Improved Two-Step Constrained Total Least-Squares TDOA Localization Algorithm Based on the Alternating Direction Method of Multipliers

Abstract

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.