Online Adaptive Quasi-Maximum Likelihood Blind Source Separation of Stationary Sources

In the context of Blind Source Separation (BSS), we consider the problem of online separation of stationary sources. Based on the Maximum Likelihood (ML) solution for semi-blind separation of temporally-diverse Gaussian sources, and assuming that a parametric model of the sources' spectra is available, we propose an online adaptive Quasi-ML (QML) separation algorithm. The algorithm operates in an alternating fashion, updating at each iteration the (nuisance) spectra-characterizing parameters first, and then the demixing-matrix estimates, according to simple, computationally efficient update expressions which we derive. Our proposed algorithm, which leads to consistent separation of the sources, is demonstrated here, both analytically and empirically in a simulation experiment, for first-order autoregressive sources.