Approximate maximum likelihood blind source separation with arbitrary source PDFs

We present a quasi-maximum likelihood approach to blind source separation (BSS) which is based on approximating the source distributions by their truncated Edgeworth expansions. The paper focuses on the 2×2 case, for which the problem is known to reduce to the estimation of a single rotation angle. Unlike existing maximum likelihood BSS techniques, the proposed algorithm is consistent for any source distribution, provided that the usual identifiability condition (at most one Gaussian source) is satisfied. Closed-form expressions are derived for the true Cramer Rao bound (CRB), for the CRB corresponding to the Edgeworth approximation, and for the large-sample variance of the proposed estimator. The proposed algorithm is compared with existing approaches via extensive simulations