Data-based

Statistical approaches represent the simpler end of the data-driven spectrum. Techniques such as Gaussian mixture models and statistical copulas can capture the joint distribution of trajectory features reasonably well, particularly when the dataset is small and the distribution is not too complex. Work at Zurich Airport demonstrated this for go-around procedures, using a reference trajectory alignment to compress 2D paths into scalar features, and then fitting a vine copula to model the dependencies between those features. The approach is elegant and interpretable, but it does not scale easily to four-dimensional trajectories or to datasets with rich internal structure.

Variational Autoencoders (VAEs) learns a compressed, continuous representation of the trajectory space, a latent space, where new trajectories can be sampled and decoded back into realistic flight paths. The key advantage over simpler generative models is that VAEs naturally capture uncertainty: the latent space encodes not just what trajectories look like, but how much variability exists around any given shape.

Within the VAE family, the architecture that has shown the strongest results for aircraft trajectory generation combines a Temporal Convolutional Network (TCN) encoder with a VampPrior, a flexible, data-driven prior distribution that adapts to the complexity of the latent space rather than assuming a simple Gaussian shape. Evaluated on 14,000 landing trajectories at Zurich Airport, this architecture significantly outperformed both simpler VAE variants and Gaussian mixture models, producing synthetic trajectories that matched the statistical distribution of real operations and remained physically flyable when replayed in the BlueSky flight simulator.

More recent work has extended these ideas to en-route trajectories using a Time-based Vector Quantized VAE (TimeVQVAE), which operates in the time-frequency domain and uses transformer-based priors to capture long-range dependencies across entire flight paths. The ability to generate class-conditional trajectories, for example, conditioned on a specific route or traffic cluster, opens the door to the kind of targeted, controlled synthesis that procedure design requires.

Transformers have also been explored for trajectory prediction tasks, specifically for completing a trajectory given its partial history. A transformer-based model conditioned on Eurocontrol flight plan messages has demonstrated the feasibility of three-hour demand forecasting in Dutch airspace, integrating ERA5 weather data alongside surveillance information.

Diffusion models represent the frontier of the field. While no published work has yet applied them directly to aircraft trajectory generation, their strong performance in time series synthesis tasks makes them a natural candidate for exploration in the next phase of the project.

The methodology planned for VITOLMINS combines these threads. The starting point is unconditioned generation of airplane trajectories using VAE-based architectures, with TCN and transformer encoders explored in parallel. The latent space will be analysed for interpretability, a central concern given that VCA-specific training data does not yet exist and the eventual goal is to generate plausible VCA trajectories by combining characteristics learned from airliner and helicopter data. Once a reliable unconditional generator is established, the work will extend to conditional generation, incorporating weather context, flight phase segmentation, and ultimately the specific procedural constraints of VCA terminal operations.

Evaluation will draw on the full range of metrics identified in the literature: statistical measures such as e-distance and KL divergence to assess distributional fidelity, flyability checks via BlueSky simulation to assess physical realism, and, where possible, expert review by pilots or air traffic controllers to assess operational credibility.