Descent 4D trajectory optimisation for curved GNSS approaches

This paper describes the 4-Dimensional Trajectory (4DT) optimisation algorithm implemented to avoid a variety Global Navigation Satellite System (GNSS) signal degradations predicted by Avionics Based Integrity Augmentation system (ABIA). The paper focusses on descent and initial curved GNSS approach phases in a dense Terminal Manoeuvring Area (TMA) scenario, with multiple aircraft converging on the same short and curved final GNSS approach leg. The reference platform for this study is the Javelin Remotely Piloted Aircraft System (RPAS). The 4DT optimisation algorithm implements three degrees-of-freedom aircraft dynamics models as well as suitable GNSS satellite visibility models based on Global Positioning System (GPS) constellation ephemeris data. Direct transcription methods of the global orthogonal (pseudospectral) collocation family are implemented, generating optimal high-integrity trajectories for curved GNSS approaches in real-time. The optimal trajectories calculated by the pseudospectral method are subsequently processed by control input smoothing and manoeuvre identification algorithms to translate the mathematical optimum into a pilot/autopilot-flyable and concisely described 4DT intent. The characteristics of the proposed 4DT optimisation algorithm are evaluated in representative simulation case studies targeting short and curved GNSS approaches in dense TMA conditions, showing very satisfactory performance.