Quadratic constrained weighted least-squares method for TDOA source localization in the presence of clock synchronization bias: Analysis and solution

Abstract Time difference of arrival (TDOA) positioning is one of the widely used techniques for locating an emitter. Besides TDOA measurement errors, clock synchronization bias is an important factor that can degrade the localization accuracy. This paper focuses on TDOA localization using a set of receivers, where timing synchronization offsets exist among different receiver groups. A theoretical analysis is conducted and a new localization solution is developed for the case of imperfect time synchronization. The analysis starts with the Cramer–Rao bound (CRB) for the problem and derives the estimation bias and mean square error (MSE) using the classical quadratic constraint weighted least-squares (QCWLS) estimator, which does not consider synchronization errors. Additionally, an alternative performance measure, namely the localization success probability (SP), is introduced to evaluate the location accuracy. An explicit formula for calculating the localization success probability is presented. In addition, an improved quadratic constraint weighted least-squares estimator that accounts for synchronization errors is proposed to reduce the positioning errors. The Lagrange multiplier technique is used to solve this estimator. As a byproduct, a closed-form solution for the estimation of clock bias is also provided. First-order perturbation analysis reveals that the performance of the proposed estimates achieves the Cramer–Rao bound. Simulations corroborate the theoretical results and the good performance of the proposed method.