Moving Source Localization Using Toa And Foa Measurements With Imperfect Synchronization

The clock bias and drift caused by imperfect time synchronization is a practical issue in localization problems. In this paper, we address the moving source localization problem using time-of-arrival and frequency-of-arrival measurements, where imperfect time synchronization is present. We transform the measurement models and formulate a nonlinear and non-convex weighted least squares (WLS) problem to jointly estimate the unknown source position, velocity, clock bias and drift. We then apply semidefinite relaxation (SDR) to the non-convex WLS problem to obtain a convex semidefinite program, which can be solved efficiently. We show through theoretical mean square error analysis that the WLS solution is able to attain the Cramer-Rao lower bound (CRLB) under small Gaussian noise condition. Simulation results show that the proposed SDR method has comparable performance with the maximum likelihood estimation method, and thus achieves the CRLB accuracy, when the noise is not too large. (C) 2021 Elsevier B.V. All rights reserved.