Power method for robust diagonal unloading localization beamforming

We propose a robust version of the diagonal unloading (DU) beamforming for the acoustic source localization problem in high noise conditions. The DU beamformer exploits the subspace orthogonality property by the removal or the attenuation of the signal subspaces, obtained through the subtraction of an opportune diagonal matrix from the covariance matrix. As a result, it provides high-resolution directional response with low computational complexity. We show that a robust DU beamformer can be implemented by subtracting the largest eigenvalue of the estimated covariance matrix from the diagonal elements, and that this implementation is valid in general (i.e., for both the single-source and the multiple-source case). We propose the use of the power method for the estimation of the largest eigenvalue in the DU procedure. We show with numerical simulations that the proposed method improves the localization performance in high noise conditions without substantial increment of the computational cost. Applications for this method include a number of scenarios involving multirotor aerial systems due to its robustness to the noise and its low computational complexity.