Near-Field Source Localization in Nonuniform Noise: An Efficient Symmetric Matrix Factorization-Based Approach

This paper investigates the near-field source localization of multiple narrowband signals in the presence of unknown nonuniform noise with an arbitrary diagonal covariance matrix. From a covariance-fitting perspective, we reformulate the near-field localization problem as a joint symmetric matrix factorization and the estimation of nonuniform noise variances. This reformulation explicitly accounts for noise heterogeneity in the covariance structure, thereby avoiding noise mismodeling and enabling robust near-field localization for nonuniform noise. To solve the intractable symmetric matrix factorization problem, we develop a computationally efficient iterative algorithm based on the block majorization-minimization principle. The proposed algorithm has light per-iteration complexity and admits a closed-form iteration update. Furthermore, we also derive the Cramér-Rao bound (CRB) for near-field localization under nonuniform noise. Extensive numerical experiments demonstrate that the proposed approach outperforms the existing state-of-the-art near-field localization methods and closely matches the CRB while maintaining strong robustness against severe nonuniform noise.