From Dual Connections to Almost Contact Structures

A dualistic structure on a smooth Riemaniann manifold $M$ is a triple $(M,g,\nabla)$ with $g$ a Riemaniann metric and $\nabla$ an affine connection, generally assumed to be torsionless. From $g$ and $\nabla$, the dual connection $\nabla^*$ can be defined and the triple $(M, \nabla,\nabla^*)$ is called a statistical manifold, a basic object in information geometry. In this work, we give conditions based on this notion for a manifold to admit an almost contact structure and some related structures: almost contact metric,contact, contact metric, cosymplectic, and coK\"ahler in the three-dimensional case.Comment: 22 page

Mathematic Models for Aircraft Trajectory Design: A Survey

Presented at the 2013 ENRI International Workshop on ATM/CNS (EIWAC2013), Tokyo, Japan, February 2013.Air traffic management ensure the safety of flight by optimizing flows and maintaining separation between aircraft. After giving some definitions, some typical feature of aircraft trajectories are presented. Trajectories are objects belonging to spaces with infinite dimensions. The naive way to address such problem is to sample trajectories at some regular points and to create a big vector of positions (and or speeds). In order to manipulate such objects with algorithms, one must reduce the dimension of the search space by using more efficient representations. Some dimension reduction tricks are then presented for which advantages and drawbacks are presented. Then, front propagation approaches are introduced with a focus on Fast Marching Algorithms and Ordered upwind algorithms. An example of application of such algorithm to a real instance of air traffic control problem is also given. When aircraft dynamics have to be included in the model, optimal control approaches are really efficient. We present also some application to aircraft trajectory design. Finally, we introduce some path planning techniques via natural language processing and mathematical programming

Analyse harmonique adaptée aux signaux à modulation de fréquence hyperbolique

The signals with an instantaneous frequency following an hyperbolic law are common in many fields of the signal processing, and particularly in the study of biologicals SONARS. In this paper we describe an harmonic analysis adapted to this kind of signals. The problem of stationnarity of stochastic processes will be adressed within the frame of the previous harmonic analysis. This allow us to define a power spectral density for second-order stationnary processes using the Bochner theorem. Some simulation results are presented showing the interest of the adapted harmonic analysis

Determination d'un groupe adapte a l'etude des chirps

Dans de nombreux domaines du traitement du signal se pose le problème de la détermination de la loi de modulation en fréquence d'un signal. Un cas particulier d'une grande importance pratique est celui des signaux présentant une phase polynomiale d'un degré maximal connu; les paramètres à déterminer sont alors les coefficients des termes du polynôme représentant la phase. Pour arriver à ce résultat, un cadre théorique permettant d'introduire une nouvelle méthode linéaire est mis en place dans cet article

Windfield estimation by radar track Kalman filtering and vector spline extrapolation

International audience; Accurate wind magnitude and direction estimation is essential for aircraft trajectory prediction. For instance, based on these data, one may compute entry and exit time from a sector or detect potential conflict between aircraft. Since the flight path has to be computed and updated on real time for such applications, wind information has to be available in real time too. The wind data which are currently available through meteorological service broadcast suffer from small measurement rate with respect to location and time. In this paper, a new wind estimation method based on radar tracks is developed. An Extended Kalman filer extracts the wind information by observation of the radar tracks in turns. After performing many evaluations in realistic framework, our approach is able to estimate the wind vectors accurately. By this mean, each aircraft can be seen as a wind sensor when it is turning. Based on those measurements, a global space-time wind field estimation using vector splines is extrapolated in order to produce wind maps in the area of interest. The underline model for wind field computation is Shallow-Water, which assumes geostrophic wind. The accuracy of this wind map is dependent of the number of aircraft turns in a given zone; then the estimation is better in the terminal area (TMA) than in en-route area because aircraft are tuning more often. Further improvements to the estimation can be made by correlating with meteorological measurements

ENRI Int. Workshop on ATM/CNS. Tokyo, Japan (EIWAC2010) [EN-023] Aircraft Conflict Resolution by Genetic Algorithm and B-Spline Approximation

Abstract Conflict resolution has always been a sensitive matter in air-traffic management. Current European projects aim partial or total automation of air traffic control to deal with the constant growth of air traffic. Technological advances on flight management system allows us to consider an automatic conflict resolution using continuous trajectories. In this paper, we present a new methodology that, first, relies on B-splines to model trajectories, secondly models air-traffic conflict resolution as an optimization problem whose decision variables are the spline control points. Finally, we use genetic algorithms to tackle this optimization problem in order to generate optimal conflict-free situations

Toward air traffic complexity assessment in new generation air traffic management systems

International audienceThe characterization of complex air traffic situations is an important issue in air traffic management (ATM). Within the current ground-based ATM system, complexity metrics have been introduced with the goal of evaluating the difficulty experienced by air traffic controllers in guaranteeing the appropriate aircraft separation in a sector. The rapid increase in air travel demand calls for new generation ATM systems that can safely and efficiently handle higher levels of traffic. To this purpose, part of the responsibility for separation maintenance will be delegated to the aircraft, and trajectory management functions will be further automated and distributed. The evolution toward an autonomous aircraft framework envisages new tasks where assessing complexity may be valuable and requires a whole new perspective in the definition of suitable complexity metrics. This paper presents a critical analysis of the existing approaches for modeling and predicting air traffic complexity, examining their portability to autonomous ATM systems. Possible applications and related requirements will be discussed

Modified Bezier curve for 4D reference trajectory definition under flight profile constraint

International audienceThe task of establishing properly spaced landing sequences is quite demanding for air traffic controllers in heavy traffic conditions. Indeed, air traffic controllers combine two or more streams into a single stream before landing by means of radar vectoring and speed instructions. This high level task of sequencing aircraft is not currently communicated to the pilot. Instead, controller translate it into clearances to the pilot, typically radar vectoring and speed instructions. In this paper, the task of merging an aircraft over a specified meter fix is addressed through a novel ?Set Reference Path? procedure in which the air traffic controller may clear an aircraft to merge at a specified meter fix at a given time. This paper focuses on the definition of a reference path for time-based operations at meter fix. It includes path stretching operations, which occur when the aircraft is predicted to overfly too early a meter fix with respect to other traffic flow constraints. This paper presents a new approach to generate a reference path with length and endpoint constraints based on modified Bezier curves. Compared to reference trajectories based on straight lines and circle arcs, which are usual in the aviation community, the proposed approach allows for smooth control cues and avoids the scheduling between straight lines and circle arcs segments. The proposed design is followed by illustrative examples which show the effectiveness of the proposed approach