A Semidefinite Relaxation Method for Source Localization Using TDOA and FDOA Measurements

Localization by a sensor network has been extensively studied. In this paper, we address the source localization problem by using time-difference-of-arrival (TDOA) and frequency-difference-of-arrival (FDOA) measurements. Owing to the nonconvex nature of the maximum-likelihood (ML) estimation problem, it is difficult to obtain its globally optimal solution without a good initial estimate. Thus, we reformulate the localization problem as a weighted least squares (WLS) problem and perform semidefinite relaxation (SDR) to obtain a convex semidefinite programming (SDP) problem. Although SDP is a relaxation of the original WLS problem, it facilitates accurate estimate without postprocessing. Moreover, this method is extended to solve the localization problem when there are errors in sensor positions and velocities. Simulation results show that the proposed method achieves a significant performance improvement over existing methods.