About Noneigenvector Source Localization Methods

Abstract

Previous studies dedicated to source localization are based on the spectral matrix algebraic properties. In particular, two noneigenvector methods, namely, propagator and Ermolaev and Gershman (EG) algorithms, exhibit a low computational load. Both methods are based on spectral matrix structure. The first method is based on the spectral matrix partitioning. The second one obtains directly an approximation of noise subspace using an adjustable power parameter of the spectral matrix and choosing a threshold value. It has been shown that these algorithms are efficient in nonnoisy or high signal to noise ratio (SNR) environments. However, both algorithms will be improved. Firstly, propagator is not robust to noise. Secondly, EG algorithm that requires the knowledge of a threshold value between largest and smallest eigenvalues, which are not available as eigendecomposition, is not performed. In this paper, we aim firstly at demonstrating the usefulness of QR and LU factorizations of the spectral matrix for these methods and secondly we propose a new way to reduce the computational load of a high resolution algorithm by estimating only the needed eigenvectors. For this, we adapt fixed-point algorithm to compute only the leading eigenvectors. We evaluate the performance of the proposed methods by a comparative study.