CDO Sensitivity Analysis for Robust Trajectory Planning under Uncertain Weather Prediction

Abstract

When planning and predicting a flight trajectory, uncertainties are inherent both in the current values of various influencing factors and in their evolution. These uncertainties can turn initially “optimized” trajectories into impossible or at least less attractive solutions later when it is executed. In order to support a more robust trajectory planning for Continuous Descent Operations (CDO), this paper investigates how variations of those influencing factors impact the trajectory optimization fidelity. For this purpose, a set of optimal trajectories are generated for each of the variations and their sensitivities are analyzed. The trajectory optimization is formalized as a multi-phase optimal control problem and is numerically solved with the Legendre-Gauss Pseudospectral Method (LGPM). An iterative process is proposed to determine the required number of collocation points to grant a pre-set level of convergence. Case studies are carried out for International Standard Atmosphere (ISA) baseline conditions as well as for wind and temperature variations as relevant representatives of the weather prediction uncertainties. The numerical simulation results show shifts from the reference trajectory depending on wind and temperature variation. Uncertain wind speed caused a larger solution space and more variation in fuel burn than temperature errors. The designed solution spaces, especially the earliest and latest ToD locations, give pilots and air traffic controllers a good reference where their aircraft is expected to match best CDO goals under the individually prevailing uncertainties. We believe that such additional flight envelope information should complement current vertical path displays in glass cockpits to foster robust flight planning and execution.