Acoustic vector-sensor beamforming and capon direction estimation

We examine the improvement afforded by using acoustic vector sensors for direction-of-arrival (DOA) estimation, instead of pressure sensors, via optimal performance bounds and particular estimators. By examining the Cramer-Rao bound in the case of a single source, we show that a vector-sensor array's smaller estimation error is a result of two distinct phenomena: i) an effective increase in signal-to-noise ratio due to a greater number of measurements of the phase delays between sensors and ii) direct measurement of the DOA information contained in the structure of the velocity field due to the vector sensors' directional sensitivity. Separate analysis of these two phenomena allows us to determine the conditions under which the use of a vector-sensor array is most advantageous and to quantify that advantage. Necessary and sufficient conditions for decoupled DOA parameters and sufficient conditions for isotropic performance are obtained. By adapting the beamforming and Capon direction estimators to vector sensors, we find that the vector sensors' directional sensitivity removes all ambiguities. In particular, linear arrays can determine both azimuth and elevation, and undersampled regular arrays may be employed to increase aperture and, hence, performance. Large sample approximations to the mean-square error matrices of the estimators are derived, and their validity is assessed by Monte Carlo simulation.