Semidefinite Relaxation for Source Localization by TOA in Unsynchronized Networks

This letter addresses the time-of-arrival based localization problem when the source and sensors are not synchronized, whereby an unknown transmission time is introduced. A non-convex weighted least squares (WLS) minimization problem is first formulated to jointly estimate the source position and the unknown transmission time by transforming the measurement model, and then semidefinite relaxation is applied to relax the WLS problem as a convex semidefinite program (SDP). The relaxed SDP problem is always tight and thus the optimal solution of the WLS problem can always be obtained. The proposed method is then extended to the moving source localization scenario, where the source velocity is assumed to be a constant for a sufficiently small observation period. Simulation results show that the proposed method is able to reach the Cramer-Rao lower bound accuracy when the noise is not very large.