Fast Surrogate Models for Adaptive Aircraft Trajectory Prediction in En route Airspace

TL;DR

This work tackles the challenge of accurate en route trajectory prediction under epistemic uncertainty by combining a fast surrogate model and real-time data assimilation. A discrete-time linear state-space surrogate emulates the BADA trajectory model, enabling rapid sampling, while a Liu–West particle filter jointly estimates aircraft state and the underlying dynamics learned from historical trajectories. Compared with BADA-based and Kalman-filter baselines, the proposed approach delivers substantially improved estimates of time-to-top-of-climb and bottom-of-descent and shorter prediction errors in distance flown, demonstrating strong potential for real-time adaptive TP and uncertainty quantification. The method shows promise for integration into a Digital Twin of enroute airspace, with opportunities for transfer learning and improved probabilistic calibration in future work.

Abstract

Trajectory prediction (TP) is crucial for ensuring safety and efficiency in modern air traffic management systems. It is, for example, a core component of conflict detection and resolution tools, arrival sequencing algorithms, capacity planning, as well as several future concepts. However, TP accuracy within operational systems is hampered by a range of epistemic uncertainties such as the mass and performance settings of aircraft and the effect of meteorological conditions on aircraft performance. It can also require considerable computational resources. This paper proposes a method for adaptive TP that has two components: first, a fast surrogate TP model based on linear state space models (LSSM)s with an execution time that was 6.7 times lower on average than an implementation of the Base of Aircraft Data (BADA) in Python. It is demonstrated that such models can effectively emulate the BADA aircraft performance model, which is based on the numerical solution of a partial differential equation (PDE), and that the LSSMs can be fitted to trajectories in a dataset of historic flight data. Secondly, the paper proposes an algorithm to assimilate radar observations using particle filtering to adaptively refine TP accuracy. Comparison with baselines using BADA and Kalman filtering demonstrate that the proposed framework improves system identification and state estimation for both climb and descent phases, with 46.3% and 64.7% better estimates for time to top of climb and bottom of descent compared to the best performing benchmark model. In particular, the particle filtering approach provides the flexibility to capture non-linear performance effects including the CAS-Mach transition.

Figures (7)

• Figure 1: Fitted s used as an emulator for the trajectories of a range of climbing and descending aircraft in the model.
• Figure 2: Comparison of the in predicting the time and location of top of climb/bottom of descent between the investigated methods.
• Figure 3: compared to , displayed by aircraft type.
• Figure 4: The difference in errors between the and filtering methods, per aircraft type, with marker size determined by number of radar blips in the test dataset for that aircraft type.
• Figure 5: Climbing trajectories sampled from the test dataset, compared to s from the investigated methods. Panels on the left display altitude against time, while those on the right indicate against time.