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Inferring Traffic Models in Terminal Airspace from Flight Tracks and Procedures

Soyeon Jung, Amelia Hardy, Mykel J. Kochenderfer

TL;DR

The paper tackles the challenge of realistically modeling aircraft trajectories in terminal airspace under IFR by capturing stage-dependent variability and inter-aircraft interactions. It develops a parsimonious, probabilistic framework based on Gaussian Mixture Models learned from both published procedures and radar-tracked trajectories, with a low-rank covariance approach via probabilistic PCA to improve robustness. A key extension introduces pairwise GMMs to model correlations between aircraft, enabling synthetic generation of traffic scenes with an arbitrary number of aircraft. Evaluation on JFK arrivals shows the method reproduces major patterns and uncertainties, with Jensen–Shannon divergence used to quantify distributional similarity and a multiple-aircraft model improving speed realism and separation performance, suggesting practical utility for ATM design and validation.

Abstract

Realistic aircraft trajectory models are useful in the design and validation of air traffic management (ATM) systems. Models of aircraft operated under instrument flight rules (IFR) require capturing the variability inherent in how aircraft follow standard flight procedures. The variability in aircraft behavior differs among flight stages. In this paper, we propose a simple probabilistic model that can learn this variability from procedural data and flight tracks collected from radar surveillance data. For each segment, we use a Gaussian mixture model to learn the deviations of aircraft trajectories from their procedures. Given new procedures, we generate synthetic trajectories by sampling a series of deviations from the Gaussian mixture model and reconstructing the aircraft trajectory using the deviations and the procedures. We extend this method to capture pairwise correlations between aircraft and show how a pairwise model can be used to generate traffic involving an arbitrary number of aircraft. We demonstrate the proposed models on the arrival tracks and procedures of the John F. Kennedy International Airport. Distributional similarity between the original and the synthetic trajectory dataset was evaluated using the Jensen-Shannon divergence between the empirical distributions of different variables and we provide qualitative analyses of the synthetic trajectories generated.

Inferring Traffic Models in Terminal Airspace from Flight Tracks and Procedures

TL;DR

The paper tackles the challenge of realistically modeling aircraft trajectories in terminal airspace under IFR by capturing stage-dependent variability and inter-aircraft interactions. It develops a parsimonious, probabilistic framework based on Gaussian Mixture Models learned from both published procedures and radar-tracked trajectories, with a low-rank covariance approach via probabilistic PCA to improve robustness. A key extension introduces pairwise GMMs to model correlations between aircraft, enabling synthetic generation of traffic scenes with an arbitrary number of aircraft. Evaluation on JFK arrivals shows the method reproduces major patterns and uncertainties, with Jensen–Shannon divergence used to quantify distributional similarity and a multiple-aircraft model improving speed realism and separation performance, suggesting practical utility for ATM design and validation.

Abstract

Realistic aircraft trajectory models are useful in the design and validation of air traffic management (ATM) systems. Models of aircraft operated under instrument flight rules (IFR) require capturing the variability inherent in how aircraft follow standard flight procedures. The variability in aircraft behavior differs among flight stages. In this paper, we propose a simple probabilistic model that can learn this variability from procedural data and flight tracks collected from radar surveillance data. For each segment, we use a Gaussian mixture model to learn the deviations of aircraft trajectories from their procedures. Given new procedures, we generate synthetic trajectories by sampling a series of deviations from the Gaussian mixture model and reconstructing the aircraft trajectory using the deviations and the procedures. We extend this method to capture pairwise correlations between aircraft and show how a pairwise model can be used to generate traffic involving an arbitrary number of aircraft. We demonstrate the proposed models on the arrival tracks and procedures of the John F. Kennedy International Airport. Distributional similarity between the original and the synthetic trajectory dataset was evaluated using the Jensen-Shannon divergence between the empirical distributions of different variables and we provide qualitative analyses of the synthetic trajectories generated.
Paper Structure (17 sections, 15 equations, 13 figures, 1 table)

This paper contains 17 sections, 15 equations, 13 figures, 1 table.

Table of Contents

  1. Introduction
  2. Trajectory and Procedure Data
  3. Trajectory Data
  4. Flight Procedure Data
  5. Single Trajectory Model
  6. Construction of Input Vector
  7. Gaussian Mixture Model
  8. Low-rank Approximation of Covariance Matrices
  9. Trajectory Generation
  10. Multiple Trajectory Model
  11. Pairwise Trajectory GMM
  12. Multiple Trajectory Generation
  13. Experiments
  14. Model Selection
  15. Model Validation and Generalization
  16. ...and 2 more sections

Figures (13)

  • Figure 1: Log-histogram of all actual arrival tracks of KJFK.
  • Figure 2: Log-histogram of actual arrival tracks to KJFK 04R and associated flight procedures.
  • Figure 3: Flowchart overview of single trajectory model
  • Figure 4: Example sequence of deviations between aircraft and procedural trajectory.
  • Figure 5: Partition of the sequence of deviations for the final approach segment to form a conditional distribution.
  • ...and 8 more figures