Semidefinite Relaxation Method for Moving Object Localization Using a Stationary Transmitter at Unknown Position

This paper addresses the multistatic localization of a moving object in position and velocity using time delay (TD) and Doppler frequency shift (DFS) measurements, where the position of the transmitter is unknown and has not yet been synchronized with the receivers. Based on the TD and DFS measurements from the direct and indirect paths, we formulate a non-convex weighted least squares (WLS) minimization problem, and then apply semidefinite relaxation (SDR) to relax the WLS problem into a convex semidefinite program. Simulation results show that the proposed SDR method is able to achieve the Cramer-Rao lower bound accuracy under mild Gaussian noise condition and outperforms the existing method.