Minimax filtering of stationary sequences with white noise. (English. Russian original) Zbl 0738.60034

Moklyachuk, M. P.

Theory Probab. Math. Stat. 43, 109-122 (1991); translation from Teor. Veroyatn. Mat. Stat., Kiev 43, 97-111 (1990).

Summary: The problem of linear mean-square optimal estimation is considered for the transform \(A\xi=\sum^ \infty_{j=0}a(j)\xi(-j)\) of a stationary random sequence \(\xi(k)\) with density \(f(\lambda)\) from observations of the sequence \(\xi(k)+\eta(k)\) when \(k\leq 0\), where \(\eta(k)\) is a white noise with variance \(\sigma^ 2\) and is uncorrelated with \(\xi(k)\). Formulas are obtained for computing the mean-square error of an optimal linear estimator of the value of \(A\xi\). Least favorable spectral densities \(f_ 0(\lambda)\in {\mathcal D}\) and minimax (robust) spectral characteristics of an optimal estimator of \(A\xi\) are found for various classes \(\mathcal D\) of densities.

MSC:

60G35	Signal detection and filtering (aspects of stochastic processes)
62M15	Inference from stochastic processes and spectral analysis
62M20	Inference from stochastic processes and prediction
60G10	Stationary stochastic processes

Keywords:

linear mean-square optimal estimation; stationary random sequence; spectral densities