Localization on the pushpin computing sensor network using spectral graph drawing and mesh relaxation

Abstract

This work approaches the problem of localizing the nodes of a distributed sensor network by leveraging distance constraints such as inter-node separations or ranges between nodes and a globally observed event. Previous work has shown this problem to suffer from false minima, mesh folding, slow convergence, and sensitivity to initial position estimates. Here, we present a localization system that combines a technique known as spectral graph drawing (SGD) for initializing node position estimates and a standard mesh relaxation (MR) algorithm for converging to finer accuracy. We describe our combined localization system in detail and build on previous work by testing these techniques with real 40-kHz ultrasound time-of-flight range data collected from 58 nodes in the Pushpin Computing network, a dense hardware testbed spread over an area of one square meter. In this paper, we discuss convergence characteristics, accuracy, distributability, and the robustness of this localization system.