Second Order Blind Separation of Temporally Correlated Sources

Blind separation of sources consists in recovering a set of statistically independent signals whose only mixtures are observed. Such instantaneous mixtures occur in narrow band array data which can then be processed without knowing the array manifold (blindness). This paper introduces a new source separation technique exploiting the possible time coherence of the source signals. In contrast to other previously reported techniques, the proposed approach relies only on second-order statistics, being based on a `joint diagonalization' of correlation matrices. The eectiveness of the method in dicult contexts is illustrated by numerical simulations. The so-called`source separation' problem consists in the identication of the independent components in a random vector. The term`source' is generic but hints at the main application of source separation which is in the eld of array processing. When an array of n sensors samples the elds radiated by m narrow band sources its output is classically modeled as a random vector made of m one-dimensional components, possibly corrupted by additive noise. Source separation may be obtained by rst identifying the directional vectors associated to each of these components and then by (obliquely) projecting the array signal onto the estimated vectors. This is a standard program in array processing, but blind source separation proposal is to perform identication without resorting to the knowledge of the array manifold. Hence, blind source separation is essentially unaected by errors in the propagation model or in array calibration. All the source separation proposed so far are based on the crucial assumption of mutual statistical independence of the source signals. This strong but plausible assumption seems to be the price for ignoring the array manifold. Various solutions have been proposed to the blind source separation problem. When the source signals are temporally white, it has been recognized that the problem cannot be solved using only second-order information. One has then to resort to higher-order statistics as in [1, 2, 3] or to non-linear spatial adaptive lters [4, 5]. On the other hand, if the source signals are correlated, blind identication is possible based on spatial correlation matrices [6]. These matrices (see below) show a simple structure which allows for straightforward blind identication procedures based on eigen-decomposition. In this paper, we introduce an original blind identication technique, based on joint diagonalization of a set of correlation matrices. Robustness is signicantly increased, at low additional cost, by processing such a matrix set rather than a unique …