A Geometric Approach to Study Aircraft Trajectories: The Benefits of OpenSky Network ADS-B Data

Abstract

To date, statistical analyses of aircraft trajectories have been under-exploited in the Airspace Traffic Management (ATM) literature. One reason is the need for advanced methods to tackle the high sampling irregularities and temporal correlations that both characterize trajectories. Differential geometry provides a relevant framework to study trajectories. By modeling trajectories as parameterized curves, shape analysis allows us 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 and geodesic paths are computed for a sample of flights that departed from Toulouse–Blagnac (LFBO) and landed at Paris–Orly (LFPO) in 2019. Its use for clustering purposes is illustrated and discussed.

Keywords

• air traffic management
• trajectory
• geometry
• clustering
• elastic distance