Determination and Estimation of Differential Mean Orbital Elements for Formation-Flying Missions

Differential mean orbital elements are often taken as control states for relative-motion operations in spacecraft formation-flying missions. This paper investigates the problem of estimating differential mean orbital elements for formation-flying missions. Semi-analytical solutions for the perturbed Earth orbits with a dimensionless and near-circular modified form are introduced. The differential mean orbital elements are estimated from the absolute positions and velocities of the chief spacecraft, as well as the relative positions and velocities between the dual spacecraft. Three representative approaches, including numerical computation, extended Kalman filter, and square-root unscented Kalman filter, are presented in detail for this purpose. Numerical simulations are provided to test the performance of each approach.