Probabilistic 4D Trajectory Prediction for UAVs Based on Brownian Bridge Motion

Unmanned aerial vehicle (UAV) flight trajectories in complex environments are often affected by multiple uncertainties, making accurate prediction challenging. To address this issue, this study proposes a probabilistic four-dimensional (4D) trajectory prediction model based on Brownian bridge motion. The UAV’s flight from mission start to endpoint is modeled as a Brownian bridge stochastic process with endpoint constraints, where the mean function sequence is constructed from path planning results and UAV performance parameters. To incorporate operational feasibility, the concept of the spatiotemporal reachable domain from time geography is introduced to dynamically constrain reachable positions, while a truncated Brownian bridge distribution is used to model probabilistic positions in three-dimensional space. A simulation platform in a realistic 3D geographical environment is developed to validate the model. Case studies show that the proposed method achieves dynamic probabilistic trajectory prediction under mission constraints with strong adaptability and practicality. The results provide theoretical support and technical reference for trajectory planning, conflict detection, and flight risk assessment in the pre-tactical phase.