A Geometric Approach to Study Aircraft Trajectories: the benefits of OpenSky Network ADS-B data

Rémi Perrichon (1) , Xavier Gendre (2) , Thierry Klein (1)

1 ENAC - Ecole Nationale de l'Aviation Civile
2 ISAE-SUPAERO - Institut Supérieur de l'Aéronautique et de l'Espace

To 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.

Mots clés: air traffic management; trajectory; geometry; clustering; elastic distance

Domaines: Mathématiques [math]; Géométrie différentielle [math.DG]

Rémi Perrichon, Xavier Gendre, Thierry Klein. A Geometric Approach to Study Aircraft Trajectories: the benefits of OpenSky Network ADS-B data. 2022. ⟨hal-03848832v2⟩