Accuracy impact of trajectory sampling and representation for Trajectory-Based Operations

In Trajectory-Based Operations (TBO) 4-dimensional trajectories (4DT) are the basis for planning and executing all aspects of flight operations. The exchange of 4DT data is therefore necessary and essential for TBO. The effectiveness of TBO is limited by trajectory accuracy, which depends on prediction errors due to assumptions and limitations in the construction process (wind errors, unknown aircraft intent, etc.) and in losses introduced in the sampling and representation of the trajectory. Trajectory sampling is the process of selecting the points included in the trajectory that is exported to clients. Trajectory representation is the set of attributes, such as location, speeds, etc., associated with each trajectory point. Emerging trajectory exchange standards need to take into account the effects of sampling and representation because the loss of accuracy in trajectory representation has a direct and significant impact on the ability to support TBO. This paper focuses on the analysis of issues and solutions related to loss of accuracy due to sampling and exclusion of high order time derivatives in 4DT data under realistic conditions. Analytical expressions of errors are derived and situations where these errors are more likely to arise are identified. The analysis examines mitigation strategies, such as segment length reduction and 4DT rebuild methods, to achieve required accuracy goals. The effects of wind uncertainty, spatial wind shear, variations of air speed and vertical rate in Optimized Profile Descent (OPD), and speed variations resulting from vertical guidance are examined under assumptions of limited sample rate and lack of acceleration information.