Decomposition of a mixture of Gaussian AR processes

We consider the problem of detecting and classifying an unknown number of multiple simultaneous Gaussian autoregressive (AR) signals with unknown variances given a finite length observation of their sum and a dictionary of candidate AR models. We show that the problem reduces to the maximum likelihood (ML) estimation of the variances of the AR components for every subset from the dictionary. The 'best' subset of AR components is then found by applying the minimum description length (MDL) principle. The ML estimates of the variances are obtained by combining the EM algorithm with the Rauch-Tung-Striebel optimal smoother. The performance of the algorithm is illustrated by numerical simulations. Possible improvements of the method are discussed.