Synthetic Aircraft Trajectories Generated with Multivariate Density Models

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.

Quantifying the closeness to a set of random curves via the mean marginal likelihood

In this paper, we tackle the problem of quantifying the closeness of a newly observed curve to a given sample of random functions, supposed to have been sampled from the same distribution. We define a probabilistic criterion for such a purpose, based on the marginal density functions of an underlying random process. For practical applications, a class of estimators based on the aggregation of multivariate density estimators is introduced and proved to be consistent. We illustrate the effectiveness of our estimators, as well as the practical usefulness of the proposed criterion, by applying our method to a dataset of real aircraft trajectories.

Asymptotic Convergence of Soft-Constrained Neural Networks for Density Estimation

A soft-constrained neural network for density estimation (SC-NN-4pdf) has recently been introduced to tackle the issues arising from the application of neural networks to density estimation problems (in particular, the satisfaction of the second Kolmogorov axiom). Although the SC-NN-4pdf has been shown to outperform parametric and non-parametric approaches (from both the machine learning and the statistics areas) over a variety of univariate and multivariate density estimation tasks, no clear rationale behind its performance has been put forward so far. Neither has there been any analysis of the fundamental theoretical properties of the SC-NN-4pdf. This paper narrows the gaps, delivering a formal statement of the class of density functions that can be modeled to any degree of precision by SC-NN-4pdfs, as well as a proof of asymptotic convergence in probability of the SC-NN-4pdf training algorithm under mild conditions for a popular class of neural architectures. These properties of the SC-NN-4pdf lay the groundwork for understanding the strong estimation capabilities that SC-NN-4pdfs have only exhibited empirically so far.