Time-difference of arrival model for spherical microphone arrays and application to direction of arrival estimation

This paper investigates different steering techniques for spherical microphone arrays and proposes a time-difference of arrival (TDOA) model for microphones on surface of a rigid sphere. The model is based on geometric interpretation of wavefront incident angle and the extra distance the wavefront needs to travel to reach microphones on the opposite side of a sphere. We evaluate the proposed model by comparing analytic TDOAs to measured TDOAs extracted from impulse responses (IR) of a rigid sphere (r = 7.5cm). The proposed method achieves over 40% relative improvement in TDOA accuracy in comparison to free-field propagation and TDOAs extracted from analytic IRs of a spherical microphone array provide an additional 10% improvement. We test the proposed model for the application of source direction of arrival (DOA) estimation using steered response power (SRP) with real reverberant recordings of moving speech sources. All tested methods perform equally well in noise-free scenario, while the proposed model and simulated IRs improve over free-field assumption in low SNR conditions. The proposed model has the benefit of only using single delay for steering the array.