A Bayesian Hierarchical Mixture of Gaussian Model for Multi-Speaker DOA Estimation and Separation

In this paper we propose a fully Bayesian hierarchical model for multi-speaker direction of arrival (DoA) estimation and separation in noisy environments, utilizing the W-disjoint orthogonality property of the speech sources. Our probabilistic approach employs a mixture of Gaussians formulation with centroids associated with a grid of candidate speakers' DoAs. The hierarchical Bayesian model is established by attributing priors to the various parameters. We then derive a variational Expectation-Maximization algorithm that estimates the DoAs by selecting the most probable candidates, and separates the speakers using a variant of the multichannel Wiener filter that takes into account the responsibility of each candidate in describing the received data. The proposed algorithm is evaluated using real room impulse responses from a freely-available database, in terms of both DoA estimates accuracy and separation scores. It is shown that the proposed method outperforms competing methods.