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