A Probabilistic Model for Aircraft in Climb using Monotonic Functional Gaussian Process Emulators

TL;DR

This paper introduces a probabilistic Gaussian Process model for aircraft climb trajectories that accounts for uncertainty, providing more accurate and sharper predictions than traditional deterministic models, enhancing safety in congested airspace.

Contribution

The paper presents a novel monotonic Gaussian Process emulator for aircraft climb trajectories that captures epistemic uncertainty and improves prediction accuracy over existing deterministic models.

Findings

21% more accurate mean predictions on test data

34% sharper forecast compared to deterministic models

Effective bounding of trajectory uncertainty

Abstract

Ensuring vertical separation is a key means of maintaining safe separation between aircraft in congested airspace. Aircraft trajectories are modelled in the presence of significant epistemic uncertainty, leading to discrepancies between observed trajectories and the predictions of deterministic models, hampering the task of planning to ensure safe separation. In this paper a probabilistic model is presented, for the purpose of emulating the trajectories of aircraft in climb and bounding the uncertainty of the predicted trajectory. A monotonic, functional representation exploits the spatio-temporal correlations in the radar observations. Through the use of Gaussian Process Emulators, features that parameterise the climb are mapped directly to functional outputs, providing a fast approximation, while ensuring that the resulting trajectory is monotonic. The model was applied as a probabilistic digital twin for aircraft in climb and baselined against BADA, a deterministic model widely used in industry. When applied to an unseen test dataset, the probabilistic model was found to provide a mean prediction that was 21% more accurate, with a 34% sharper forecast.