Source separation using a criterion based on second-order statistics

It is often assumed that blind separation of dynamically mixed sources cannot be done with second-order statistics. It is shown that separation of dynamically mixed sources indeed can be performed using second-order statistics only. A criterion based on second-order statistics for the purpose of separating crosswise mixtures is stated. The criterion is used in order to derive a gradient-based separation algorithm, as well as a Newton-type separation algorithm. The uniqueness of the solution representing the separation is also investigated. This reveals that (1) the channel system is parameter identifiable under weak conditions, and (2) if the sources have the same color, there exists at most two solutions. The local convergence behavior of the proposed algorithm is studied and reveals a sufficient condition for local convergence. Furthermore, the estimates of the channel system are shown to be consistent or to locally minimize the criterion.