Time Series Embeddings for Air Traffic Management
This section presents embedding approaches for transforming flight trajectories into compact vector representations. These embeddings enable trajectory clustering, anomaly detection, core-set extraction, and transfer learning applications.
Embedding Approaches
TCVAE Framework
Figure 1: TCVAE Embedding Process. Flight trajectories are processed into compact latent representations for clustering, anomaly detection, and core-set extraction.
TCVAE transforms flight trajectories into vector embeddings using temporal convolutional encoding and variational latent representations.
Latent Flow Matching Framework
Figure 39: Transfer Learning with Latent Flow Matching. Two-phase process: pretraining on source airport data, then transferring to target airport with limited data. Enables modeling of airports with sparse datasets.
Latent Flow Matching combines VAE representations with flow matching for transfer learning applications, using a two-phase approach from source to target airports.
Trajectory Clustering Applications
Landing Trajectory Analysis
The TCVAE embeddings enable clustering of landing trajectories, revealing approach patterns for different airports.
Dublin (EIDW) Landing Trajectories
Figure 7: Dublin Raw Landing Trajectories. Collection of raw landing trajectories for Dublin airport.
Figure 8: Dublin GMM Clustering. Gaussian Mixture Model clustering identifying distinct approach patterns for Dublin.
Figure 10: Dublin HDBSCAN Clustering (With Outliers). Complete clustering including anomalous trajectories.
Figure 9: Dublin HDBSCAN Clustering (No Outliers). Main approach pattern clusters for Dublin airport.
Figure 11: Dublin Representative Trajectories. Core representative trajectories for each identified cluster.
London (EGLL) Landing Trajectories
Figure 12: London Raw Landing Trajectories. Raw landing trajectories showing London Heathrow's complex approach patterns.
Figure 13: London GMM Clustering. GMM clustering results for London Heathrow approach patterns.
Figure 15: London HDBSCAN Clustering (With Outliers). Complete clustering analysis including outlier detection.
Figure 14: London HDBSCAN Clustering (No Outliers). Primary approach clusters for London Heathrow.
Figure 16: London Representative Trajectories. Representative trajectories for each approach pattern cluster.
Paris (LFPG) Landing Trajectories
Figure 17: Paris Raw Landing Trajectories. Raw landing trajectories for Paris Charles de Gaulle airport.
Figure 18: Paris GMM Clustering. Gaussian Mixture Model clustering for Paris approach patterns.
Figure 20: Paris HDBSCAN Clustering (With Outliers). Complete clustering including anomaly identification.
Figure 19: Paris HDBSCAN Clustering (No Outliers). Main approach pattern identification for Paris CDG.
Figure 21: Paris Representative Trajectories. Core trajectories representing each cluster's characteristics.
Zurich (LSZH) Landing Trajectories
Figure 22: Zurich Raw Landing Trajectories. Raw landing trajectories showing Zurich's approach patterns.
Figure 23: Zurich GMM Clustering. GMM clustering results for Zurich approach patterns.
Figure 25: Zurich HDBSCAN Clustering (With Outliers). Complete clustering with outlier trajectory identification.
Figure 24: Zurich HDBSCAN Clustering (No Outliers). Primary approach clusters for Zurich airport.
Figure 26: Zurich Representative Trajectories. Representative trajectories for each identified cluster.
End-to-End Route Analysis
Complete Route Trajectories
The embeddings also enable analysis of complete end-to-end flight routes, revealing patterns in full journey trajectories.
Amsterdam to Milan Route (EHAM-LIMC)
Figure 27: EHAM-LIMC Raw Trajectories. Raw trajectories for flights between Amsterdam and Milan.
Figure 28: EHAM-LIMC GMM Clustering. Route clustering showing different path preferences.
Stockholm to Paris Route (ESSA-LFPG)
Figure 31: ESSA-LFPG Raw Trajectories. Raw trajectories for flights between Stockholm and Paris.
Figure 32: ESSA-LFPG GMM Clustering. Route pattern identification for Stockholm-Paris flights.
Vienna to London Route (LOWW-EGLL)
Figure 35: LOWW-EGLL Raw Trajectories. Raw trajectories for flights between Vienna and London.
Figure 36: LOWW-EGLL GMM Clustering. Route clustering for Vienna-London flights.
Transfer Learning Applications
Transfer learning extends trajectory generation to airports or routes with limited historical data, demonstrating knowledge transfer between different operational contexts.
Performance Comparison with 5% Target Data
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Comparison showing improved trajectory quality when using transfer learning with only 5% of target airport data
Performance Comparison with 20% Target Data
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Trajectory quality comparison showing sustained transfer learning benefits with increased target data availability
Key transfer learning findings:
- Improved trajectory quality with minimal target airport data
- Knowledge preservation of general flight dynamics across different operational contexts
- Data efficiency enabling generation with as little as 5-20% of full datasets
- Applicability for airports or routes with limited historical trajectory data
Transfer learning applications include:
- Regional airports with sparse historical data
- New routes requiring trajectory modeling
- Seasonal operations with limited data periods
- Emergency scenarios with rare operational patterns
Applications
Operational Analysis
- Pattern discovery across routes and airports
- Anomaly detection for unusual trajectories
- Trajectory clustering for operational insights
Simulation and Modeling
- Core-set extraction of representative trajectories
- Transfer learning between airports
- Synthetic data generation
Performance Benefits
- Reduced computational requirements
- Efficient analysis of large trajectory datasets
- Scalable across multiple airports
Summary
These embedding frameworks capture the spatial-temporal dynamics of flight trajectories, enabling trajectory clustering, transfer learning between airports, and operational applications. Transfer learning allows models trained on data-rich airports to work effectively with limited target data (as little as 5-20% of full datasets), supporting route optimization across airports with varying data availability.