Second-Order Cone Relaxation for TOA-Based Source Localization With Unknown Start Transmission Time

The time-of-arrival (TOA)-based source localization problem with unknown start transmission time is investigated. Without synchronization between the source and the sensors, the TOA measurement model has an unknown start transmission time in addition to the unknown source location. In this paper, we propose two different formulations to jointly estimate the start transmission time and the source location. We then apply the second-order cone relaxation technique to approximately solve the two problems. Simulation results demonstrate that the performance of the proposed methods can be close to the Cramer-Rao bound (CRB).