Direction of Arrival Estimation on a Sphere

The direction of arrival (DOA) of a sound source emitting in the three dimensional (3D) space can be defined by both its azimuth and elevation angles. Estimating these two angles, using a multiple microphone array, enables to build a two dimensional (2D) histogram to track sources, and such depict the current audio scene. The observation data collected in the histogram are analyzed and modeled, providing multiple, varying DOA values. An analytic function, which fulfills periodicity and continuity over a sphere, is proposed to parametrize the 2D histogram as a statistical model in order to run an iterative algorithm, such as the expectation-maximization (EM) one, providing eventually the corresponding DOA values.