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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. <\/jats:p>","DOI":"10.1142\/s2301385024410024","type":"journal-article","created":{"date-parts":[[2023,7,28]],"date-time":"2023-07-28T16:36:35Z","timestamp":1690562195000},"page":"511-522","source":"Crossref","is-referenced-by-count":2,"title":["Efficient Box Approximation for Data-Driven Probabilistic Geofencing"],"prefix":"10.1142","volume":"12","author":[{"given":"Pengcheng","family":"Wu","sequence":"first","affiliation":[{"name":"Department of Mechanical and Aerospace Engineering, University of California San Diego, La Jolla, CA 92093, USA"},{"name":"Department of Aerospace Engineering, San Diego State University, San Diego, CA, 92182, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9896-6898","authenticated-orcid":false,"given":"Jun","family":"Chen","sequence":"additional","affiliation":[{"name":"Department of Aerospace Engineering, San Diego State University, San Diego, CA, 92182, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"219","published-online":{"date-parts":[[2023,9,15]]},"reference":[{"key":"S2301385024410024BIB001","doi-asserted-by":"publisher","DOI":"10.1142\/S2301385023500140"},{"key":"S2301385024410024BIB002","first-page":"1","author":"Fusic S. 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