Stéphane Puechmorel

A light-propagation model for aircraft trajectory planning

Predicted air traffic growth is expected to double the number of flights over the next 20xa0years. If current means of air traffic control are maintained, airspace capacity will reach its limits. The need for increasing airspace capacity motivates improved aircraft trajectory planning in 4D (space+time). In order to generate sets of conflict-free 4D trajectories, we introduce a new nature-inspired algorithm: the light propagation algorithm (LPA). This algorithm is a wavefront propagation method that yields approximate geodesic solutions (minimal-in-time solutions) for the path planning problem, in the particular case of air-traffic congestion. In simulations, LPA yields encouraging results on real-world traffic over France while satisfying the specific constraints in air-traffic management.

Wind parameters extraction from aircraft trajectories

When supervising aircraft, air traffic controllers need to know the current wind magnitude and direction since they impact every flying vessel. The wind may accelerate or slow down an aircraft, depending on its relative direction to the wind. Considering several aircraft flying in the same geographical area, one can observe how the ground speed depends on the direction followed by the aircraft. If a sufficient amount of trajectory data is available, approximately sinusoidal shapes emerge when plotting the ground speeds. These patterns characterize the wind in the observed area. After visualizing this phenomenon on recorded radar data, we propose an analytical method based on a least squares approximation to retrieve the wind direction and magnitude from the trajectories of several aircraft flying in different directions. After some preliminary tests for which the use of the algorithm is discussed, we propose an interactive procedure to extract the wind from trajectory data. In this procedure, a human operator selects appropriate subsets of radar data, performs automatic and/or manual curve fitting to extract the wind, and validates the resulting wind estimates. The operators can also assess the wind stability in time, and validate or invalidate their previous choices concerning the time interval used to filter the input data. The wind resulting from the least squares approximation is compared with two other sources - the wind data provided by Meteo-France and the wind computed from on-board aircraft parameters - showing the good performance of our algorithm. The interactive procedure received positive feedback from air traffic controllers, which is reported in this paper.

TAS and wind estimation from radar data

Accurate wind magnitude and direction estimation is essential for aircraft trajectory prediction. For instance, based on these data, one may compute entry and exit times 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 track measures is proposed. When on board true air speed measures are available, a linear model is developed for which a Kalman filter is used to produce high quality wind estimate. When only aircraft position measures are available, an observability analysis shows that wind may be estimated only if trajectories have one or two turns depending of the number of aircraft located in a given area. Based on this observability conditions, closed forms of the wind has been developed for the one and two aircraft cases. By this mean, each aircraft can be seen as a wind sensor when it is turning. After performing evaluations in realistic frameworks, our approach is able to estimate the wind vectors accurately. Based on those local wind estimates, a global space-time wind field estimation using vector splines is interpolated 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 wind estimates in a given zone. Further improvements to the estimation can be made by correlating with meteorological measurements.

3D airspace design by evolutionary computation

This paper presents a new method for 3D cutting of geometrical space with application to airspace sectoring. This problem comes from the air traffic management but the proposed method may be applied to many other areas. This problem consists in finding a cutting of a 3D volume into sectors in order to balance the weights of sectors and which minimizes the flow cut on sector boundaries. A mathematical modeling of this problem has been proposed for which state space, objective functions and constraints are defined. The complexity of such problem being NP_Hard, stochastic optimization have been used to address it. An Evolutionary Algorithm has been implemented for which chromosome coding and operators have been developed. Realistic problem instances have been tested on this algorithm for which the solutions produced fulfill our objective.

4D Trajectories: A functional data perspective

3D or 4D trajectories are fundamental objects within the frame of ATM and can be defined as mappings from a bounded interval to the space R3. However, this functional aspect is almost never used in applications. A great improvement over existing procedures for statistical analysis of trajectories can be obtained by explicitly considering trajectory data as functional data. Since raw functional data is by essence infinite dimensional, no computation can be made unless a finite representation has been found: all the complexity of functional data analysis is hidden in this stage. The present paper will first analyze the functional aspect of trajectories in order to extract operationally relevant quantities then will give a way of representing optimally aircraft trajectories with a finite number of parameters, allowing further processing. Applications to trajectory prediction and classification will be briefly discussed at the end.

