Speaker tracking with spherical microphone arrays

In prior work, we investigated the application of a spherical microphone array to a distant speech recognition task. In that work, the relative positions of a fixed loud speaker and the spherical array required for beamforming were measured with an optical tracking device. In the present work, we investigate how these relative positions can be determined automatically for real, human speakers based solely on acoustic evidence. We first derive an expression for the complex pressure field of a plane wave scattering from a rigid sphere. We then use this theoretical field as the predicted observation in an extended Kalman filter whose state is the speaker's current position, the direction of arrival of the plane wave. By minimizing the squared-error between the predicted pressure field and that actually recorded, we are able to infer the position of the speaker.