To improve precision in source localization from a time difference of arrival (TDOA) that has large measurement errors, this paper proposes a TDOA positioning algorithm based on an improved two-step constrained total least-squares algorithm; the algorithm comprise an iterative technique based on the alternating direction method of multipliers (ADMM). The algorithm linearizes the obtained time difference observation equation, and by considering the influence of the TDOA measurement errors on its accuracy, it provides the optimal TDOA positioning model. It first transforms the initial unary optimization problem into a binary optimization problem by introducing intermediate variables. It then obtains a coarse estimate of the source position with ADMM. It subsequently calculates a measurement matrix through the coarse estimate and the finally uses ADMM again to find the final source position. Simulation results show that the proposed algorithm can approach Cramer-Rao lower bound (CRLB) better and outperforms several existing methods when there are large TDOA measurement errors.

This paper proposes a time difference of arrival (TDOA) passive positioning sensor selection method based on tabu search to balance the relationship between the positioning accuracy of the sensor network and system consumption. First, the passive time difference positioning model, taking into account the sensor position errors, is considered. Then, an approximate closed-form constrained total least-squares (CTLS) solution and a covariance matrix of the positioning error are provided. By introducing a Boolean selection vector, the sensor selection problem is transformed into an optimization problem that minimizes the trace of the positioning error covariance matrix. Thereafter, the tabu search method is employed to solve the transformed sensor selection problem. The simulation results show that the performance of the proposed sensor optimization method considerably approximates that of the exhaustive search method. Moreover, it can significantly reduce the running time and improve the timeliness of the algorithm.