https://hal-enac.archives-ouvertes.fr/hal-03848832Perrichon, RémiRémiPerrichonENAC - Ecole Nationale de l'Aviation CivileKlein, ThierryThierryKleinENAC - Ecole Nationale de l'Aviation CivileGendre, XavierXavierGendreISAE-SUPAERO - Institut Supérieur de l'Aéronautique et de l'EspaceA Geometric Approach to Study Aircraft Trajectories: the benefits of OpenSky Network ADS-B dataHAL CCSD2022air traffic managementtrajectorygeometryclusteringelastic distance[MATH] Mathematics [math][MATH.MATH-DG] Mathematics [math]/Differential Geometry [math.DG]Perrichon, Remi2022-11-11 06:51:502022-11-17 03:19:082022-11-16 10:06:04enPreprints, Working Papers, ...application/pdf1To date, the statistical analysis of aircraft trajectories has been under-exploited in the Airspace Traffic Management (ATM) literature. One reason is the need for advanced methods to tackle the high sampling irregularity and temporal correlation that both characterize a trajectory. Differential geometry provides a relevant framework to study trajectories. Modeling trajectories as parametrized curves, shape analysis allows to answer operational questions. This work presents a geodesic distance that rigorously defines and quantifies shape differences between aircraft trajectories. The key idea is to compare how the shape of a given trajectory changes from one popular data set (the Eurocontrol R&D data archive) to another one (OpenSky Network ADS-B data). Distances as well as geodesic paths are computed for a sample of flights departing from Toulouse-Blagnac (LFBO) and landing at Paris-Orly (LFPO) in 2019. Its use for clustering purposes is illustrated and discussed.