# Filtering Problem for Stationary Sequences with Missing Observations

### Abstract

We deal with the problem of the mean-square optimal linear estimation of linear functionals which depend on the unknown values of a stationary stochastic sequence from observations of the sequence with a stationary noise sequence. Formulas for calculating the mean-square errors and the spectral characteristics of the optimal linear estimates of functionals are derived 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 of spectral uncertainty, where spectral densities are not known exactly while sets of admissible spectral densities are given. Formulas that determine the least favorable spectral densities and the minimax spectral characteristics are proposed for some special sets of admissible densities.### References

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*Statistics, Optimization & Information Computing*,

*4*(4), 308-325. https://doi.org/10.19139/soic.v4i4.241

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