Formation Tracking in Sparse Airborne Networks

A swarm of unmanned air vehicles (UAVs) may form a dynamic 3-D network whose topology changes frequently. Tracking the geometric formation of the network is a critical problem. Recent advantage of wireless ranging technologies (e.g., ultrawideband) enables inter-UAV distance measurement up to hundreds meters with errors in centimeter level. This makes it possible to track the network topology by the partially measured distance matrix among the UAVs, which is known as the <italic>formation tracking</italic> problem. But the measured distances are generally sparse and noisy, and the topology of UAV network is changing continuously. These cause the formation tracking highly challenging. Existing methods are generally fragile to the measurement noises and network sparsity. This paper exploits a fact that well-connected subcomponents, whose local structures can be calculated reliably, exist widely because the unevenness of node distribution in sparse networks. Therefore, a weighted component stitching (WCS) method to find the reliable components and stitch their local structures with weights is proposed for calculating the formation of the network accurately. In particular, we propose efficient two-center four-vertex-connected star-graph (2-4-star) detection and merging algorithms to extract the reliable global rigid components. A WCS algorithm and a weighted component-based Kalman filter algorithm with complexity both <inline-formula> <tex-math notation="LaTeX">$O(n^{3})$ </tex-math></inline-formula> are proposed for robust formation tracking in <inline-formula> <tex-math notation="LaTeX">$n$ </tex-math></inline-formula> vertex UAV networks. Extensive experiments were conducted, showing that the proposed methods can improve the formation tracking accuracy 21&#x0025;&#x2013;48&#x0025; over existing state-of-the-art methods, especially in sparse, noisy UAV networks under different parameter settings.