Optimal and self-tuning deconvolution in time domain

This paper is concerned with both the optimal (minimum mean square error va riance) and self tuning deconvolution problems for discrete-time systems. W hen the signal model, measurement model, and noise statistics are known, a novel approach for the design of optimal deconvolution filter, predictor, a nd smoother is proposed based on projection theory and innovation analysis in time domain. The estimators are given in terms of an autoregressive movi ng average (ARMA) innovation model and one unilateral linear polynomial equ ation, where the ARMA innovation model is obtained by performing one spectr al factorization, A self-tuning scheme can be incorporated when the noise s tatistics, the input model, and/or colored noise model are unknown. The sel f-tuning estimator is designed by identifying two ARMA innovation models.