InferLoc: Hypothesis-based Joint Edge Inference and Localization in Sparse Sensor Networks

Ranging-based localization is a fundamental problem in the Internet of Things (IoT) and Unmanned Aerial Vehicles (UAV) networks. However, the nodes’ limited-ranging scope and users’ broad coverage purpose inevitably cause network sparsity or subnetwork sparsity. The performances of existing localization algorithms are extremely unsatisfactory in sparse networks. A crucial way to deal with the sparsity is to exploit the hidden knowledge provided by the unmeasured edges, which inspires this paper to propose a hypothesis-based Joint Edge Inference and Localization algorithm, i.e., InferLoc. InferLoc mines the Unmeasured but Inferable Edges (UIEs). Each UIE is an unmeasured edge, but it is restricted through other edges in the network to be inside a rigid component, so it has only a limited number of possible lengths. We propose an efficient method to detect UIEs and geometric approaches to infer possible lengths for UIEs in 2D and 3D networks. The inferred possible lengths of UIEs are then treated as multiple hypotheses to determine the node locations and the lengths of UIEs simultaneously through a joint graph optimization process. In the joint graph optimization model, to make the 0/1 decision variables for hypotheses selection differentiable, differentiable functions are proposed to relax the 0/1 selections, and rounding is applied to select the final length after the optimization converges. We also prove the condition when a UIE can contribute to sparse localization. Extensive experiments show remarkably better accuracy and efficiency performances of InferLoc than the state-of-the-art network localization algorithms. In particular, it reduces the localization errors by more than \(90\% \) and speeds up the convergence time over 100 times than the widely used G2O-based methods in sparse networks.