Orbit determination across unknown maneuvers using the essential Thrust-Fourier-Coefficients

Any maneuver performed by a satellite transitioning between two arbitrary orbital states can be represented as an equivalent maneuver involving Thrust-Fourier-Coefficients (TFCs). With a selected TFC set as a basis, a thrust acceleration can be constructed to interpolate two unconnected states across an unknown maneuver. This representation technique with TFCs enables us to facilitate the analytical propagation of uncertainties of the satellite state. This approach allows for the usage of existing pre-maneuver orbit estimation to compute the orbit solution after the unknown maneuver. In this paper, we applied this approach to orbit determination (OD) problems across unknown maneuvers by appending different combinations of TFCs to the state vector in the batch filter. The aim is to investigate how different maneuver representations with different TFC sets affect the OD solution across unknown maneuvers. Simulation results show that each TFC set provides different representations of the unknown perturbing acceleration, which yields varying magnitudes of delta velocity for a given maneuver. However, OD solutions across unknown maneuvers using different TFC sets display equivalent performance over the post-maneuver arc as long as those TFC sets are capable of generating the apparent secular motion caused by a given unknown maneuver.