H∞ deconvolution filtering, prediction, and smoothing: a Krein space polynomial approach

This correspondence is concerned with the infinite horizon H∞ deconvolution for discrete time-invariant systems described by polynomial equations. A simple frequency domain approach in Krein space is developed for the deconvolution problem. With the help of an ARMA innovation model, solutions to the problems of deconvolution filtering, prediction, and fixed lag smoothing are obtained. The estimators are calculated by performing one J-spectral factorization