Acoustic vector-sensor beamforming and Capon direction estimation

We examine the improvement attained by using acoustic vector-sensors for direction-of-arrival (DOA) estimation, instead of traditional 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: (1) an effective increase in signal-to-noise ratio due to a greater number of measurements of phase delays between sensors and (2) 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 array size, array shape, and SNR conditions under which the use of a vector-sensor array is most advantageous and to quantify that advantage. By extending the beamforming and Capon (1969) direction estimators to vector-sensors, we find that the vector-sensors' directional sensitivity removes all bearing ambiguities. In particular, even simple structures such as linear arrays can determine both azimuth and elevation, and spatially undersampled regularly spaced arrays may be employed to increase the aperture and, hence, the performance. Large sample approximations to the mean-square error matrices of the estimators are derived and their validity is assessed by Monte Carlo simulation.