A Novel Algorithm for Distributed Localization in Wireless Sensor Networks

Abstract

We present a novel algorithm for localization of Wireless Sensor Networks (WSNs) called Distributed Randomized Gradient Descent (DRGD) and prove that in the case of noise-free distance measurements, the algorithm converges and provides the true location of the nodes. For noisy distance measurements, the convergence properties of DRGD are discussed and an error bound on the location estimation error is obtained. In contrast to several recently proposed methods, DRGD does not require that the blind nodes be contained in the convex hull of the anchor nodes, and it can accurately localize the network with only a few anchors. Performance of DRGD is evaluated through extensive simulations and compared with three other algorithms, namely, the relaxation-based Second-Order Cone Programming (SOCP), the Simulated Annealing (SA), and the Semi-Definite Programing (SDP). Similar to DRGD, SOCP and SA are distributed algorithms, whereas SDP is centralized. The results show that DRGD successfully localizes the nodes in all the cases, whereas in many cases SOCP and SA fail. Finally, we present a modification of DRGD for mobile WSNs and demonstrate the efficacy of DRGD for localization of mobile networks with several simulation results.