Acoustic vector-sensor correlations in ambient noise

Most array-processing methods require knowledge of the correlation structure of the noise. While such information may sometimes be obtained from measurements made when no sources are present, this may not always be possible. Furthermore, measurements made in-situ can hardly be used to analyze system performance before deployment. The development of models of the correlation structure under various environmental assumptions is therefore very important. In this paper, we obtain integral and closed form expressions for the auto- and cross-correlations between the components of an acoustic vector sensor (AVS) for a wideband-noise field, under the following assumptions concerning its spatial distribution: 1) azimuthal independence; 2) azimuthal independence and elevational symmetry; and 3) spherical isotropy. We also derive expressions for the cross-covariances between all components of two spatially displaced AVSs in a narrowband-noise field under the same assumptions. These results can be used to determine the noise-covariance matrix of an array of acoustic vector sensors in ambient noise. We apply them to a uniform linear AVS array to asses its beamforming capabilities and localization accuracy, via the Cramér-Rao bound, in isotropic and anisotropic noise.