arxiv.org/abs/2309.14941

B738
Samples of the thrust function with optimised bounds, compared to the nominal BADA thrust profile.(bottom)
Sampled trajectories and uncertainty bounds when thrust samples and bounds run through BADA.(middle)
Test data compared to the generative model mean and optimised uncertainty bounds and nominal BADA (top)

Learning Generative Models for Climbing Aircraft from Radar Data

Nick Pepper, Marc Thomas

Accurate trajectory prediction (TP) for climbing aircraft is hampered by the presence of epistemic uncertainties concerning aircraft operation, which can lead to significant misspecification between predicted and observed trajectories. This paper proposes a generative model for climbing aircraft in which the standard Base of Aircraft Data (BADA) model is enriched by a functional correction to the thrust that is learned from data. The method offers three features: predictions of the arrival time with 66.3% less error when compared to BADA; generated trajectories that are realistic when compared to test data; and a means of computing confidence bounds for minimal computational cost.

Subjects:	Systems and Control (eess.SY); Machine Learning (cs.LG)
Cite as:	arXiv:2309.14941 [eess.SY]
	(or arXiv:2309.14941v1 [eess.SY] for this version)
	https://doi.org/10.48550/arXiv.2309.14941

Submission history

From: Nick Pepper [view email]
[v1] Tue, 26 Sep 2023 13:53:53 UTC (21,196 KB)

 

Why I'm Commenting: I did some track processing using Mode S multilateration sensors and squitter data fused with ASDE-3 primary radar for the FAA AMASS runway incursion reduction program which covered landing and takeoff, runway roll, and taxiway traffic.[SLP]

 

About the authors and their background:

Nick Pepper (First author)

• Works at The Alan Turing Institute and The British Library in London, UK.
• He is currently working as a Research Associate on Project Bluebird, a Prosperity Partnership between NATS, the UK’s largest air traffic provider, and the Turing. The aim of the project is to develop the world’s first AI system to safely control a section of airspace in live trials. Within the project, he is a member of a team that is developing a Digital Twin that predicts the movement of aircraft through a sector of airspace.
  
• His research focuses on probabilistic machine learning methods for trajectory prediction.
• Previously published work on Gaussian process models for aircraft climbs and uncertainty quantification.
• Also has publications on adaptive learning for reliability analysis.
• See Research Gate profile
  

Marc Thomas (Second author)

• Works at NATS, which is the main air navigation service provider in the UK.
• Currently industry lead building a digital twin of UK airspace as part of Project Bluebird, a partnership between NATS and The Alan Turing Institute which will deliver the world’s first artificial intelligence (AI) system to control a section of airspace in live trials..
• No other previous publications listed for him based on the information given.

The Alan Turing Institute is a major research center in the UK focused on data science and artificial intelligence.

NATS is the UK's air navigation services provider and would be a key stakeholder for integrating data-driven trajectory prediction methods into operational systems.

Epistemic uncertainties referring to aircraft operation relate to unknowns or lack of knowledge about how aircraft are actually being flown and operated in real conditions. Some examples of these uncertainties include:

• Aircraft mass - The exact mass can vary from flight to flight based on passenger load, fuel etc. This affects aircraft performance.
• Thrust setting - The thrust level selected by pilots can vary and is not known to air traffic control.
• Airline procedures - Aircraft on certain routes may follow specific airline operating procedures that differ from typical assumptions.
• Wind conditions - The actual winds experienced by an aircraft in flight may differ from forecast winds.
• Speed profile - The chosen speeds during different phases of flight are not precisely shared with air traffic management.

These uncertainties mean there can be significant discrepancies between the real aircraft trajectory and what is predicted by models like BADA using assumed nominal parameters.

key points:

The paper proposes a generative model to learn corrections to the thrust profile in the BADA aircraft performance model from secondary surveillance Mode S radar data. This aims to improve trajectory prediction for climbing aircraft.
The model fits an effective thrust term to BADA using observed climb rates from radar data. This term represents corrections to thrust and misspecifications in other BADA parameters like mass and speed profile.
Functional PCA is used to model variability in the fitted thrust profiles across different flights. This allows generating realistic synthetic climbs and defining confidence bounds on performance.
The model is evaluated on real radar data from over 700,000 flights across UK airspace. Key results:

1. The mean trajectory prediction error is reduced by 66.3% compared to default BADA.
2. The generated distributions of climb times match the real data well.
3. The analytically computed 95% confidence bounds contain 95.4% of the test data on average.

The hybrid approach improves BADA's accuracy for specific routes while retaining its physical constraints. The ability to generate bounds and synthetic climbs is also useful for trajectory prediction applications.
Overall, the data-driven generative model enhances BADA's climbing aircraft performance for trajectory prediction. The confidence bounds and realistic samples are valuable features.

