A probabilistic model for aircraft in climb using monotonic functional Gaussian process emulators

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