Sensor Network Localization via Distributed Randomized Gradient Descent

A novel algorithm referred to as distributed randomized gradient descent (DRGD), is presented for the localization of nodes in a wireless sensor network. It is proven that, in the case of noise-free measurements, the algorithm converges and provides the true location of the nodes. In the case of noisy distance measurements the convergence properties of the algorithm are discussed and an error bound on the location estimation error is obtained. In contrast to several recently proposed methods, DRGD converges for only a few anchor nodes and the blind nodes do not need to be contained in the convex hull of the anchor nodes. Through extensive simulations and for several networks with and without distance errors, the performance of the proposed algorithm is evaluated and compared with three other recently proposed 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 the proposed algorithm successfully localizes the nodes in all the cases whereas, in most cases where only a few anchors are used, SOCP and SA fail.