Doppler Shift Based Target Localization Using Semidefinite Relaxation

Abstract

We propose a novel approach to the target localization problem using Doppler frequency shift measurements. We first reformulate the maximum likelihood estimation (MLE) as a constrained weighted least squares (CWLS) estimation, and then perform the semidefinite relaxation to relax the CWLS problem as a convex semidefinite programming (SDP) problem, which can be efficiently solved using modern convex optimization methods. Finally, the SDP solution can be used to initialize the original MLE which can provide estimates achieve the Cramer-Rao lower bound accuracy. Simulations corroborate the good performance of the proposed method.