Ground-based aircraft trajectory prediction is a major concern in air traffic control and management. A safe and efficient prediction is a prerequisite to the implementation of new automated tools. In current operations, trajectory prediction is computed using a physical model. It models the forces acting on the aircraft to predict the successive points of the future trajectory. Using such a model requires knowledge of the aircraft state (mass) and aircraft intent (thrust law, speed intent). Most of this information is not available to ground-based systems. This paper focuses on the climb phase. We improve the trajectory prediction accuracy by predicting some of the unknown point-mass model parameters. These unknown parameters are the mass and the speed intent. This study relies on ADS-B data coming from The OpenSky Network. It contains the climbing segments of the year 2017 detected by this sensor network. The 11 most frequent aircraft types are studied. The obtained data set contains millions of climbing segments from all over the world. The climbing segments are not filtered according to their altitude. Predictive models returning the missing parameters are learned from this data set, using a Machine Learning method. The trained models are tested on the two last months of the year and compared with a baseline method (BADA used with the mean parameters computed on the first ten months). Compared with this baseline, the Machine Learning approach reduce the RMSE on the altitude by 48 % on average on a 10 minutes horizon prediction. The RMSE on the speed is reduced by 25 % on average. The trajectory prediction is also improved for small climbing segments. Using only information available before the considered aircraft takeoff , the Machine Learning method can predict the unknown parameters, reducing the RMSE on the altitude by 25 % on average. The data set and the Machine Learning code are publicly available.