Low-Rank Matrix Completion via Nonconvex Rank Approximation for IoT Network Localization

Accurate node localization is essential for many Internet of Things (IoT) applications. However, incomplete and noisy distance measurements often degrade the reliability of the Euclidean Distance Matrix (EDM), which is critical for range-based localization. To address this issue, a Low-Rank Matrix Completion approach based on nonconvex rank approximation (LRMCN) is proposed to recover the true EDM. First, the observed EDM is decomposed into a low-rank matrix representing the true distances and a sparse matrix capturing noise. Second, a nonconvex surrogate function is used to approximate the matrix rank, while the l1-norm is utilized to model the sparsity of the noise component. Third, the resulting optimization problem is solved using the Alternating Direction Method of Multipliers (ADMMs). This enables accurate recovery of a complete and denoised EDM from incomplete and corrupted measurements. Finally, relative node locations are estimated using classical multi-dimensional scaling, and absolute coordinates are determined based on a small set of anchor nodes with known locations. The experimental results show that the proposed method achieves superior performance in both matrix completion and localization accuracy, even in the presence of missing and corrupted data.