Due to recent improvements in the quality of DORIS and GNSS observations, the achievable quality in real-time orbit determination has improved drastically, achieving radial position accuracies down to 3 cm. The limited amount of computational power available in real-time scenarios results in a need for more computationally efficient yet still sufficiently accurate dynamical models.
An important aspect of this model is the set of dynamics used to solve for the state transition and sensitivity matrices, which describe the change in orbital state that can be achieved by an earlier change in the orbital state or dynamic parameters. In this work, an approximation of these state transition and sensitivity matrices was investigated, based on the Hill-Clohessy-Wiltshire equations of relative orbital motion. We show that these approximations result in significant computational savings and that they are compatible with centimetre-level orbit determination.