HGO: Hierarchical Graph Optimization for Accurate, Efficient, and Robust Network Localization

Inferring nodes' locations by inter-node measurements is a crucial problem in the IoT era. Despite the various approaches to this problem, obtaining accurate results is still challenging when the measurements are noisy, sparse, or uneven. Such unsatisfactory measurements are, however, inevitable for the general consideration of the deployment cost and the limited sensing scope.This paper proposes a Hierarchical Graph Optimization (HGO) framework to address the network localization problem when the measurements are sparse and noisy. It firstly efficiently extracts the dense sub-graphs and realizes their local structures in local coordinate systems. The local structures of dense components are rather accurate for the local sufficiency of the measurements. Then, the noises of the inter-edges that sparsely connect the dense sub-graphs are found as the main course of the network localization errors. A close-loop condition is derived and two denoising algorithms are proposed to set up linear equation arrays to correct the noises of these critical edges. After that, a projection algorithm is proposed to realize a smoothed backbone graph using the corrected critical edges, and finally, a hierarchical registration method is proposed to register the realized backbone and the dense sub-components to produce the global network structure. A parallel implementation is further developed, which speeds up HGO in large scale networks. Extensive simulations verify that HGO consistently outperforms existing network localization algorithms in terms of accuracy, efficiency, and reliability under various measurement settings.