Synthetic Aircraft Trajectories Generated with Multivariate Density Models

Abstract

Aircraft trajectory generation is a high stakes problem with a wide scope of applications, including collision risk estimation, capacity management and airspace design. Most generation methods focus on optimizing a criterion under constraints to find an optimal path, or on predicting aircraft trajectories. Nevertheless, little in the way of contribution has been made in the field of the artificial generation of random sets of trajectories. This work proposes a new approach to model two-dimensional flows in order to build realistic artificial flight paths. The method has the advantage of being highly intuitive and explainable. Experiments were conducted on go-arounds at Zurich Airport, and the quality of the generated trajectories was evaluated with respect their shape and statistical distribution. The last part of the study explores strategies to extend the work to non-regularly shaped trajectories.

Deep Generative Modelling of Aircraft Trajectories in Terminal Maneuvering Areas

“…Generative modelling involves the estimation of the joint distribution over all the variables to mimic the generation process of observed data. For aircraft trajectories described by (track 𝑖 , groundspeed 𝑖 , altitude 𝑖 , time 𝑖 ) for 𝑖 in [0, … 𝑛] with 𝑛 = 200 observations, the model has to estimate a distribution in dimension 800, which cannot be done with classical statistical methods such as marginal-copula decomposition, as applied in Krauth et al (2021). When it comes to the estimation of complex multivariate probability densities, resorting to dimensionality reduction is often a good practice, as a high number of features often leads to weaker goodness of fit due to the Curse of Dimensionality.…”

“…However, introducing randomness into these deterministic models is complicated, and it is difficult to capture the full amount of variability present in complex flight patterns (requirements i and iii). Data-driven models (Krauth, Morio, Olive, Figuet, & Monstein, 2021) mimic the distribution of observed trajectories to produce synthetic trajectories that are identically distributed (requirement i). Therefore, they are very effective in capturing the high uncertainty present in the trajectories (iii), but generation may lack physical realism (requirement ii).…”

“…The authors show that resorting to dimensionality reduction is a promising idea to deal with 4dimensional trajectories, but the method only allows to modify existing patterns, and not to perform a proper generation, as PCA is not designed to decode points from the latent space that do not correspond to observed trajectories. Krauth et al (2021) apply dimensionality reduction for the sole purpose of improving the probability density estimate of the observed trajectories. The trajectories are not represented by their latitude and longitude anymore, but by their projection on fixed perpendicular lines.…”

“…The generation of go-arounds would require to build a dedicated dataset on several years of observation. This was done previously in Krauth et al (2021). The sample used for the study is represented on Fig.…”

“…However, missedapproaches studies might require a special treatment as they are rarely observed. Krauth et al (2021) treated the problem by specifically constructing a dataset of go-around trajectories. One might also want to use the dataset provided by Monstein, Figuet, Krauth, Waltert, and Dettling (2022).…”