4D Trajectories Complexity Metric Based on Lyapunov Exponents

International audienceThe ATM system has to cope with an increasing number of flights, pushing the capacity to its limits. As an example, the average daily traffic above Europe was 26286 flights/day, with a peak traffic demand in excess of 31000 flights..

Quantization and clustering on Riemannian manifolds with an application to air traffic analysis

International audienceThe goal of quantization is to find the best approximation of a probability distribution by a discrete measure with finite support. When dealing with empirical distributions, this boils down to finding the best summary of the data by a smaller number of points, and automatically yields a k-means-type clustering. In this paper, we introduce Competitive Learning Riemannian Quantization (CLRQ), an online quantization algorithm that applies when the data does not belong to a vector space, but rather a Riemannian manifold. It can be seen as a density approximation procedure as well as a clustering method. Compared to many clustering algorihtms, it requires few distance computations, which is particularly computationally advantageous in the manifold setting. We prove its convergence and show simulated examples on the sphere and the hyperbolic plane. We also provide an application to real data by using CLRQ to create summaries of images of covariance matrices estimated from air traffic images. These summaries are representative of the air traffic complexity and yield clusterings of the airspaces into zones that are homogeneous with respect to that criterion. They can then be compared using discrete optimal transport and be further used as inputs of a machine learning algorithm or as indexes in a traffic database

Entropy minimizing curves with application to automated flight path design

International audience; 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 norm. With the increase of traffic, it is expected that the system will reach its limits in a near future: a paradigm change in ATM is planned with the introduction of trajectory based operations. This paper investigate a mean of producing realistic air routes from the output of an automated trajectory design tool. For that purpose, an entropy associated with a system of curves is defined and a mean of iteratively minimizing it is presented. The network produced is suitable for use in a semi-automated ATM system with human in the loop. Document type: Part of book or chapter of boo

The Fisher-Rao geometry of beta distributions applied to the study of canonical moments

This paper studies the Fisher-Rao geometry on the parameter space of beta distributions. We derive the geodesic equations and the sectional curvature, and prove that it is negative. This leads to uniqueness for the Riemannian centroid in that space. We use this Riemannian structure to study canonical moments, an intrinsic representation of the moments of a probability distribution. Drawing on the fact that a uniform distribution in the regular moment space corresponds to a product of beta distributions in the canonical moment space, we propose a mapping from the space of canonical moments to the product beta manifold, allowing us to use the Fisher-Rao geometry of beta distributions to compare and analyze canonical moments

THE CHALLENGE OF THE PASSENGER CENTRIC TRANSPORTATION - SMART4PAX

International audienceToday, new services, offers, products open a realm of possibilities to the imagination of individuals, leading to profound changes in the way we move. While transport was very often viewed as a constraint, mobility becomes a way of life. In human societies, mobility is increasingly understood in terms of social links' creation, opportunities and synergies rather than pure problem of travelled distance (Amar [1]). The Human mobility becomes individual in the sense where each one conceives his own "mobility cocktail". Changes in individual preferences, behaviors and lifestyles together with innovative Information Communication Technologies (ICT) are likely to impact the way travelers plan their mobility behavior and value their own mobility choices. This mobility behavior and choices concern all the different transport modes that have to be used to perform the full trip i.e. the door-to-door travel is therefore intrinsically multimodal. Multimodality presupposes the availability of a large range of transport options and various combinations of them that can transfer passengers from their origin to their destination. One stake of multimodality is the ease to change scale, for instance when travelling successively by air with an intercontinental flight and by route with bus or car. Communication technologies and data sharing henceforth are essential part of transport systems. They enable transport mode operators to propose new services to facilitate the traveller's empowerment and autonomy. Beyond traditional transport modes organized by operators, additional services indeed provide travelers with means to organize, control and optimize their own door-to-door mobility and to turn their travel time into useful or even enjoyable time. These services add value to the travelers' mobility space-time and may change their perception of travel time. Along the way these services can impact travelers' mobility choices. Today the transportation system is oriented on the various means of transport, the objective here is to put the passenger in the centre of the transportation system, and to provide Smart solutions to improve Passenger Seamless Mobility and experience. We will address the challenge of the Passenger Centric Transportation through 4 pillars: • Smart for Enhancing passenger experience, new relation to the journey putting the passenger in the centre of the decision-making process, taking into account its profiles its needs and expectations

Wavelet Coefficients of Levy Process

International audienceCet article présente une expression de la fonction caractéristique des coefficients de décomposition en ondelettes d'un processus de Levy. Le cas particulier de l'ondelette de Haar et d'un processus entrelacé est traité plus en détail

Multivariate Functional Data Clusterization by PCA in Sobolev Space Using Wavelets

International audienceNous présentons une méthode basée sur la classification en espace fonctionnel appliquée aux trajectoires avion. La particularité des données est de se présenter comme des fonctions deux fois continuement différentiable par morceaux, l'information discriminante se situant des les sauts. L'utilisation d'une décomposition en ondelettes permet une implémentation simple en espace de Sobolev et permet de séparer correctement des trajectoires présentant des points de branchement

Performance Assessment of a New Routing Protocol in AANET

Routing is a critical issue in mobile ad hoc networks. The routing algorithm must take into account the specific properties of the network such as its topology, the mobility of the nodes and their number. In this paper, we present a simulation-based study of the performances of our innovative routing protocol named NoDe-TBR (Node Density TBR) that takes into account the actual node density distribution. The considered ad hoc network is an Aeronautical Ad hoc NETwork (AANET), a future communication system enabling air↔air and air↔ground communications beyond the radio range of the sender. This context and the communication architecture have been modeled in a realistic way based on replayed aircraft trajectories, a realistic access layer, and application that should be deployed in the future