4D trajectories : a functional data perspective

Stéphane Puechmorel (1) , Daniel Delahaye (2)

1 ENAC - Ecole Nationale de l'Aviation Civile
2 DGAC - Direction Générale de l'Aviation Civile

3D or 4D trajectories are fundamental objects within the frame of ATM and can be defined as mappings from a bounded interval to the space R3. However, this functional aspect is almost never used in applications. A great improvement over existing procedures for statistical analysis of trajectories can be obtained by explicitly considering trajectory data as functional data. Since raw functional data is by essence infinite dimensional, no computation can be made unless a finite representation has been found: all the complexity of functional data analysis is hidden in this stage. The present paper will first analyze the functional aspect of trajectories in order to extract operationally relevant quantities then will give a way of representing optimally aircraft trajectories with a finite number of parameters, allowing further processing. Applications to trajectory prediction and classification will be briefly discussed at the end.

Mots clés: aerospace control; aircraft; data analysis; data mining; databases; diffusion tensor imaging; research and development; statistical analysis; statistics; trajectory

Domaines: Optimisation et contrôle [math.OC]

Stéphane Puechmorel, Daniel Delahaye. 4D trajectories : a functional data perspective. DASC 2007, 26th Digital Avionics Systems Conference, Oct 2007, Dallas, United States. pp 1.C.6-1 - 1.C.6-12, ⟨10.1109/DASC.2007.4391832⟩. ⟨hal-00938181⟩