On Minimax Estimation Problems for Periodically Correlated Stochastic Processes

2025/10/19 by Dubovets'ka, Iryna, Moklyachuk, Mykhailo · 2 citations
Engineering · Computer Science · #Control Systems and Identification #Distributed Sensor Networks and Detection Algorithms #Stability and Control of Uncertain Systems

paper · pdf · doi:10.48550/arxiv.2510.16906

Abstract

The aim of this article is to overview the problem of mean square optimal estimation of linear functionals which depend on unknown values of periodically correlated stochastic process. Estimates are based on observations of this process and noise. These problems are investigated under conditions of spectral certainty and spectral uncertainty. Formulas for calculating the main characteristics (spectral characteristic, mean square error) of the optimal linear estimates of the functionals are proposed. The least favorable spectral densities and the minimax-robust spectral characteristics of optimal estimates of the functionals are presented for given sets of admissible spectral densities.

Citations

• Robust extrapolation problem for stochastic sequences with stationary increments

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