An ICA-SCT-PHD Filter Approach for Tracking and Separation of Unknown Time-Varying Number of Sources

In this paper we present a solution to the problem of tracking and separation of a mixture of concurrent sources in a reverberant environment where the number of sources is unknown and varies with time: new sources can appear and existing sources can disappear or undergo silence periods. In order to deal with this challenging problem, we synergistically combine two key ideas, one in the front end and the other at the back end. In the front end we employ independent component analysis (ICA) to demix the mixtures and the state coherence transform (SCT) to represent the signals in a direction of arrival (DOA) detection framework. By exploiting the frequency sparsity of the sources, ICA/SCT is even effective when the number of simultaneous sources is greater than the number of sensors therefore allowing for minimal number of sensors to be used. At the back end, the probability hypothesis density (PHD) filter is incorporated in order to track the multiple DOAs and determine the number of sources. The PHD filter is based on random finite sets (RFS) where the multi-target states and the number of targets are integrated to form a set-valued variable with uncertainty in the number of sources. A Gaussian mixture implementation of the PHD filter (GM-PHD) is utilized that solves the data association problem intrinsically, hence providing distinct DOA tracks. The distinct tracks also make the separation task possible by going back and rearranging the outputs of the ICA stage. The tracking and separation capabilities of the proposed method is demonstrated using simulations of multiple sources in reverberant environments.