Joint localization of multiple sources from incomplete noisy Euclidean distance matrix in wireless networks

One major challenge of massive wireless networks is to identify the locations of source nodes from partially observed and noisy distance information. This is especially important for wireless sensor networks (WSN) and wireless local area networks (WLAN). In this paper, we propose a unified localization framework of multiple sources from an Euclidean distance matrix (EDM) with noise and outliers both in WSN and WLAN scenarios. We first develop a semidefinite programming (SDP) based low rank matrix completion (LRMC) estimator by using the semidefinite embedding lemma to recover EDM. Based on our recovered EDM, two robust localization estimators, namely, semidefinite relaxation localization (SDRL) and weighted semidefinite relaxation localization (WSDRL), are derived to efficiently relax our non-convex localization problem into a convex one, and yield more accuarate location estimates. As compared with existing techniques, our proposed techniques are more robust to noise and outliers with higher accuracies both in EDM recovery and source localization. Simulations and real data experiments are included to evaluate the performance of the proposed algorithms by comparing them with some existing methods.