Acoustic vector-sensor correlations in ambient noise

Most array-processing methods require knowledge of the correlation structur e of the noise. While such information may sometimes be obtained from measu rements 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 correlatio n structure under various environmental assumptions is therefore very impor tant. 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 co ncerning its spatial distribution: 1) azimuthal independence; 2) azimuthal independence and elevational symmetry; and 3) spherical isotropy. We also d erive expressions for the cross-covariances between all components of two s patially displaced AVSs in a narrowband-noise field under the same assumpti ons. 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 un iform linear AVS array to asses its beamforming capabilities and localizati on accuracy, via the Cramer-Rao bound, in isotropic and anisotropic noise.