A facial reduction approach for the single source localization problem

The single source localization problem (SSLP) appears in several fields such as signal processing and global positioning systems. optimization of SSLP is nonconvex difficult to find its globally optimal solution. It can be reformulated a rank constrained Euclidean distance matrix (EDM) completion with number equality constraints. In this paper, we propose facial reduction approach solve an EDM problem. For the constraints fixed distances between sensors, reduce them face cone derive closed formulation face. We prove constraint nondegeneracy for each feasible point resulting without constraint, which guarantees quadratic convergence semismooth Newton’s method. To tackle apply majorized penalty developed by Zhou et al. (IEEE Trans Signal Process 66(3):4331-4346, 2018). Numerical results verify fast speed proposed while giving comparable quality solutions other methods.