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A Maximum Likelihood “identification-correction” scheme of sub-optimal “SeDJoCo” solutions for semi-Blind Source Separation

The “Sequentially Drilled” Joint Congruence (SeDJoCo) transformation is a set of matrix transformation equations, which coincide with the Likelihood Equations for semi-blind source separation, when each source is modeled as a zero-mean Gaussian process with a known (and distinct) temporal covariance matrix. Therefore, with such a model a solution of SeDJoCo can lead to the Maximum Likelihood (ML) estimate of the separating matrix, which is asymptotically optimal. However, as we have shown in previous work, multiple solutions of SeDJoCo may exist, and the selection of the optimal solution among these (corresponding to the global maximum of the likelihood function) is therefore of considerable interest. In this paper we further extend our results by proposing a new ML approach for the identification and correction of a sub-optimal solution, assuming sources of unrestricted, general temporal covariance structures. We demonstrate the resulting improvement in simulation with non-stationary sources.