Eulalia Hernández-Romero1, Alfonso ValenzuelaI and Damián Rivas1

Matthias Steiner2 and James Pinto2

1 Department of Aerospace Engineering. Universidad de Sevilla, Spain.

2 Research Applications Laboratory. National Center for Atmospheric Research, Boulder CO, USA.

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This research was conducted at the National Center for Atmospheric Research,

Boulder Colorado, financed by the Najeeb E. Halaby Graduate Student Fellowship.

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The development of automated decision support tools is key in the future of Air Traffic Management (ATM) system. These tools must integrate and manage uncertainty present in the ATM.

Sources of uncertainty:

Uncertainty in data and sensors

Decisions taken by individuals

Weather uncertainty

It is expected that by considering the weather prediction uncertainty, the safety and efficiency of the air traffic may be improved.

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En-route probabilistic conflict detection

En-route probabilistic conflict resolution

Terminal Area prob. conflict detection

Objective: Analyze the effects of wind uncertainty on the problem of aircraft conflict detection in the TMA

SID2017

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▪ Distance of closest approach▪ Conflict starting time▪ Conflict duration▪ Probability of conflict

…

Uncertainty source:

wind

Conflict indicators

Probabilistic conflict detection

Propagate wind uncertainty into the trajectory prediction

Probabilistic Transformation Method (PTM)

𝑃𝑐𝑜𝑛

Converging 3D air traffic - TMA

1. North-East reference system fixed to Earth.

2. A and B fly with approaching 3D trajectories.

3. The aircraft initial positions are certain.

4. Airspeeds and vertical speeds are constant and known.

5. A/C affected by the same uncertain horizontal wind.

6. The wind is defined by its two components (𝑤𝑥 and 𝑤𝑦) and it is dependent on the altitude.

7. There is no loss of separation at the starting point.

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▪ Normalized aircraft distance:

Δ 𝐴, 𝐵 𝑡 = max𝑑 𝑡

𝐷,ℎ 𝑡

𝐻

▪ Distance of closest approach

𝛿 𝐴, 𝐵 = min Δ 𝐴, 𝐵 𝑡

▪ There is a conflict between aircraft A and B if

𝛿 𝐴, 𝐵 < 1

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A loss of separation takes place when an aircraft violates the

protected zone of another aircraft

5 NM

1000 ft

Conflict indicator

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The wind components are defined as random processes:

𝑤𝑥 𝑧 = ഥ𝑤𝑥 𝑧 + 𝛿𝑤𝑥𝑧 𝑎

𝑤𝑦 𝑧 = ഥ𝑤𝑦 𝑧 + 𝛿𝑤𝑦𝑧 𝑏

Each realization of the random process corresponds to a different vertical wind profile.

The random variables a and b range from -1 to 1

𝑓𝑎 , 𝑎 ∈ [−1,1]𝑓𝑏, 𝑏 ∈ [−1, 1]

The wind model parameters are obtained from the available probabilistic weather forecast.

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PTM

Transformed random variable

Probabilistic wind model𝑤𝑥 𝑧 = ഥ𝑤𝑥 𝑧 + 𝛿𝑤𝑥

𝑧 𝑎

𝑤𝑦 𝑧 = ഥ𝑤𝑦 𝑧 + 𝛿𝑤𝑦𝑧 𝑏

𝑓𝑎 𝑓𝑏

Conflict detection𝛿 𝐴, 𝐵 = 𝑔(𝑤𝑥, 𝑤𝑦)

Transformed random variable

Input random variables

Transformation

𝜎[𝑣1] = න−∞

∞

𝑣12𝑓𝑣1 𝑣1 𝑑𝑣1 − 𝐸[𝑣1]

2

1/2

P 𝑣1 < 𝑎 = න−∞

𝑎

𝑓𝑣1 𝑣1 𝑑𝑣1

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PTM

𝑓𝑢1,𝑢2(𝑢1, 𝑢2)

𝑓𝑣1,𝑣2(𝑣1, 𝑣2)

𝑣1 = 𝑔1(𝑢1, 𝑢2)𝑣2 = 𝑔2(𝑢1, 𝑢2)

𝑓𝑣1 𝑣1 = න−∞

∞

𝑓𝑣1,𝑣2 𝑣1, 𝑣2 𝑑𝑣2

𝐸[𝑣1] = න−∞

∞

𝑣1𝑓𝑣1 𝑣1 𝑑𝑣1

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Two aircraft with 3D segmented trajectories approaching to a common navigation point.

RNAV STAR routes JNETT.CREDE3 and WOLLF.CREDE3 to Denver International Airport (DEN).

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Two aircraft with 3D segmented trajectories approaching to a common navigation point.

RNAV STAR routes JNETT.CREDE3 and WOLLF.CREDE3 to Denver International Airport (DEN).

𝑉𝐴 = 260 𝑘𝑡

𝑉𝐵 = 250 𝑘𝑡

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Wind data retrieved from High-Resolution Rapid Refresh (HRRR) forecast: 3D Lambert Conformal 3km gridded wind component data at 40 pressure levels over the US.

Forecast lead time of 2h, initialized at 00:00UTC on 22-Dec 2017.

ℎ = 19000 𝑓𝑡

JNETT

CRSTE

COFMN

TUCKK

POWDR

LBASN

TLRID

MOGLS

JNETT

CRSTE

COFMN

TUCKK

POWDR

LBASN

TLRID

MOGLS

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Search area

k=40NM

1917 wind profiles

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ഥ𝑤𝑥 𝑧

ഥ𝑤𝑦 𝑧

𝛿𝑤𝑥𝑧

𝛿𝑤𝑦𝑧

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ഥ𝑤𝑥 𝑧

ഥ𝑤𝑦 𝑧

𝛿𝑤𝑥𝑧

𝛿𝑤𝑦𝑧

𝑤𝑥 𝑧 = ഥ𝑤𝑥 𝑧 + 𝛿𝑤𝑥𝑧 𝑎

𝑤𝑦 𝑧 = ഥ𝑤𝑦 𝑧 + 𝛿𝑤𝑦𝑧 𝑏

PTM Det.

𝐸[𝛿(𝐴, 𝐵)] 0.881 0.891

𝜎[𝛿(𝐴, 𝐵)] 0.131 -

𝑷𝒄𝒐𝒏 76.3% 100%

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Distance of closest approach:

Probability distribution

Mean value

Standard deviation

Probability of conflict

*PTM results have been validated by the Monte-Carlo method.

1. We have studied the propagation of wind uncertainty to the problem of aircraft conflict detection in the TMA

2. The Probabilistic Transformation Method has been successfully applied, allowing the assessment of

the mean value and standard deviation of the aircraft distance of closest approach, and

the probability of conflict.

3. It is expected that by considering weather uncertainty in the trajectory prediction process, the safety and efficiency of the air traffic may be improved.

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Different wind characterization

Terminal Area prob. conflict detection

Considering different types of aircraft

Terminal Area prob. CONFLICT RESOLUTION

𝑤 = 𝑤(𝑥, 𝑦, 𝑧, 𝑡)

Unmanned aerial

vehicles

↓ 𝑃𝑐𝑜𝑛

This research was conducted at the National Center for Atmospheric Research,

Boulder Colorado, financed by the Najeeb E. Halaby Graduate Student Fellowship.

Supported by theSpanish Ministerio de Economía y Competitividad

through Grant TRA2014-58413-CR and co-financed by FEDER funds.