A robust EDM optimization approach for 3D single-source localization with angle and range measurements

Accurate source localization in Multi-Platform Radar Networks (MPRNs) benefits from jointly exploiting range and angle measurements, especially under noisy conditions. In this paper, we propose a robust Euclidean distance matrix (EDM) optimization model for 3D single-source localization (3DSSL), which integrates range measurements and angle information into a unified distance-based formulation and naturally supports the least absolute deviation (ℓ₁-norm) criterion. In this formulation, the angle information is incorporated through lower and upper bounds on the source-to-sensor distances, which form box constraints in the EDM model. This is achieved by reducing the 3D angle constraints to two-dimensional nonlinear optimization subproblems, whose global minimum and maximum values provide the required distance bounds. To solve the resulting rank-constrained EDM problem, we develop an efficient algorithm based on the majorization penalty method. Extensive numerical experiments confirm that the proposed EDM model outperforms leading vector-based solvers in localization accuracy while maintaining competitive computational efficiency, particularly in low Signal-to-Noise Ratio (SNR) scenarios.