Performance Analysis and Dimension-Reduction Taylor Series Algorithms for Locating Multiple Disjoint Sources Based on TDOA Under Synchronization Clock Bias

Time difference of arrival (TDOA) localization technology, which does not require the time stamp of the source signals, is playing an increasingly important role in passive localization. Besides TDOA measurement noise and receiver position errors, another factor affecting TDOA positioning accuracy is the synchronization clock bias between different receivers. In this paper, the problem of TDOA source localization is considered under the condition that the TDOA measurements from multiple disjoint sources are subject to the same receiver position displacements and synchronization clock bias. First, based on the orthogonal projection matrix, the Cramér-Rao lower bounds of unknown parameters are derived in the presence of synchronization clock bias. Subsequently, according to the maximum likelihood (ML) criterion and Taylor series (TS) positioning method, the estimates obtained by ignoring the clock bias are shown to be biased, and the mean square error is found to increase quadratically with the 2-norm of the clock bias vector. To suppress the effect of synchronization clock bias, two dimension-reduction TS algorithms are proposed, and their asymptotically optimal performance is demonstrated under first-order error analysis. In addition, an ML-based closed-form solution for the clock bias vector is provided. Finally, simulation results verify the validity of the theoretical derivation and show the superiority of the proposed algorithms compared to the existing closed-form method.