# Filtering problem for periodically correlated stochastic sequences with missing observations

## DOI:

https://doi.org/10.17721/1812-5409.2023/2.4## Keywords:

periodically correlated stochastic sequence, minimax (robust) estimate, least favorable spectral density, minimax spectral characteristics## Abstract

The problem of the mean-square optimal estimation of the linear functionals which depend on the unknown values of a periodically correlated stochastic sequence from observations of the sequence with missings is considered. Formulas for calculation the mean-square error and the spectral characteristic of the optimal estimate of the functionals are proposed in the case where spectral densities of the sequences are exactly known. Formulas that determine the least favorable spectral densities and the minimax spectral characteristics are proposed in the case of spectral uncertainty, when spectral densities of sequences are not exactly known but the class of admissible spectral densities is given.

* Pages of the article in the issue*: 30 - 43

** Language of the article**: English

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*Bulletin of Taras Shevchenko National University of Kyiv. Physical and Mathematical Sciences*, (2), 30–43. https://doi.org/10.17721/1812-5409.2023/2.4

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