Visualizing 3D trajectories to extract insights about their similarities and spatial configuration is a critical task in several domains. Air traffic controllers for example deal with large quantities of aircrafts routes to optimize safety in airspace and neuroscientists attempt to understand neuronal pathways in the human brain by visualizing bundles of fibers from DTI images. Extracting insights from masses of 3D trajectories is challenging as the multiple three dimensional lines have complex geometries, may overlap, cross or even merge with each other, making it impossible to follow individual ones in dense areas. As trajectories are inherently spatial and three dimensional, we propose FiberClay: a system to display and interact with 3D trajectories in immersive environments. FiberClay renders a large quantity of trajectories in real time using GP-GPU techniques. FiberClay also introduces a new set of interactive techniques for composing complex queries in 3D space leveraging immersive environment controllers and user position. These techniques enable an analyst to select and compare sets of trajectories with specific geometries and data properties. We conclude by discussing insights found using FiberClay with domain experts in air traffic control and neurology.

This paper describes the application of high-confidence-interval prediction methods to the aircraft trajectory prediction problem, more specifically to the altitude prediction during climb. We are interested in methods for finding two-sided intervals that contain, with a specified confidence, at least a desired proportion of the conditional distribution of the response variable. This paper introduces two-sided Bonferroni-quantile confidence intervals, which is a new method for obtaining high-confidence two-sided intervals in quantile regression. This paper also uses the Bonferroni inequality to propose a new method for obtaining tolerance intervals in least squares regression. The latter has the advantages of being reliable, fast, and easy to calculate. We compare physical point-mass models to the introduced models on an air traffic management data set composed of traffic at major French airports. Experimental results show that the proposed interval prediction models perform significantly better than the conventional point-mass model currently used in most trajectory predictors. When comparing with a recent state-of-the-art point-mass model with adaptive mass estimation, the proposed methods give altitude intervals that are slightly wider but more reliable.

In this paper, we apply machine learning methods to improve the aircraft climb prediction in the context of ground-based applications. Mass is a key parameter for climb prediction. As it is considered a competitive parameter by many airlines, it is currently not available to ground-based trajectory predictors. Consequently, most predictors today use a reference mass that may be different from the actual aircraft mass. In previous papers, we have introduced a least squares method to estimate the mass from past trajectory points, using the physical model of the aircraft. Another mass estimation method, based on an adaptive mechanism, has also been proposed by Schultz et al. We now introduce a new approach, in which the mass is considered the response variable of a prediction model that is learned from a set of example trajectories. This machine learning approach is compared with the results obtained when using the base of aircraft data (BADA) reference mass or the two state-of-the-art mass estimation methods. In these experiments, nine different aircraft types are considered. When compared with the baseline method (respectively, the mass estimation methods), the Machine Learning approach reduces the RMSE (Root Mean Square Error) on the predicted altitude by at least 58% (resp. 27%) when assuming the speed profile to be known, and by at least 29% (resp. 17%) when using the BADA speed profile except for the aircraft types E145 and F100. For these types, the observed speed profile is far from the BADA speed profile.