Trajectory Planning Method in Time-Variant Wind Considering Heterogeneity of Segment Flight Time Distribution

The application of Trajectory-Based Operation (TBO) and Free-Route Airspace (FRA) can relieve air traffic congestion and reduce flight delays. However, this new operational framework has higher requirements for the reliability and efficiency of the trajectory, which will be significantly influenced if the analysis of wind uncertainty during trajectory planning is insufficient. In the literature, trajectory planning models considering wind uncertainty are developed based on the time-invariant condition (i.e., three-dimensional), which may potentially lead to a significant discrepancy between the predicted flight time and the real flight time. To address this problem, this study proposes a trajectory planning model considering time-variant wind uncertainty (i.e., four-dimensional). This study aims to optimize a reliable and efficient trajectory by minimizing the Mean-Excess Flight Time (MEFT). This model formulates wind as a discrete variable, forming the foundation of the proposed time-variant predicted method that can calculate the segment flight time accurately. To avoid the homogeneous assumption of distributions, we specifically apply the first four moments (i.e., expectation, variance, skewness, and kurtosis) to describe the stochasticity of the distributions, rather than using the probability distribution function. We apply a two-stage algorithm to solve this problem and demonstrate its convergence in the time-variant network. The simulation results show that the optimal trajectory has 99.2% reliability and reduces flight time by approximately 9.2% compared to the current structured airspace trajectory. In addition, the solution time is only 2.3 min, which can satisfy the requirement of trajectory planning.