@article{Wu2024, 
author = {Pengcheng Wu and Jun Chen},
title = {Efficient Box Approximation for Data-Driven Probabilistic Geofencing},
year = {2024},
journal = {Unmanned Systems},
volume = {12},
number = {3},
pages = {511-522},
keywords = {Probabilistic geofence, box approximation, integer linear programming},
url = {https://www.sciopen.com/article/10.1142/S2301385024410024},
doi = {10.1142/S2301385024410024},
abstract = {Advanced Air Mobility (AAM) using electrical vertical take-off and landing (eVTOL) aircraft is an emerging way of air transportation within metropolitan areas. A key challenge for the success of AAM is how to manage large-scale flight operations with safety guarantees in high-density, dynamic, and uncertain airspace environments in real time. To address these challenges, we introduce the concept of a data-driven probabilistic geofence, which can guarantee that the probability of potential conflicts between eVTOL aircraft is bounded under data-driven uncertainties. To evaluate the probabilistic geofences online, Kernel Density Estimation (KDE) based on Fast Fourier Transform (FFT) is customized to model data-driven uncertainties. Based on the FFT-KDE values from data-driven uncertainties, we introduce an optimization framework of Integer Linear Programming (ILP) to find a parallelogram box to approximate the data-driven probabilistic geofence. To overcome the computational burden of ILP, an efficient heuristic algorithm is further developed. Numerical results demonstrate the feasibility and efficiency of the proposed algorithms.}
}