Blind separation of mixtures of piecewise AR(1) processes and model mismatch

Abstract

Modeling real-world acoustic signals and namely speech signals as piecewise stationary random processes is a possible approach to blind separation of linear mixtures of such signals. In this paper, the piecewise AR(1) modeling is studied and is compared to the more common piecewise AR(0) modeling, which is known under the names Block Gaussian SEParation (BGSEP) and Block Gaussian Likelihood (BGL). The separation based on the AR(0) modeling uses an approximate joint diagonalization (AJD) of covariance matrices of the mixture with lag 0, computed at epochs (intervals) of stationarity of the separated signals. The separation based on the AR(1) modeling uses the covariances of lag 0 and covariances of lag 1 jointly. For this model, we derive an approximate Cramér-Rao lower bound on the separation accuracy for estimation based on the full set of the statistics (covariance matrices of lag 0 and lag 1) and covariance matrices with lag 0 only. The bounds show the condition when AR(1) modeling leads to significantly improved separation accuracy.