Novel closed-form auxiliary variables based algorithms for sensor node localization using AOA

Node localization is a key issue for wireless sensor networks (WSNs). The triangulation method and the maximum likelihood (ML) estimator are usually adopted for angle of arrival (AOA) based node localization in WSNs. However, the localization accuracy of the triangulation is low, and the ML estimator requires a good initialization close to the true location to avoid the divergence problem. In this paper, we develop two efficient closed-form AOA based localization algorithms derived from effective auxiliary variables based method. First, we formulate the node localization problem as a linear least squares problem using auxiliary variables. Based on its closed-form solution, a new auxiliary variables based pseudo-linear estimator (AVPLE) is developed. Then, we further propose an auxiliary variables based total least square (AVTLS) estimator to improve the localization accuracy. In addition, we investigate the impact of the orientation of the unknown node on estimation performance of the new algorithms. Simulation results demonstrate that the new algorithms achieve much higher localization accuracy than the triangulation method and also avoid local minima and divergence problem in ML estimator. Moreover, the AVTLS estimator has higher localization accuracy than the AVPLE, and its localization accuracy remains robust when the orientation angle of the unknown node varies from 0 to 180 degrees.