### Filtering of multidimensional stationary sequences with missing observations

#### Abstract

The problem of mean-square optimal linear estimation of linear functionals which depend on the unknown values of a multidimensional stationary stochastic sequence is considered.

Estimates are based on observations of the sequence with an additive stationary stochastic noise sequence at points which do not belong to some finite intervals of a real line.

Formulas for calculating the mean-square errors and the spectral characteristics of the optimal linear estimates of the functionals are proposed under the condition of spectral certainty, where spectral densities of the sequences are exactly known. The minimax (robust) method of estimation is applied in the case where spectral densities are not known exactly while some sets of admissible spectral densities are given. Formulas that determine the least favorable spectral densities and minimax spectral characteristics are proposed for some special sets of admissible densities.

Estimates are based on observations of the sequence with an additive stationary stochastic noise sequence at points which do not belong to some finite intervals of a real line.

Formulas for calculating the mean-square errors and the spectral characteristics of the optimal linear estimates of the functionals are proposed under the condition of spectral certainty, where spectral densities of the sequences are exactly known. The minimax (robust) method of estimation is applied in the case where spectral densities are not known exactly while some sets of admissible spectral densities are given. Formulas that determine the least favorable spectral densities and minimax spectral characteristics are proposed for some special sets of admissible densities.

#### Keywords

stationary sequence, minimax-robust estimate, mean square error, least favorable spectral density, minimax spectral characteristic

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