High-Order Discrete-Time Observers for Short-Term Aircraft Trajectory Prediction

Accurate short-term aircraft trajectory prediction is essential for applications such as air traffic management and air defense, particularly under maneuvering conditions and limited decision time. This paper investigates discrete-time optimal and robust observer formulations for one-step-ahead aircraft trajectory prediction, with emphasis on high-order (HO) disturbance modeling via state augmentation. Standard and HO versions of H2, H∞, and LQR observers are formulated and evaluated for two-dimensional position prediction. Prediction performance is assessed using both synthetic trajectories and real aircraft data, under realistic measurement noise and a sampling interval of 1 Hz. Results show that, under model-matched conditions, standard observers achieve the lowest prediction error, while HO augmentation provides limited benefit. In contrast, under model mismatch and for real flight trajectories exhibiting maneuvering behavior, HO observers consistently reduce prediction error relative to their non-HO counterparts. A statistical comparison based on generalized least squares (GLS) regression confirms that these improvements are statistically significant across observer families.