Periodically Correlated Processes Estimates

Description of methods of estimation of linear functionals depending on the unknown values of periodically correlated random processes based on observations of the processes and noise is presented. The crucial assumption in application of traditional methods of finding solution to the estimation problem for random processes is that spectral densities of processes are exactly known. However, in practical situations complete information on spectral densities is impossible and the established results cannot be directly applied to practical estimation problems. We propose to apply the minimax-robust method of estimation and derive the minimax estimates since they minimize the maximum value of the mean-square errors for all spectral densities from given set of admissible densities simultaneously. Relations for determining least favourable spectral densities and minimax-robust spectral characteristics of the optimal estimates are proposed.

Autorentext

Dr. Mikhail Moklyachuk is a Professor of the Department of Probability Theory, Statistics and Actuarial Mathematics, Taras Shevchenko National University of Kyiv. Dr. Iryna Golichenko is an Assistant Professor, Department of Mathematical Analysis and Probability Theory, National Technical University of Ukraine.