Localization of sensor networks via low rank approximation

Abstract

In this paper, a novel algorithm is proposed for locating sensor networks. In general, Euclidean distance matrices are incomplete due to their limited communication power. Furthermore, distance measurements are contaminated by noise. For the purpose of localization, unknown distances are first estimated via low rank approximation. Relative coordinates of sensors are then obtained by eigenvalue decomposition of the Gram matrix, which is constructed by the Euclidean distance matrix estimated. To improve the localization accuracy, subnetworks are constructed by each sensor and its neighbors. Since neighboring sensors of each sensor are more prone to communicate with each other, the local Euclidean distance matrix could be denser than the global one, leading to a more accurate estimate. Another advantage of the proposed algorithm is that it can be implemented in a distributed manner, which is desirable for sensor networks without central computational unit. Two sets of simulations demonstrate that the proposed algorithm can achieve better localization accuracy than other localization algorithms using global Euclidean distance matrices.