Diagonal Unloading Beamforming in the Spherical Harmonic Domain for Acoustic Source Localization in Reverberant Environments

Spherical microphone arrays allow the sound field analysis in three dimensions with the advantage of having the same resolution in all directions. By considering the frequency-independent character of the steering vectors in the spherical harmonic (SH) domain, we propose a very low-complexity SH diagonal unloading (DU) beamforming with a novel frequency smoothing power transform (FSPT) of the covariance matrices. We consider the direction of arrival (DOA) estimation problem of acoustic sources in reverberant conditions. The DU beamforming provides high resolution directional response since it exploits the subspace orthogonality property of the covariance matrix by the removal or the attenuation of the signal subspaces, obtained through the subtraction of an opportune diagonal matrix from the covariance matrix. The FSPT aims at smoothing the narrowband covariance matrices of the entire set of frequency domain components, and it pursues this goal by minimizing the narrowband error contributions due to reverberation in the broadband frequency smoothing covariance matrix. We analyze the DOA estimation performance using speech signals with simulations and real acoustic data in reverberant conditions. The results show that the proposed SH-DU-FSPT has a DOA estimation performance comparable to that of high resolution state-of-the-art methods with a significant reduction of the computational cost, since the steering directional responses are computed on the broadband frequency smoothing covariance matrix.