A Multivariate Functional Data Analysis of Aircraft Trajectories

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

1 ENAC - Ecole Nationale de l'Aviation Civile
2 IMT - Institut de Mathématiques de Toulouse UMR5219

While advanced methods for functional data analysis have recently been developed in the literature, applications to aircraft trajectories have remained scarce, despite operational relevance. One reason is the practical difficulties affiliated with the multivariate nature of trajectories and associated physical constraints. Indeed, an aircraft trajectory usually involves three dimensions in space (longitude, latitude, altitude) but also weather values (say wind speed and direction), each dimension having its specificities. To name a few, smoothing altitude values requires to ensure both non-negativity and boundary constraints. Wind directions have support on the unit circle. Additional to constrained smoothing challenges, phase variations are to be taken into account as flights are never of the same duration. To tackle these issues, two smoothing methods respectively based on constrained splines and asymmetric kernels are implemented on real data. For each approach, two strategies to handle the circular nature of wind directions are compared. Registration is performed. A joint pointwise test is proposed to demonstrate that delayed flights have experienced less favorable wind conditions.

Mots clés: functional data analysis; curve registration; constraint smoothing; two sample tests; aircraft trajectories

Domaines: Statistiques [math.ST]

Remi Perrichon, Xavier Gendre, Thierry Klein. A Multivariate Functional Data Analysis of Aircraft Trajectories. 2023. ⟨hal-03667323v2⟩