Functional Decomposition for Bundled Simplification of Trail Sets

Bundling visually aggregates curves to reduce clutter and help finding important patterns in trail-sets or graph drawings. We propose a new approach to bundling based on functional decomposition of the underling dataset. We recover the functional nature of the curves by representing them as linear combinations of piecewise-polynomial basis functions with associated expansion coefficients. Next, we express all curves in a given cluster in terms of a centroid curve and a complementary term, via a set of so-called principal component functions. Based on the above, we propose a two-fold contribution: First, we use cluster centroids to design a new bundling method for 2D and 3D curve-sets. Secondly, we deform the cluster centroids and generate new curves along them, which enables us to modify the underlying data in a statistically-controlled way via its simplified (bundled) view. We demonstrate our method by applications on real-world 2D and 3D datasets for graph bundling, trajectory analysis, and vector field and tensor field visualization.

Dynamical systems complexity with a view towards air traffic management applications

The growth of air traffic in future years requires a paradigm shift in the way the aircraft are controlled. Major innovative projects (SESAR in Europe, NexGen in USA) have started in order to define and implement control tools based on time-space constraints on aircraft trajectories. As a consequence, an increasing level of automation is expected. In this framework, it is of primary importance to be able to quantify the hardness to produce conflict free trajectories for a given situation and the robustness of the solution found. In this paper, a characterisation based on the lyapunov exponents of a dynamical system interpolating the observed data will be presented. A first part will be devoted to vector field fitting, and a second one to efficient lyapunov exponents computation. Then, some practical implementation issues will be discussed.

Air Traffic Controller Keyboard Optimization by Artificial Evolution

The annual number of daily flights in France has increased from about 3500 in 1982 to about in 8000 in 2000. The number of flights simultaneously present on the radar screen of the controller has also increased. Usually controllers manage about 15 aircraft on their position and sometime this number reach a maximum of 20. On the radar screen, aircraft are represented by spots (with some previous positions and their speed vector) and the associated label which give the flight ID, the speed and the altitude of the aircraft. The controller in charge of the controlled area, has to be able to select any aircraft in order to manipulate some parameters of the flight such as heading, speed, altitude etc. Aircraft selection is done by the mean of a virtual keyboard where the controller pressed the keys of the flight ID. This ID is composed by a sequence of three letters (maximum) which represents the airline code, followed by the flight number. When such a selection is done, the associated flight is made highlighting on the radar screen. Depending of the flight ID distribution on a control position, the virtual keyboard can be optimized in order to speed up the aircraft selections and to improve the work of the controllers mainly when the sectors are overloaded. This keyboard optimization problem may be addressed like a pure assignment problem which is NP_Hard. This paper shows how artificial evolution has been used for solving such a problem with very good results on real instance associated to the Roissy departure sector.

Routing in aeronautical ad-hoc networks

Routing is one of the main challenges that Aeronautical Ad-hoc NETworks (AANETs) are facing, mostly because of the mobility of the nodes, the geographic size of the network and the number of nodes. To handle this problem, we propose in this paper an innovative routing algorithm called NoDe-TBR (Node Density-TBR), derived from Trajectory-Based Routing (TBR). In this routing algorithm, each aircraft computes a geographic path between itself and the destination of its message. In order to improve delivery probability, this path takes into account the actual aircraft density in each area. The performances of this algorithm have been assessed through simulations, with replayed aircraft trajectories over the North Atlantic Tracks (NATs). They are compared to the performances of classic routing algorithms designed for Mobile Ad-hoc NETworks (MANETs). Our solution exhibits better performances than classic routing protocols, but for a fraction of the signalization traffic volume. This is particularly desirable in resource-constraint networks such as AANETs.

On the Geodesic Distance in Shapes K-means Clustering

In this paper, the problem of clustering rotationally invariant shapes is studied and a solution using Information Geometry tools is provided. Landmarks of a complex shape are defined as probability densities in a statistical manifold. Then, in the setting of shapes clustering through a K-means algorithm, the discriminative power of two different shapes distances are evaluated. The first, derived from Fisher–Rao metric, is related with the minimization of information in the Fisher sense and the other is derived from the Wasserstein distance which measures the minimal transportation cost. A modification of the K-means algorithm is also proposed which allows the variances to vary not only among the landmarks but also among the clusters.