wind and temperature networking applied to aircraft...

Wind and Temperature Networking Applied to AircraftTrajectory Prediction

K. Legrand and D. Delahaye and C. Rabut

Applied Mathematics Laboratory (MAIAA)French Civil Aviation University

Toulouse, FranceICRAT 2016

18 juillet 2016

K. Legrand and D. Delahaye and C. Rabut ( Applied Mathematics Laboratory (MAIAA) French Civil Aviation University Toulouse, France ICRAT 2016 )Wind and Temperature Networking Applied to Aircraft Trajectory Prediction18 juillet 2016 1 / 49

Why trajectory Prediction is Critical for Air Traffic Management ?

What is the Wind Networking Concept ?

Trajectory Prediction Improvement with Wind Networking

Needs for Trajectory Prediction

Conflict detection

Sequencing and merging

Airspace sector overload detection

Traffic structuring

etc ...

Real need for SESAR and NextGen

4D Trajectory Planning fully depends on TP

Conflict detection

Traffic structuring

etc ...

Conflict detection

Traffic structuring

etc ...

Conflict detection

Traffic structuring

etc ...

Conflict detection

Traffic structuring

etc ...

Conflict detection

Traffic structuring

etc ...

Conflict detection

Traffic structuring

etc ...

Impact of Temperature and Wind on Aircraft Speeds

TAS = aM =√γRTsM

a is the speed of sound

M is the Mach number

γ is the specific gas ratio constant (1.4 for standard conditions)

R is the air specific gas constant 287.05287 J/(K .kg)

Ts is the static air temperature in Kelvin

−→GS =

−−→TAS +

−→W

Trajectory Prediction Features

TP is mainly done on the ground (information limitation)

or can be done on board and down linked to the ground (futurecontext)

Trajectory Prediction Features

TP is mainly done on the ground (information limitation)

or can be done on board and down linked to the ground (futurecontext)

Uncertainties

t t + 10’ t + 20’

Trajectory Prediction Limitation Factors

1 Wind ( ~V = ~T + ~W )

2 Temperature, pressure (engine thrust, drag d = 12 .cx .ρ.S .v

3 Weight

On-board trajectory prediction

FMS in open loop : +−15Nm after one hour flight.

Radar Tracker

Aircraft Position and speed are computed with Radar Tracker (KalmanFilter)

Tracker Feature

1 Compute accurate current position (noise reduction)

2 Predict future short term positions

3 Estimate the current speed vector

Radar Tracker

Tracker Feature

Radar Tracker

Tracker Feature

Radar Tracker

Tracker Feature

Radar Tracker

Tracker Feature

SESAR and NextGen

Trajectory Prediction Improvement

1 The FMS compute the future trajectories (right model, exact weight,estimated wind)

2 This prediction is down linked on the ground

3 It is then updated with more accurate weather information

4 Such new updated trajectory is then uploaded on board.

SESAR and NextGen

Aeronautical Wind Data

One wind map every three hours at a given FL.

A wind map is produce and updated every 3 hours for a given flight level.K. Legrand and D. Delahaye and C. Rabut ( Applied Mathematics Laboratory (MAIAA) French Civil Aviation University Toulouse, France ICRAT 2016 )Wind and Temperature Networking Applied to Aircraft Trajectory Prediction18 juillet 2016 11 / 49

Automatic Dependent Surveillance-Broadcast

One measure every second

Wind Networking

Wind Interpolation

Wind Interpolation Model

~X = ~f (~X )

Optimization Problem. ~f ? such that :

minE1 =i=N∑i=1

‖ ~Vi − ~f (~Xi )‖2

minE2 =

α‖∇div~f (~X )‖2 + β‖∇curl~f (~X )‖2d ~X

For α = β

‖∆~f (~x)‖2d~x with ∆~f =

∂2fx∂x2

+ ∂2fx∂y2 + ∂2fx

∂2fy∂x2

+∂2fy∂y2 +

∂2fy∂z2

∂2fz∂x2

+ ∂2fz∂y2 + ∂2fz

Non Linear Extension in Space

Exact Solution (Amodei 1991)

~f (~X ) =N∑i=1

[Φ(‖~X − ~Xi‖)].~ai + [A]. ~X + ~B

with[Φ(‖~X − ~Xi‖)] = [Q(‖~X − ~Xi‖3)]

[Q] =1α∂

2xx + 1

β (∂2yy + ∂2zz) ( 1α −

1β )∂2xy ( 1

α −1β )∂2xz

( 1α −

1β )∂2xy

1α∂

2yy + 1

β (∂2xx + ∂2zz) ( 1α −

1β )∂2yz

( 1α −

1β )∂2xz ( 1

α −1β )∂2yz

1α∂

2zz + 1

β (∂2xx + ∂2yy )

Application to Oceanic Traffic

How It Works Today ?

Time Constraint for Oceanic Traffic

No Radar ⇒ Large Time Separations

10 minutes

15 minutes 15 minutes

Wind Field over Atlantic Ocean

For given Flight Level.

Back Propagation of the Wind Measures

Estimated Wind True Wind Updated Wind

For given Flight Level.

Test Framework

387 aircraft trajectories from August 4th 2006

USA → Europe traffic

Exit Time Statistics

µ(minutes) σ(minutes)

NO WN 3.45 3.18

WN 1.12 0.53

In those experiments the FMS is working in open loop.

