Sensor Network Localization Using Sensor Perturbation

Sensor network localization is an instance of the NP-HARD graph realization problem. Thus, methods used in practice are not guaranteed to find the correct localization, even if it is uniquely determined by the input distances. In this paper, we show the following: if the sensors are allowed to wiggle, giving us perturbed distance data, we can apply a novel algorithm to realize arbitrary generically globally rigid (GGR) graphs (or maximal vertex subsets in non-GGR graphs whose relative positions are fixed). And this algorithm works in any dimension. In the language of structural rigidity theory, our approach corresponds to calculating the approximate kernel of a generic stress matrix for the given graph and distance data. To make our algorithm suitable for real-world application, we present techniques for improving the robustness of the algorithm under noisy measurements, and a strategy for reducing the required number of measurements.