Accurate Localization of Multiple Sources Using Semidefinite Programming Based on Incomplete Range Matrix

We address the problem of locating multiple sources from the Euclidean distance matrix (EDM), which can be obtained from the received signal strength or time of arrival measurements. In EDM-based localization, EDM is usually corrupted by some inevitable factors, such as non-line-of-sight propagation, hardware failures, and strong interference. Note that EDM is a low-rank matrix but not a positive semidefinitematrix, classical semidefinite programming (SDP)-based algorithms cannot be implemented directly to handle the case. We derive an SDP-based low-rank solution to reconstruct EDM based on the semidefinite embedding lemma. Based on the recovered EDM, unlike some existing conventional non-convex estimators, a semidefinite relaxation method is developed to fix the locations of sources. In particular, we relax the non-convex localization problem into convex one by using square range information. Numerical simulation results demonstrate that the proposed algorithm performs higher accuracy while increasing slightly computational complexity as compared with the other existing approaches.