In this article, we present an algorithm for direction of arrival (DOA) tracking and separation of multiple speakers with a microphone array using the factor graph statistical model. In our model, the speakers can be located in one of a predefined set of candidate DOAs, and each time-frequency (TF) bin can be associated with a single speaker. Accordingly, by attributing a statistical model to both the DOAs and the associations, as well as to the microphone array observations given these variables, we show that the conditional probability of these variables given the microphone array observations can be modeled as a factor graph. Using the loopy belief propagation (LBP) algorithm, we derive a novel inference scheme which simultaneously estimates both the DOAs and the associations. These estimates are used in turn for separating the sources, by directing a beamformer towards the estimated DOAs, and then applying a TF masking according to the estimated associations. A comprehensive experimental study demonstrates the benefits of the proposed algorithm in both simulated data and real-life measurements recorded in our laboratory.

In this paper, we present a multiple-speaker direction of arrival (DOA) tracking algorithm with a microphone array that utilizes the recursive EM (REM) algorithm proposed by Cappé and Moulines. In our model, all sources can be located in one of a predefined set of candidate DOAs. Accordingly, the received signals from all microphones are modeled as Mixture of Gaussians (MoG) vectors in which each speaker is associated with a corresponding Gaussian. The localization task is then formulated as a maximum likelihood (ML) problem, where the MoG weights and the power spectral density (PSD) of the speakers are the unknown parameters. The REM algorithm is then utilized to estimate the ML parameters in an online manner, facilitating multiple source tracking. By using Fisher-Neyman factorization, the outputs of the minimum variance distortionless response (MVDR)-beamformer (BF) are shown to be sufficient statistics for estimating the parameters of the problem at hand. With that, the terms for the E-step are significantly simplified to a scalar form. An experimental study demonstrates the benefits of the using proposed algorithm in both a simulated data-set and real recordings from the acoustic source localization and tracking (LOCATA) data-set.