Aircraft trajectory forecasting using local functional regression in Sobolev space

• We construct an algorithm of 4D short to mid-term aircraft trajectory prediction.
• A novel approach based on local functional linear regression using wavelets.
• We use localization of aircraft trajectories in order to classify them on tubes.
• Wavelet decomposition provides a fast version of PCA.
• A Sobolev space was used to take into account the speed of aircraft.

This paper considers the problem of short to mid-term aircraft trajectory prediction, that is, the estimation of where an aircraft will be located over a 10–30 min time horizon. Such a problem is central in decision support tools, especially in conflict detection and resolution algorithms. It also appears when an air traffic controller observes traffic on the radar screen and tries to identify convergent aircraft, which may be in conflict in the near future. An innovative approach for aircraft trajectory prediction is presented in this paper. This approach is based on local linear functional regression that considers data preprocessing, localizing and solving linear regression using wavelet decomposition. This algorithm takes into account only past radar tracks, and does not use any physical or aeronautical parameters. This approach has been successfully applied to aircraft trajectories between several airports on the data set that is one year air traffic over France. The method is intrinsic and independent from airspace structure.