Tracking of Moving Targets Through Asynchronous Measures

Unmanned Aerial Vehicles (UAVs) have progressively gained interest in recent years due to the wide range of related applications, from aerial communications and autonomous flight to agriculture and logistics. However, accurate 3D localization is crucial for enabling these kinds of applications, and commonly used tracking algorithms are often performing unsatisfactorily in critical scenarios like urban canyons and environments, characterized by dense multipath and line of sight obstruction. In this work we derive a novel 3D tracking algorithm which, despite its mathematical simplicity, can efficiently track moving targets handling asynchronous arrival of the anchor measurements or obstructions of line-of-sight links and outperforming commonly used algorithms like the Extended Kalman Filter (EKF) and the Particle Filter (PF). The proposed algorithm tracks the 3D position, velocity, and acceleration of a moving target through the combination of range measurements, between the target and different anchors, which become available in numbers and time instants not necessarily ordered as usually assumed in these applications. We denote this condition as asynchronous measurements, meaning that the ranging measurements are not available from all the anchors and they refer to different positions of the UAV during the tracking. We also show that our estimator is optimal among the linear ones, meaning that within this class, it minimizes the estimation error variance. Finally, we explore the accuracy that can be achieved in simulated scenarios defined by realistic UAV altitudes, velocities, and trajectories, as well as typical ranging errors of wideband localization systems.