Predict with sufficient precision aircraft trajectories is essential for air traffic control systems, in particular to avoid conflicts between trajectories and collisions between aircraft. For many applications, it is not possible to be content with trajectory transmitted by the aircraft . This is particularly the case for many algorithms used in air conflict resolution and which requires testing a large number of alternative paths.

Most predictors use a mass-energy model (or "total energy") to predict aircraft future positions and velocities. Each plane is equivalent to its center of mass, which apply engine thrust, gravity, drag and aerodynamic lift. The aircraft dynamics is expressed in the form of differential equations. The future trajectory is calculated by integrating these equations over an interval of time, knowing the aircraft initial state(weight, thrust, position, speed, etc.), weather conditions (wind, temperature), and steering intentions (push Profile, target speed, road).

Unfortunately, most of these informations are either unknown by ground systems, either uncertain because of the wind and temperature. Mass and velocity data in profile climb are considered as sensitive information by some companies. The actual engine thrust, controlled by the position of the throttle, is not transmitted to the ground. With the establishment of air-ground links , all the necessary information will probably be transmitted to ground systems.

Pending an improvement in the data quality, several tracks can be explored to improve the trajectories prediction including :

- the use of statistical methods or learning methods (Machine Learning)
- the combination of such methods with the model of total energy (eg learning by mass or thrust)

Here are some recent work developped by MAIAA on "trajectory prediction" subject:

- Trajectories forecast by functional regression. It is a local linear regression in Sobolev space, based on a wavelet decomposition of aircraft trajectories
- Improved prediction of trajectories in relation to set-forecast provided by Météo France. This work is conducted in collaboration with Météo France.
- Prediction of tolerance intervals for the trajectories uphill. The objective is to obtain altitude intervals containing at least one given proportion (eg 95%) of occurrences of the aircraft presence, with some degree of certainty (eg 98%). This work is in collaboration with the IRIT.
- Learning parameters of the total energy model (mass, thrust profile) from the trajectory past point and a base of examples.This work is in collaboration with IRIT.
- Comparison between mass-energy model and regression methods (neural networks, linear regression, gradient boosting, Gaussian networks, etc.) to predict trajectories uphill. Working in collaboration with IRIT.