Sequential Orbit Determination with the Cubed-Sphere Gravity Model

The cubed-sphere model provides rapid evaluation of the gravity field for more efficient orbit propagation. This paper characterizes the improved computational efficiency of sequential orbit determination, specifically the extended and unscented Kalman filters, when using this new model instead of the common spherical harmonic model. To use the new gravity model with the extended Kalman filter, capabilities to represent the Jacobian of the gravity acceleration are added to numerically integrate the state transition matrix. Filter tests consider improvements for several simulated satellite scenarios with several combinations of measurements provided for estimation. Since cubed-sphere models of higher degree require only a slight change in computation time, orbit propagation and determination systems may now use this model to improve fidelity without any significant change in cost. Using the cubed-sphere model reduces the computational burden of the orbit determination process, with larger benefits found for high-degree filter models. Differences in the estimated trajectories when using the disparate gravity models remain several orders of magnitude less than the absolute filter error for the cases examined.