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Centre dÉtudes de la navigation aérienne Air Traffic Complexity : A new concept.

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Presentation on theme: "Centre dÉtudes de la navigation aérienne Air Traffic Complexity : A new concept."— Presentation transcript:

1 centre dÉtudes de la navigation aérienne Air Traffic Complexity : A new concept

2 centre dÉtudes de la navigation aérienne Why is a complexity metric needed ? Correlated with the controller workload. Airspaces comparison (US/Europe). ATM optimization

3 centre dÉtudes de la navigation aérienne Previous related works Dynamic Density (Mitre,Nasa) Geometric metrics (Enac,Cena,Mit) Spanning trees and neural networks (Nasa) Structural metrics (Enac,Cena,Mit)

4 centre dÉtudes de la navigation aérienne Our approach Mathematical feature associated with a dynamical system. It measures the ability to mix the trajectories. Example : –Laminar flow : weak complexity (the relative distance between particules does not change with time). –Turbulent flow : strong complexity (close particules follow very different trajectories).

5 centre dÉtudes de la navigation aérienne Dynamical System Principle : find a dynamical system which trajectories fit the aircraft observations (Least Squares Minimization). Problem : model is not unique. Solution : select the model with most regular trajectories.

6 centre dÉtudes de la navigation aérienne Linear Dynamical System The eigenvalues of A, control the dynamics of the system

7 centre dÉtudes de la navigation aérienne Eigenvalues properties

8 centre dÉtudes de la navigation aérienne Example

9 centre dÉtudes de la navigation aérienne Full Convergence 8 aircraft converging at the same place

10 centre dÉtudes de la navigation aérienne Kolmogorov Entropy (full cv)

11 centre dÉtudes de la navigation aérienne Random convergence 41 aircraft converging at the same area

12 centre dÉtudes de la navigation aérienne Kolmogorov Entropy (random cv)

13 centre dÉtudes de la navigation aérienne Full organized rotation 8 aircraft moving in rotation

14 centre dÉtudes de la navigation aérienne Kolmogorov entropy (circle)

15 centre dÉtudes de la navigation aérienne Spiral moving 8 aircraft on a spiral moving

16 centre dÉtudes de la navigation aérienne Kolmogorov entropy (spiral)

17 centre dÉtudes de la navigation aérienne General Dynamical Systems Linear models have limited behaviour. In real trafic, they are restricted to general trend (drift, rotation, expansion or contraction). Extension to non linear models of the form

18 centre dÉtudes de la navigation aérienne Vector Splines Vector fields obtained by adding a linear term and a sum of so-called spline functions. Optimal interpolation of observations with respect to a variational criterion. Easy computation by elementary linear algebra (Singular Value Decomposition).

19 centre dÉtudes de la navigation aérienne Non Linear Dynamical System Based on vector spline function Solution of the equation : where are the aircraft positions and are adjusted parameters.

20 centre dÉtudes de la navigation aérienne Eight Aircraft Circle Spline Model

21 centre dÉtudes de la navigation aérienne Two Four-Aircraft Circles Spline Model

22 centre dÉtudes de la navigation aérienne Linear Model

23 centre dÉtudes de la navigation aérienne Spline Model

24 centre dÉtudes de la navigation aérienne Spatial Distribution of Complexity Previous trafic situation. Complexity value for each point of the sector integrated over time. The peaks represent the two crossing points.

25 centre dÉtudes de la navigation aérienne ATC Database ATC data come from many sources : –Real traffic. –Arithmetic simulation. –Real time simulation. Different formats. Different space and/or time referentials.

26 centre dÉtudes de la navigation aérienne A Unified Descriptor : The UEL UEL means « Uniform Event Locator », analogy with the URLs. Unambiguous data location. Independance request format / database format.

27 centre dÉtudes de la navigation aérienne Example ATC:spheroid/fr/bord/TA?map=cautra4&timeZon e=localtime&first=12/01/ :00:00 &last=12/01/ :00:00 Context. ATC is for real traffic. Earth model. Here spheroid. Space zone (named in this ex) fr/bord/TA means for TA sector from the Bordeaux ACC. Argument after ? give information about the referentials and the time interval. Here the space reference is cautra4, the time reference is the local time.

28 centre dÉtudes de la navigation aérienne Example : comments A UEL request insures that the data will be given in the right time and space referentials and will not be sensitive to the database format. If spheroid earth model is replaced by the WGS84 the format conversion will be automatic. In the same way the argument : mapType=stereographic&position= will produce stereographic projection data with a map centered on lat=20, long=0.

29 centre dÉtudes de la navigation aérienne Database structure DBManager DB UELResolver Interface CORBA XML UELResolver


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