  This paper presents a model based on an hybrid system to numerically simulate
the climbing phase of an aircraft. This model is then used within a trajectory
prediction tool. Finally, the Covariance Matrix Adaptation Evolution Strategy
(CMA-ES) optimization algorithm is used to tune five selected parameters, and
thus improve the accuracy of the model. Incorporated within a trajectory
prediction tool, this model can be used to derive the order of magnitude of the
prediction error over time, and thus the domain of validity of the trajectory
prediction. A first validation experiment of the proposed model is based on the
errors along time for a one-time trajectory prediction at the take off of the
flight with respect to the default values of the theoretical BADA model. This
experiment, assuming complete information, also shows the limit of the model. A
second experiment part presents an on-line trajectory prediction, in which the
prediction is continuously updated based on the current aircraft position. This
approach raises several issues, for which improvements of the basic model are
proposed, and the resulting trajectory prediction tool shows statistically
significantly more accurate results than those of the default model.
