Bayesian framework for direction of arrival analysis using spherical harmonics

A common task in acoustical applications is the determination of directions of arrival (DoAs) of sound at a receiver. This work aims to address this problem in situations involving potentially multiple simultaneous sound sources by means of a two-level framework of Bayesian inference. This process involves first estimating the number of sound sources present, followed by estimating their directional information, based on sound data collected with a spherical microphone array. Analytical models are formulated using spherical harmonic beamforming techniques, which are incorporated into the Bayesian analysis as part of the prior information. The experimental data are also incorporated to update the information available prior to analysis. All necessary prior information is assigned based on the principle of maximum entropy. Through this technique, the number of sources is first estimated, and then, the DoA information of those sources is extracted from the most concise model that adequately fits the experimental data. This paper presents the Bayesian formulation and analysis results to demonstrate the potential usefulness of model-based Bayesian inference for determining DoAs in complex noise environments with potentially multiple concurrent sources.