TDOA-Based Passive Localization for Multidisjoint Sources Without Time Synchronization

Source localization based on time difference of arrival (TDOA) measurements faces significant challenges when sensors operate asynchronously with unknown and mutually independent clock offsets. Most existing approaches either assume a uniform clock offset for all sensors relative to a reference sensor, or cluster sensors with intra-cluster synchronization and inter-cluster asynchrony, which does not generalize to fully asynchronous networks. This paper addresses the problem where each sensor maintains an independent clock, resulting in unique clock offsets for every sensor pair, while leveraging the key observation that these offsets remain identical across TDOA observations from multiple disjoint sources. By exploiting this shared clock offset structure, we formulate the joint estimation of source locations and sensor clock offsets as a unified optimization problem. We first analyze the Cramér-Rao lower bound (CRLB), demonstrating that incorporating the shared nature of clock offsets across sources fundamentally improves both synchronization and localization accuracy. To efficiently solve the resulting highly nonlinear estimation problem, we propose a three-stage framework. The first stage employs a semidefinite programming (SDP) relaxation to jointly estimate sensor clock offsets and source positions, yielding sufficiently accurate clock offset estimates for TDOA correction. In the second stage, the refined TDOA measurements enable a source-only SDP, providing coarse position estimates, which are subsequently refined via a Gauss-Newton maximum likelihood iterative procedure. This approach achieves near-optimal estimation performance, attaining the CRLB under moderate noise conditions. Extensive simulations validate the superiority of the proposed method in both localization accuracy and robustness, outperforming conventional maximum likelihood and state-of-the-art SDP-based algorithms across a wide range of challenging scenarios.