Mixture-based extension of the AR model and its recursive Bayesian identification

An extension of the AutoRegressive (AR) model is studied, which allows transformations and distortions on the regressor to be handled. Many important signal processing problems are amenable to this Extended AR (i.e., EAR) model. It is shown that Bayesian identification and prediction of the EAR model can be performed recursively, in common with the AR model itself. The EAR model does, however, require that the transformation be known. When it is unknown, the associated transformation space is represented by a finite set of candidates. What follows is a Mixture-based EAR model, i.e., the MEAR model. An approximate identification algorithm for MEAR is developed, using a restricted Variational Bayes (VB) method. This restores the elegant recursive update of sufficient statistics. The MEAR model is applied to the robust identification of AR processes corrupted by outliers and burst noise, respectively, and to click removal for speech.