Power estimation of acoustical sources by an array of microphones

The problem of estimating the power of signals impinging an array of sensors when the arrival directions are known is presented. It is assumed that the signal field at the array is comprised of P independent plane-wave arrivals from known directions. In practice the directions of arrival are rarely known exactly, however this difficulty can be overcome by using the standard MUSIC (Multiple Signal Classification) algorithm, which constitutes an angular pseudo-spectrum and an indicator of directions of arrival of different signals. The problem then reduces to the estimation of the signal powers from each of the P directions. Five estimators are presented in this communication. The conventional beamformer, the Capon estimator, the robust Capon estimator, the covariance vector estimator and the least squares fit estimator of the observed cross-spectral matrix of the array. Numerical and experimental results are presented showing that the performances of the covariance vector estimators are better than other estimators.