Mixed-field source localization based on robust matrix propagator and reduced-degree polynomial rooting

Abstract

This paper develops two new algorithms based on multiple signal classification (MUSIC) and matrix propagator for near-field (NF) and far-field (FF) source localization, which substantially reduce the computational complexities and can be applied no matter whether the source number is known as a priori. In the developed algorithms, two special fourth-order cumulant (FOC) matrices are constructed. Then the noise subspace is obtained by incorporating lower-upper (LU) decomposition into the matrix propagator approach. This avoids the computationally burdensome eigenvalue decomposition (EVD) or singular value decomposition (SVD) as well as the dependence of source number. The direction-of-arrivals (DOAs) of FF and NF sources are distinguished by the oblique projection and then estimated based on the MUSIC spectrum. To further improve the computational efficiency, an alternating root-propagator scheme is proposed to determine DOAs, where the real lower-degree polynomial is formulated, which increases the computational speed by a factor about eight compared to the standard root-MUSIC. Finally, the NF ranges are calculated from the FOC and the DOA estimates via the least square (LS) criterion. The effectiveness and performance of the proposed approach are validated by using numerical simulation.