The first aircraft have less benefit than the following ones.

Exit Time Statistics

µ(minutes) σ(minutes)

NO WN 3.45 3.18

WN 1.12 0.53

In those experiments the FMS is working in open loop.

The first aircraft have less benefit than the following ones.

TP Improvement between two Reporting Positions

Application to Continental Airspace

We consider a day of traffic over France with about 8000 flights (August6, 2012 in this case).

Having the wind forecasts for this day (every 3 hours) and the aircrafttypes (Bada), one can compute for any aircraft the estimated futurepositions (with and without wind networking).

Thanks to Meteo France, an “a posteriori” accurate wind map hasbeen computed for this day. This will be considered as the actualwind.

Future positions have been predicted at t + 5′, t + 10′,...t + 30′.

Then, one can compute the actual positions (radar) and the predictedones in both cases (with or without wind networking).

Wind Prediction Improvement

True Wind

Predicted Wind

Updated Wind

Wind-Temp Errors

PredWindError = ‖PredWind‖ − ‖TrueWind‖PredTempError = ‖PredTemp‖ − ‖TrueTemp‖

UpdatedWindError = ‖UpdatedPred‖ − ‖TrueWind‖UpdatedTempError = ‖UpdatedTemp‖ − ‖TrueTemp‖

True Wind

Predicted Wind

Updated Wind

Wind-Temp Errors

True Wind

Predicted Wind

Updated Wind

Wind-Temp Errors

True Wind

Predicted Wind

Updated Wind

Wind-Temp Errors

Predicted Wind True Wind Updated Wind

Results for the Wind-Temp Errors

NbTraj 100 1 000 3 000 5 000 8 000

WindPredErr(kts) 5.11 5.13 5.12 5.11 5.14WindUpd-Err(kts) 2.30 0.78 0.64 0.5 0.48

TempPredErr(dg) 3.00 3.01 3.01 3.01 3.01TempUpd-Err(dg) 1.45 0.45 0.39 0.38 0.37

Maps of Wind Errors

Figure: This figure represents the predicted wind error on each trajectorysample. The red areas indicate an error of 15 knots.

Maps of Wind Errors

Figure: This figure represents the updated wind error on each trajectory sample.The red areas indicate an error of 15 knots.

Locations of Improvement

Figure: This figure shows where the wind estimate improvement is higher.Thegreen areas locate where wind networking brings the most improvement (highdensity areas).

Reporting Time Prediction Improvement

True Time

Predicted Time

Updated Time

Reporting Time Errors

PredTimeError = |PredTime − TrueTime|

UpdatedTimeError = |UpdatedTime − TrueTime|

True Time

Predicted Time

Updated Time

True Time

Predicted Time

Updated Time

True Time

Predicted Time

Updated Time

Predicted Time

Updated Time

True Time

Time to reach this point ?

For different prediction horizon times (HT), we have computed :

Average Predicted Time Error

Average Updated Time Error

For different prediction horizon times (HT), we have computed :

Average Predicted Time Error

Average Updated Time Error

Wind Networking OnlyHT 5 10 15 20 30 45

PreDErr 4.5 9 13.3 16.8 20.3 22.4

UpdErr (sec) 0.4 0.8 1.3 1.8 2.2 2.7

Temp Networking OnlyHT(minutes) 5 10 15 20 30 45

PreDErr(sec) 1.99 3.91 5.78 7.32 9.15 10.34

UpdErr (sec) 0.47 0.97 1.54 2.06 2.7 3.33

Wind and Temp NetworkingHT(minutes) 5 10 15 20 30 45

PreDErr(sec) 5.2 10.42 15.68 20.20 25.97 29.0

UpdErr (sec) 0.7 1.41 2.21 3.10 3.83 4.75

Conflict Detection Improvement

Conflict ?

The real challenge for Air Traffic Controllers is to detect conflicts.

No way to use radar data (no actual conflicts)

For this experiment we consider two wind maps at 9AM and 12AM

The first one will be considered as the forecast and the second onethe actual.

Based on those two wind maps and the 8000 flight plans, we canmeasure the benefit of the wind networking.

As for TP, detection has been performed 30’, 25’,... and 5’ ahead.

Ps = Pr{0/0}+ Pr{1/1}

Pe = Pr{1/0}+ Pr{0/1}

Evolution of Ps with or without wind networking

30’ 25’ 20’ 15’ 10’ 5’

NO WN 0.568 0.644 0.717 0.756 0.811 0.917On the Ground

WN 0.908 0.943 0.975 0.982 0.995 0.999On Board

Remark :Ps evolves also in space (better in TMA and areas where thereare more aircraft).

Conclusion

Wind Networking Benefits

Wind-Temp Networking Concept represents a real value for ATM

Trajectory prediction

Conflict detection

Oceanic Traffic Management

Easy to implement.

Future Works

Interpolation based on weather wind model (Geostrophic WindModel)

Conclusion

Conflict detection

Easy to implement.

Future Works

Conclusion

Conflict detection

Easy to implement.

Future Works

Conclusion

Conflict detection

Easy to implement.

Future Works

Conclusion

Conflict detection

Easy to implement.

Future Works

Conclusion

Conflict detection

Easy to implement.

Future Works

Conclusion

Conflict detection

Easy to implement.

Future Works

Conclusion

Conflict detection

Easy to implement.

Future Works

wind and temperature networking applied to aircraft...

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