An Improved Two-Stage RARE Algorithm for Mixed Far-Field and Near-Field Source Localization Under Unknown Mutual Coupling with the Uniform Linear Sensor Array

An Improved Two-Stage Rank Reduction (ITS-RARE) algorithm is proposed for the localization of mixed far-field (FF) and near-field (NF) sources under unknown mutual coupling with the uniform linear sensor array. Our algorithm includes two steps: in the first step, the eigenvectors are exploited when the rank reduction occurs at the right DOAs in our method. The eigenvectors corresponding to the smallest eigenvalues inherently represent the mutual coupling coefficient vectors. Based on it, the joint estimation of FF source DOAs and mutual coupling factors is achieved without pre-calibration. In the second step, after the DOA estimation of NF sources (NFSs), the ranges are estimated in closed form. As a result, the computational complexity is significantly reduced compared to existing methods. Furthermore, the full array aperture is preserved through the covariance matrix reconstruction (CMR) method during the FF/NF source classification. The simulation results demonstrate that the proposed algorithm is not only computationally efficient and effective in source classification but also preserves a larger effective aperture, thereby improving estimation accuracy.