Air Traffic Complexity : A new concept

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Air Traffic Complexity A new concept
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Why is a complexity metric needed ?

• Correlated with the controller workload.
• Airspaces comparison (US/Europe).
• ATM optimization

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Previous related works

• Dynamic Density (Mitre,Nasa)
• Geometric metrics (Enac,Cena,Mit)
• Spanning trees and neural networks (Nasa)
• Structural metrics (Enac,Cena,Mit)

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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).

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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.

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Linear Dynamical System
The eigenvalues of A, control the dynamics of the
system
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Eigenvalues properties
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Example
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Full Convergence
8 aircraft converging at the same place
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Kolmogorov Entropy (full cv)
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Random convergence
41 aircraft converging at the same area
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Kolmogorov Entropy (random cv)
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Full organized rotation
8 aircraft moving in rotation
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Kolmogorov entropy (circle)
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Spiral moving
8 aircraft on a spiral moving
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Kolmogorov entropy (spiral)
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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

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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).

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Non Linear Dynamical System

• Based on vector spline function
• Solution of the equation where
  are the aircraft positions and
  are adjusted parameters.

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Eight Aircraft Circle Spline Model
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Two Four-Aircraft CirclesSpline Model
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Linear Model
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Spline Model
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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.

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ATC Database

• ATC data come from many sources
• Real traffic.
• Arithmetic simulation.
• Real time simulation.
• Different formats.
• Different space and/or time referentials.

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A Unified Descriptor The UEL

• UEL means  Uniform Event Locator , analogy with
  the URLs.
• Unambiguous data location.
• Independance request format / database format.

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Example

• ATCspheroid/fr/bord/TA?mapcautra4timeZonelocal
  timefirst12/01/2001 100000
  last12/01/2001 110000

• 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.

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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 mapTypestereographi
  cposition20.00.0 will produce stereographic
  projection data with a map centered on lat20,
  long0.

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Database structure
DB
Interface
DBManager
DB
Interface
UELResolver
CORBA
XML
UELResolver