation risks, as $\varepsilon\to0$,
is obtained. It is proved that such rates are optimal in a minimax sense. In contrast to the
complete observation case, the rates are reduced, due to incomplete information.
Received: 12.06.2006 Revised: 11.09.2006
Citation:
P.-L. Chow, R. Z. Khas'minskii, “On-line Estimation of Smooth Signals with Partial
Observation”, Probl. Peredachi Inf., 42:4 (2006), 77–86; Problems Inform. Transmission, 42:4 (2006), 330–339
Linking options:
https://www.mathnet.ru/eng/ppi62 https://www.mathnet.ru/eng/ppi/v42/i4/p77
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Statistics & downloads: |
Abstract page: | 339 | Full-text PDF : | 128 | References: | 35 | First page: | 3 |
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