Copula-Kinematic Performance Model for Aircraft Four-Dimensional Trajectory Generation

Four-dimensional trajectory generation is a fundamental technology for implementing strategic air traffic management. Current mainstream generation techniques based on kinematic models do not account for the coupling characteristics between aircraft motion parameters, leading to significant deviations between generated trajectories and actual flight paths. To address the limitations of conventional kinematic models, this paper proposes a four-dimensional trajectory generation method for aircraft based on a copula-kinematic performance model. This method, framed within the kinematic model, utilizes a Gaussian mixture copula function to capture the correlations between motion parameters, establishing a joint distribution model for these parameters. To ensure the continuity and realism of flight trajectories, separate kinematic models are developed for straight and turning flights, with trajectory generation performed using the Monte Carlo sampling method. The method is validated using flights arriving at and departing from Shanghai Pudong International Airport, examined from both spatial and temporal perspectives. Results indicate that the trajectories generated by the copula-kinematic model outperform those from conventional kinematic models and align closely with actual flight paths. Furthermore, applying this method to strategic conflict identification allows for the detection of potential aircraft conflicts, including their locations and timings, from flight plans.