Data-driven zonotopic approximation for n-dimensional probabilistic geofencing

Advanced air mobility is a promising way of metropolitan air transportation. One critical concern that arises is how to ensure operational safety in high-dense, dynamic, and uncertain airspace environments in real time. To address this challenge, we seek a probabilistic geofence that bounds system states with high confidence. To identify the n-dimensional probabilistic geofence for arbitrary unknown uncertainties not limited to Gaussian ones, we present an online algorithm based on a data-driven approach of kernel density estimator. Considering the irregular shape of the probabilistic geofence, we formulate an optimization framework of integer linear programming whose solution determines a zonotope which provides a convex approximation for the probabilistic geofence. Leveraging this formulation, a heuristic algorithm is developed to find its solution efficiently without losing notable accuracy. This heuristic algorithm is tested on case studies that demonstrate it enjoys efficiency, accuracy, near-optimality, and robustness simultaneously.