ADMM-Based Sensor Network Localization Using Low-Rank Approximation

In this paper, we present an efficient localization algorithm for sensor networks using range information. Since each sensor can only communicate with its neighbors, the Euclidean distance matrix (EDM), composed by squared distances between each pair of sensors, is incomplete. The first step of the proposed algorithm is to fulfill the EDM completion and relative maps of sensor networks are then achieved by the multidimensional scaling technique. Besides the EDM, the centralized Gram matrix of sensors’ coordinates is also used to model the localization problem. Compared with other EDM-based localization algorithms, mathematical properties of both the EDM and the Gram matrix are appropriately exploited so as to improve the estimation accuracy. The resulting localization model is formulated as a semidefinite programming problem. An alternating direction method of multipliers is further developed to enhance the scalability of the proposed algorithm. The numerical experiments demonstrate that the proposed algorithm can effectively improve the estimation accuracy of both the EDM completion and the final localization.