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Problemy Peredachi Informatsii, 1998, Volume 34, Issue 4, Pages 23–38
(Mi ppi422)
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This article is cited in 3 scientific papers (total in 3 papers)
Methods of Signal Processing
Upper and Lower Bounds and Asymptotics of Optimal Filtering Error of a Stationary Process with a Small Information Rate
M. S. Pinsker, V. V. Prelov
Abstract:
Upper and lower bounds are obtained for the mean-square error of the optimal (nonlinear) filtering of a discrete-time stationary process $X=\{X_j\}$ from the observations $Y=\{Y_j\}$, where $Y=X+Z$ and $Z=\{Z_j\}$ is a sequence of i.i.d. random variables. These bounds are linear functions of the information rate $\overline I(X;Y)$. It is shown that the lower bound is asymptotically tight in the case where both $\overline I(X;Y)$ and the peak power of the signal $X$ tend to zero. The situations where $X_n$ is estimated from either the observations $\{Y_j, j\leq n-1\}$ or the observations $\{Y_j, j\leq n\}$ are both considered.
Received: 30.10.1997
Citation:
M. S. Pinsker, V. V. Prelov, “Upper and Lower Bounds and Asymptotics of Optimal Filtering Error of a Stationary Process with a Small Information Rate”, Probl. Peredachi Inf., 34:4 (1998), 23–38; Problems Inform. Transmission, 34:4 (1998), 309–321
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https://www.mathnet.ru/eng/ppi422 https://www.mathnet.ru/eng/ppi/v34/i4/p23
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Abstract page: | 502 | Full-text PDF : | 103 | References: | 63 |
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