Semidefinite programming approaches for source localization problems

This paper addresses the problems of locating a source from the received signal time of arrival (TOA) or time difference of arrival (TDOA) collected using a group of collaborative wireless sensors. Based on the TOA and TDOA measurement models, we present, respectively, two constrained weighted least squares (CWLS) estimators, which are difficult to be solved directly due to their nonconvex nature. However, by performing the semidefinite relaxation technique, each of the CWLS problems can be relaxed into a semidefinite programming problem (SDP), which can be efficiently solved using modern convex optimization algorithms. Moreover, these relaxations are proved to be tight, and hence guarantee the good performance. Simulation results corroborate the theoretical results and good performance of the proposed methods.