Bias reduction for TDOA localization in the presence of receiver position errors and synchronization clock bias

Time difference of arrival (TDOA) localization does not require time stamping of the source signal and is playing an increasingly important role in passive location. In addition to measurement noise, receiver position errors and synchronization clock bias are two important factors affecting the performance of TDOA positioning. This paper proposes a bias-reduced solution for passive source localization using TDOA measurements in the presence of receiver position errors and synchronization clock bias. Like the original two-step weighted least-squares solution, the new technique has two stages. In the first stage, the proposed method expands the parameter space in the weighted least-squares (WLS) formulation and imposes a quadratic constraint to suppress the bias. In the second stage, an effective WLS estimator is given to reduce the bias generated by nonlinear operations. With the aid of second-order error analysis, theoretical biases for the original solution and proposed bias-reduced solution are derived, and it is proved that the proposed bias-reduced method can achieve the Cramér–Rao lower bound performance under moderate Gaussian noise, while having smaller bias than the original algorithm. Simulation results exhibit smaller estimation bias and better robustness for all estimates, including those of the source position, refined receiver positions, and clock bias vector, when the measurement noise or receiver position error increases.