Person:

Gortler, Steven

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 article, 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 graphs (GGR), or certain vertex subsets in non-GGR graphs whose relative positions are fixed (which include vertex sets of GGR subgraphs). And this strategy 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 applications, we also present: (i) various techniques for improving the robustness of the algorithm in the presence of measurement noise; (ii) an algorithm for detecting certain subsets of graph vertices whose relative positions are fixed in any generic realization of the graph and robustly localizing these subsets of vertices, (iii) a strategy for reducing the number of measurements needed by the algorithm. We provide simulation results of our algorithm.

We present a novel approach to localization of sensors in a network given a subset of noisy inter-sensor distances. The algorithm is based on "stitching" together local structures by solving an optimization problem requiring the structures to fit together in an "As-Rigid-As-Possible" manner, hence the name ARAP. The local structures consist of reference "patches" and reference triangles, both obtained from inter-sensor distances. We elaborate on the relationship between the ARAP algorithm and other state-of-the-art algorithms, and provide experimental results demonstrating that ARAP is significantly less sensitive to sparse connectivity and measurement noise. We also show how ARAP may be distributed.