Wind optimal trajectory planning is a critical issue for airlines in order to save fuel for all their flights. This planning is difficult due to the uncertainties linked to wind data. Based on the current weather situation, weather forecast institutes compute wind maps prediction with a given level of confidence. Usually, 30-50 wind maps prediction can be produced. Based on those predictions, airlines have to compute trajectory planning for their aircraft in an efficient way. Such planning has to propose robust solutions which take into account wind variability for which average and standard deviation have to be taken into account. It is then better to plan trajectories in areas where wind has low standard deviation even if some other plannings induce less fuel consumption but with a higher degree of uncertainty. In this paper, we propose an efficient wind optimal algorithm based on two phases. The first phase considers the wind map predictions and computes for each of them the associated wind optimal trajectory also called geodesic. Such geodesics are computed with a classical Bellman algorithm on a grid covering an elliptical shape projected on the sphere. This last point enable the algorithm to address long range flights which are the most sensitive to wind direction. At the end of this first phase, we get a set of wind optimal trajectories. The second phase of the algorithm extract the most robust geodesic trajectories by the mean of a new trajectory clustering algorithm. This clustering algorithm is based on a new mathematical distance involving continuous deformation approach. In order to measure this mathematical distance between two trajectories, a continuous deformation between them is first built. This continuous deformation is called homotopy. For any homotopy, one can measure the associated energy used to shift from the first trajectory to the second one. The homotopy with the minimum energy is then computed, for which the associated energy measure the mathematical distance between trajectories. Based on this new distance, an EM clustering algorithm has been used in order to identify the larger clusters which correspond to the most robust wind optimal trajectories. This new approach avoids the main drawback of the classical approach which uses the mean of the trajectories issued from the first phase. This algorithm has been successfully applied to north Atlantic flights.

Aircraft optimal trajectory planning in the presence of wind is a critical issue for airlines to save fuel. Planning is difficult due to the uncertainties linked to wind. Based on wind predictions, airlines have to compute trajectory planning for their aircraft in an efficient way. Such planning has to propose robust solutions which take into account wind variability. In this paper, we propose a robust wind optimal trajectory design algorithm based on two phases. The first phase considers the wind map predictions and computes for each of them the associated wind optimal trajectory also called geodesic. Such geodesics are computed with a Bellman algorithm on a grid covering an elliptical shape projected on the sphere. The second phase of the algorithm extract the most robust geodesic trajectories by the mean of a new trajectory clustering algorithm. This clustering algorithm is based on a new mathematical distance involving continuous deformation approach applied to north Atlantic flights 1 .

Trajectory prediction estimates the future position of aircraft along their planned trajectories in order to detect potential conflicts and to optimize air space occupancy. This prediction is a critical task in the Air Traffic Control (ATC) process and has been studied for many years. For the future automation processes developed in the SESAR [1], NextGen [2] and CARATS [3] projects, such trajectory prediction will be even more critical. In these projects the trajectory predictors generate aircraft forecast trajectories, typically for client applications. As there is always a deviation between the predicted wind (from the weather forecasts) and the encountered wind, the main longitudinal (along-track) error source between the predicted and the actual trajectory is linked to wind estimation. Based on the current performances of Air Traffic Control systems, controllers are able to efficiently detect conflict 20 minutes in advance ; for a larger time horizon (look-ahead time), the induced trajectory prediction uncertainty strongly reduces the reliability of the conflict detection. The goal of this work is to measure the potential benefit produced by sharing wind measures between aircraft (this concept will be called wind networking (WN)). To reach this goal, aircraft measure their local atmospheric data (wind, temperature, density and pressure) and broadcast them to the other aircraft. Having such distributed weather information, each aircraft is able to compute an enhanced local wind map as a function of location (3D) and time. These updated wind fields could be shared with other aircraft and/or with ground systems. Using this enhanced weather information, each aircraft is able to improve drastically its own trajectory prediction. This concept has been simulated in the French airspace with 8 000 flights. Comparisons have been investigated on trajectory prediction performances with and without wind networking. Statistics have been conducted in order to measure the benefit of such concept in both time and space dimensions showing higher improvement in high traffic areas, as expected.

Trajectory prediction estimates the future position of aircraft along their planned trajectories in order to detect potential conflicts and to optimize air space occupancy. This prediction is a critical task in the Air Traffic Control (ATC) process and has been studied for many years. For the future automation processes developed in the SESAR [1], NextGen [2] and CARATS [3] projects, such trajectory prediction will be even more critical. In these projects the trajectory predictors generate aircraft forecast trajectories, typically for client applications. As there is always a deviation between the predicted wind (from the weather forecasts) and the encountered wind, the main longitudinal (along-track) error source between the predicted and the actual trajectory is linked to wind estimation. Based on the current performances of Air Traffic Control systems, controllers are able to efficiently detect conflict 20 minutes in advance ; for a larger time horizon (look-ahead time), the induced trajectory prediction uncertainty strongly reduces the reliability of the conflict detection. The goal of this work is to measure the potential benefit produced by sharing wind measures between aircraft (this concept will be called wind networking (WN)). To reach this goal, aircraft measure their local atmospheric data (wind, temperature, density and pressure) and broadcast them to the other aircraft. Having such distributed weather information, each aircraft is able to compute an enhanced local wind map as a function of location (3D) and time. These updated wind fields could be shared with other aircraft and/or with ground systems. Using this enhanced weather information, each aircraft is able to improve drastically its own trajectory prediction. This concept has been simulated in the French airspace with 8 000 flights. Comparisons have been investigated on trajectory prediction performances with and without wind networking. Statistics have been conducted in order to measure the benefit of such concept in both time and space dimensions showing higher improvement in high traffic areas, as expected.