Source Localization Using TDOA with Sensor Position Errors Based on Constrained Total Least Squares and ADMM

Source localization for the nonlinear measurement model based on time difference of arrival (TDOA) measurements remains a vital research area and has been intensively studied for the past few decades. However, the localization accuracy decreases significantly as the random measurement noise becomes large. In addition, when sensors are mounted on moving platforms like vehicles or aircrafts, inevitable sensor position errors might pose more severe challenges on source localization accuracy. This paper proposes to construct a pseudo-linear measurement model that introduces both the TDOA measurement noise and the sensor position error firstly. Next, the constrained total least squares (CTLS) formulation is presented, and the iterative alternating direction method of multipliers (ADMM) is employed to solve the resulting optimization model. Simulation results show that the proposed method can approach Cramer Rao lower bound (CRLB) better and outperforms several existing methods when considering sensor position uncertainties and large TDOA measurement errors.