Diagonal Unloading Beamforming for Source Localization

In sensor array beamforming methods, a class of algorithms commonly used to estimate the position of a radiating source, the diagonal loading of the beamformer covariance matrix is generally used to improve computational accuracy and localization robustness. This paper proposes a diagonal unloading (DU) method which extends the conventional response power beamforming method by imposing an additional constraint to the covariance matrix of the array output vector. The regularization is obtained by subtracting a given amount of white noise from the main diagonal of the covariance matrix. Specifically, the DU beamformer aims at subtracting the signal subspace from the noisy signal space and it is computed by constraining the regularized covariance matrix to be negative definite. It is hence a data-dependent covariance matrix conditioning method. We show how to calculate precisely the unloading parameter, and we present an eigenvalue analysis for comparing the proposed DU beamforming, the minimum variance distortionless response (MVDR) filter and the multiple signal classification (MUSIC) method. Theoretical analysis and experiments with acoustic sources demonstrate that the DU beamformer localization performance is comparable to that of MVDR and MUSIC. Since the DU beamformer computational cost is comparable to that of a conventional beamformer, the proposed method can be attractive in array processing due to its simplicity, effectiveness and computational efficiency.