The BADA (Base of Aircraft Data) model is a total energy model that is widely used for aircraft trajectory prediction in air traffic management. Some key points about BADA:

• It is a physics-based model that describes the flight mechanics and performance of different aircraft types.
• The model uses equations representing thrust, drag, energy usage etc along with aircraft-specific parameters.
• Parameters like thrust profiles, fuel flow, speed schedules are provided for many common commercial aircraft.
• These parameters are calibrated using reference data to capture typical global performance.
• BADA aims to provide a common aircraft performance model that can be applied worldwide in ATM systems.
• However, it can sometimes be inaccurate for specific routes where airline procedures differ.
• The model is deterministic and does not account for uncertainties like wind, mass, airline procedures.
• So the paper proposes learning corrections to BADA from radar data to improve its accuracy for climbing flights.

In summary, BADA is a standardized global aircraft performance model based on physics and reference data. It is widely used in air traffic management but can be mis-specified for local operations. The paper aims to improve BADA's climbing flight predictions using real trajectory data.

Based on the details provided in the paper, the radar data used for training the model came from real-world aircraft surveillance data collected across southern UK airspace (London FIR) over a period of 3 months (July - September 2019).

Specifically:

• The raw dataset contained over 700,000 flights tracked by Mode S radar over the time period.
• It included a range of common commercial aircraft types like A320, B738, B772 etc.
• The data was filtered to only include radar points with climb rates ≥ 500 ft/min in the flight level range 150-325.
• This focuses the training on enroute climbing trajectories in upper airspace.
• The climbs in this altitude range are less prone to local operational constraints.
• The filtered dataset was split 66:33 into train and test sets.
• For each aircraft type, the effective thrust term was fitted to the training climbs via functional PCA.
• This produced a dataset of thrust profiles to learn corrections to BADA's nominal thrust schedule.

So in summary, real Mode S surveillance radar data from hundreds of thousands of flights was used to train the model. The training data focused specifically on enroute climb trajectories in upper airspace for frequent aircraft types. This enabled learning improved thrust profiles tailored to real climb performance on common routes.

Mode S is a type of radar technology used for aircraft surveillance and tracking in air traffic control systems. Some key points about Mode S radar:

• It is a secondary radar system that relies on signals transmitted from an interrogator on the ground.
• Aircraft equipped with Mode S transponders can reply to interrogations with detailed flight information.
• This allows selective interrogation of individual aircraft unlike primary radar.
• The replies contain the aircraft callsign, altitude, speed, heading and other data derived from onboard instruments such as radio altimeter and GPS. There may be some variable delay in transmission.
  
• Mode S uses digital communications between the ground station and aircraft transponders.
• It provides enhanced surveillance and accuracy compared to older analog secondary radar.
• The discrete address of each Mode S transponder prevents garbling of replies from multiple aircraft.
• By requesting altitude updates from specific aircraft, vertical rate can also be determined.
• Ground tracking and flight plan correlation is also improved with the detailed flight parameter replies.
• Most commercial and civilian aircraft today are fitted with Mode S transponders.

Mode S is a digital secondary radar technology that enables selective interrogation of aircraft transponders and receipt of detailed flight parameter data for surveillance purposes. The ability to extract vertical rates and accurate flight profiles from Mode S radar made it very suitable for training the data-driven climb model described in this paper.

Regarding Mode S radar errors:

• Altitude measurements are typically accurate to within 25 feet.
• The quantization level is usually 25 or 100 feet.
• Horizontal position accuracy is around 0.05 NM.
• Vertical rate measurements can have errors up to ±500 fpm under ideal conditions.

So in summary, epistemic uncertainties cover unknowns in how aircraft are operated in real flights. Mode S radar provides relatively precise surveillance data but still has some quantization and measurement errors that need consideration.

The reporting rate and sample rates for Mode S surveillance data depend on the specific setup and configuration, but some typical values are:

• Mode S squitter rate (unsolicited broadcast): ~1-2 seconds
• Mode S radar interrogation rate: ~2-5 seconds
• Altitude sampling on aircraft: ~1-2 times per second
• Horizontal position sampling: ~1-5 times per second

So in summary:

• The Mode S squitter provides an unsolicited altitude report around every 1-2 seconds.
• The ground radar actively interrogates aircraft around every 2-5 seconds requesting altitude, position etc.
• On the aircraft side, sensors like the altimeter and GPS sample at 1-2 Hz and 1-5 Hz respectively.
• This means the effective radar track reporting rate is around once per 2 seconds at a minimum.
• The paper indicates a reporting rate of ~4 seconds between consecutive radar samples.

So the Mode S data provides discrete altitude and position samples at a relatively high frequency of 0.25-0.5 Hz. This allows reconstructing an accurate vertical profile for climbing trajectories. The paper uses a smoothing/interpolation process to create continuous climb profiles from the discrete radar samples for training the model.

Exact statistics are not provided, we can infer from the context that:

• The training data was filtered to active climb segments only.
• The climb rates were distributed mostly between 1000-4000 ft/min during these segments.
• There may have been some faster climbs above 4000 ft/min as well in the data.
• But most commercial jet enroute climbs would likely be in the 1000-4000 ft/min range based on typical flight performance.

 The interaction between climb rate, sensor sample time, data quantization/rounding, and data link report time creates a predictable, but apparently random error in position and altitude data which should be considered in tracking. Its like synchronized traffic lights . They appear to be random to the average driver, but they are quite predictable, and with the right speed, traffic can flow with minimum interruption.This effect was strong in the data analyzed for AMASS RIRP.