According to the physical meaning of the frequencydomain blind source separation (FD-BSS), each mixing matrix estimated by Independent Component Analysis (ICA) contains information on the physical acoustic propagation related to each source and then can be used for localization purposes. In this paper we analyze the Generalized State Coherence Transform (GSCT) which is a non-linear transform of the space represented by the whole demixing matrices. The transform enables an accurate estimation of the propagation time-delay of multiple sources in multiple dimensions. Furthermore, it is shown that with appropriate non-linearities and a statistical model for the reverberation, GSCT can be considered an approximated kernel density estimator of the acoustic propagation time-delay. Experimental results confirm the good properties of the transform and its effectiveness in addressing multiple source TDOA detection (e.g. 2D TDOA estimation of several sources with only three microphones).
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