4D Trajectories: A functional data perspective

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.