# 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

## TL;DR

This paper introduces an improved algorithm for accurately locating both far-field and near-field sources in sensor arrays while accounting for unknown mutual coupling effects.

## Contribution

The novel ITS-RARE algorithm enables joint estimation of source directions and mutual coupling without calibration, preserving array aperture and reducing computational complexity.

## Key findings

- The algorithm achieves accurate DOA estimation for far-field sources and mutual coupling factors without pre-calibration.
- Near-field source ranges are estimated in closed form, reducing computational complexity.
- Simulation results show improved estimation accuracy and effective source classification.

## Abstract

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.