Bias Reduced Semidefinite Relaxation Method for Multistatic Localization in the Absence of Transmitter Position and Its Synchronization

This paper addresses the challenging problem of multistatic localization of a stationary object with a set of synchronized receivers, when the transmitter position is unknown and the synchronization with the transmitter is unavailable. Using the time delay measurements from the direct and indirect paths, we propose to jointly estimate the object and transmitter positions together with the clock offset. To accomplish the joint estimation, we first formulate a non-convex constrained weighted least squares (CWLS) minimization problem, where the approximations involved could introduce a large amount of estimation bias. We then extend the formulation to arrive at a bias-reduced CWLS (BR-CWLS) problem that has the ability of reducing the bias. The BR-CWLS problem, which is non-convex, is handled by applying the semidefinite relaxation technique to reach a convex semidefinite program that can be directly solved by a software package. Simulation results demonstrate the good performance of the proposed method in achieving the CRLB performance and reducing the bias.