Adaptive blind separation of independent sources: a second-order stable algorithm for the general case

In this paper, the adaptive separation of convolutive mixtures of independent sources is addressed. The case where the number of sensors is strictly greater than the number of sources is considered. Under a mild assumption on the unknown transfer function, it is shown that the separation can be nearly achieved by a three-step procedure: a linear prediction algorithm in the singular case; a separation of an instantaneous mixture; and the implementation of the inverse of the prediction filter. The main difficulty of this approach is to control the stability of this IIR filter. For that purpose, we use a normalized lattice structure, which is stable for any choice of its parameters.