Improved signal processing observed with semi-Markov noises

Abstract

Abstract This paper considers the problem of improved adaptive estimating a periodic signal observed in the transmission channel with the dependent noise defined by semi-Markov processes with unknown probabilities and spectral characteristics. Improved adaptive model selection procedure is proposed. The comparison between improved and least squares methods is studied. Sharp oracle inequality for the procedure risk is obtained. The efficiency of the proposed procedure is established. The Monte Carlo simulation results are given.