Abstract

International audience; In Functional Data Analysis, the underlying structure of a raw observation is functional and data are assumed to be sample paths from a single stochastic process. When data considered are functional in nature thus infinite-dimensional, like curves or images, the multivariate statistical procedures have to be generalized to the infinite-dimensional case. By approximating random functions by a finite number of random score vectors, the Principal Component Analysis approach appears as a dimension reduction technique and offers a visual tool to assess the dominant modes of variation, pattern of interest, clusters in the data and outlier detection. A functional statistics approach is applied to univariate and multivariate aircraft trajectories.

Abstract

Best paper award; International audience; Clustering is a common operation in statistics. When data considered are functional in nature, like curves, dedicated algorithms exist, mostly based on truncated expansions on Hilbert basis. When additional constraints are put on the curves, like in applications related to air traffic where operational considerations are to be taken into account, usual procedures are no longer applicable. A new approach based on entropy minimization and Lie group modeling is presented here, yielding an efficient unsupervised algorithm suitable for automated traffic analysis. It outputs cluster centroids with low curvature, making it a valuable tool in airspace design applications or route planning. Keywords–curve clustering; probability distribution estimation; functional statistics; minimum entropy; air traffic management. I. INTRODUCTION Clustering aircraft trajectories is an important problem in Air Traffic Management (ATM). It is a central question in the design of procedures at takeoff and landing, the so called sid-star (Standard Instrument Departure and Standard Terminal Arrival Routes). In such a case, one wants to minimize the noise and pollutants exposure of nearby residents while ensuring runway efficiency in terms of the number of aircraft managed per time unit. The same question arises with cruising aircraft, this time the mean flight path in each cluster being used to optimally design the airspace elements (sectors and airways). This information is also crucial in the context of future air traffic management systems where reference trajectories will be negotiated in advance so as to reduce congestion. A special instance of this problem is the automatic generation of safe and efficient trajectories, but in such a way that the resulting flight paths are still manageable by human operators. Clustering is a key component for such tools: major traffic flows must be organized in such a way that the overall pattern is not too far from the current organization, with aircraft flying along airways. The classification algorithm has thus not only to cluster similar trajectories but at the same time make them as close as possible to operational trajectories. In particular, straightness of the flight segments must be enforced, along with a global structure close to a graph with nodes corresponding to merging/splitting points and edges the airways.

Abstract

International audience; In air transportation, especially in airport safety, radar tracks are continuously recorded and may be used for detecting incidents on airport surface. However, all known statistical algorithms, even those based on functional data, are unable to distinguish between a safety critical flight and another one departing from standard behavior, but otherwise safe. In this work, we propose a change of paradigm by representing curves as points in a shape manifold. In this framework, it is possible to use Finsler distances between shapes that explicitly take into account the second derivative and can be able to 1 correctly detect skid situations from deviant trajectories that cannot be considered as a slipped trajectory. This metric is next used in curve clustering for detecting bad runway conditions. Some results on datasets of synthetic and real trajectories are presented, as well as a comparison of existing metrics.; Sur la plupart des plateformes aéroportuaires, les déplacements des aéronefs sont enregistrés en continu par des radars de surveillance et les trajectoires ainsi obtenues peuvent être utilisées pour détecter ou prévenir des incidents lors du roulage, en particu-lier des dérapages. Cependant, l'exploitation de ces données est rendue difficile par le fait que les algorithmes statistiques connus, même ceux basés sur des données fonctionnelles, ne sont pas capables de distinguer les situations réellement dangereuses des déviations au comportement standard qui sont sans gravité. Dans cette étude, nous proposons un chan-gement de paradigme en représentant les trajectoires comme des points dans un espace de formes. Dans ce nouveau cadre, il est possible de construire des distances de type Fins-ler, prenant explicitement en compte les dérivées secondes des trajectoires, et qui sont en mesure de bien séparer les trajectoires présentant un dérapage de celles dont la déviation par rapport au comportement nominal n'est pas due à un manque d'adhérence. Cette métrique est ensuite utilisée dans des méthodes de clustering pour détecter un mauvais état de la piste d'atterrissage. Des résultats sur des jeux de données de trajectoires syn-thétiques et réelles sont présentés ainsi qu'une comparaison avec des métriques existantes. Mots-clés. Similarité entre courbes, espace de formes, données fonctionnelles, classification non supervisée de courbes, sécurité aéroportuaire.