A Distributed Algorithm for Sensor Network Localization with Limited Measurements of Relative Distance

Sensor network localization (SNL) is to determine physical coordinates of all sensors in a network given global coordinates of anchors and measurable distances among sensors and anchors. The SNL problem is generally NP-hard due to its nonconvex constraints. Many relaxation approaches have been proposed for solving SNL, among which semidefinite programming (SDP) relaxation is commonly viewed as an efficient method. However, since the rank constraint is ignored, the SDP relaxation requires a stringent graph condition to obtain the exact solution to SNL. In this paper, by considering the rank constraint, we solve SNL under a milder graph condition. To capture high efficiency and robustness, a distributed algorithm is also presented. We start with the centralized algorithm in which the rank constraint is converted into a linear matrix inequality and solved iteratively. Next, the SNL problem is decomposed into a group of subproblems and each subproblem is solved iteratively in a distributed manner. Furthermore, synchronous and asynchronous properties are analyzed for the proposed methods. Finally, simulation cases are presented to validate the improved localization accuracy, efficiency, and robustness by comparing to the state-of-the-art SNL method.