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Optimal filtering of square-integrable signals in Gaussian noise. (English. Russian original) Zbl 0452.94003

Probl. Inf. Transm. 16, 120-133 (1980); translation from Probl. Peredachi Inf. 16, No. 2, 52-68 (1980).
Summary: Expressions are considered for the optimal mean-square error \(\delta^2\) of restoration of signals from \(L_2(0,T)\), in Gaussian noise \(\xi_1(t)\), the exact asymptotic form of \(\delta^2\) is obtained for the case in which \(\xi_1(t)=\varepsilon\xi_(t)\), \(\varepsilon^2\to 0\), while \(\theta(t)\in\mathfrak A\), \(\mathfrak A\) is an ellipsoid in \(L_2(0,T)\), and also when \(T\to\infty\). It is shown that the linear estimates are asymptotically optimal.

MSC:

94A12 Signal theory (characterization, reconstruction, filtering, etc.)
93E11 Filtering in stochastic control theory
60G15 Gaussian processes
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