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Entropy 2016, 18(9), 337; doi:10.3390/e18090337

Entropy Minimizing Curves with Application to Flight Path Design and Clustering

Laboratoire de Mathématiques Appliquées, Informatique et Automatique pour l’Aérien (MAIAA), Département Sciences et Ingénierie de la Navigation Aérienne (SINA), École Nationale de l’Aviation Civile (ENAC), 7 avenue Edouard Belin CS 54005, 31055 Toulouse, France
This paper is an extended version of our paper published in the 2nd Conference on Geometric Science of Information, Paris, France, 28–30 October 2015.
Author to whom correspondence should be addressed.
Academic Editors: Frédéric Barbaresco and Frank Nielsen
Received: 26 July 2016 / Revised: 8 September 2016 / Accepted: 8 September 2016 / Published: 15 September 2016
(This article belongs to the Special Issue Differential Geometrical Theory of Statistics)
View Full-Text   |   Download PDF [1018 KB, uploaded 15 September 2016]   |  


Air traffic management (ATM) aims at providing companies with a safe and ideally optimal aircraft trajectory planning. Air traffic controllers act on flight paths in such a way that no pair of aircraft come closer than the regulatory separation norms. With the increase of traffic, it is expected that the system will reach its limits in the near future: a paradigm change in ATM is planned with the introduction of trajectory-based operations. In this context, sets of well-separated flight paths are computed in advance, tremendously reducing the number of unsafe situations that must be dealt with by controllers. Unfortunately, automated tools used to generate such planning generally issue trajectories not complying with operational practices or even flight dynamics. In this paper, a means of producing realistic air routes from the output of an automated trajectory design tool is investigated. For that purpose, the entropy of a system of curves is first defined, and a mean of iteratively minimizing it is presented. The resulting curves form a route network that is suitable for use in a semi-automated ATM system with human in the loop. The tool introduced in this work is quite versatile and may be applied also to unsupervised classification of curves: an example is given for French traffic. View Full-Text
Keywords: curve system entropy; curves manifold; curve clustering; probability distribution estimation; air traffic management curve system entropy; curves manifold; curve clustering; probability distribution estimation; air traffic management

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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Puechmorel, S.; Nicol, F. Entropy Minimizing Curves with Application to Flight Path Design and Clustering. Entropy 2016, 18, 337.

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