A Localization Algorithm Based on Alternating Direction Multiplier Method

Over the past few years, as 5G communication has advanced, the demand for positioning based on sensor networks has been increasing. Aiming at the problem of low accuracy of traditional analytical localization algorithms when the TDOA measurement noise is large, a TDOA iterative localization method based on improved constrained total least squares (ICTLS) is proposed. Firstly, the constrained total least squares (CTLS) solution with TDOA measurement errors is analyzed and deduced, and the well-performance of the ADMM algorithm in solving non-convex optimization problems is utilized to improve the traditional CTLS solution. The estimated constraint relationship between vector internal elements by the traditional CTLS method is used as the new constraint, and the objective optimization function is modified to obtain the form of the improved CTLS solution. According to the principle of the ADMM method, the improved CTLS solution is rewritten into an augmented Lagrangian function form to obtain an unconstrained localization optimization problem, and then the target position is estimated through ADMM iterations. Finally, the results of the experiments demonstrate that the proposed ICTLS algorithm has better resistance to measurement noise and a smaller RMSE value than CTLS algorithm and TSWLS algorithm When the standard deviation of TDOA measurement noise is poor. At the same time, when the noise is small, the RMSE value of the ICTLS algorithm can closely match the CRLB curve, indicating good positioning performance. Overall, the proposed algorithm shows good positioning performance in sensor networks with a small number of anchor nodes and large TDOA measurement errors.