Orbit determination for impulsively maneuvering spacecraft using a modified state transition tensor

This paper proposes a method to accurately resolve orbit determination (OD) for a spacecraft with unknown impulsive maneuvers. The proposed method handles the unknown impulsive maneuver by incorporating the magnitude, direction, and time of the impulsive maneuver into the estimation parameter vector. First, a modified state transition tensor (STT) is proposed via orbit division and segment connection, allowing the orbit to be directly propagated under the effects of impulsive maneuver uncertainties. Then, based on the modified STT, a second-order measurement model is established with the estimation parameter vector as the input. Combining the second-order measurement model with observations, a second-order optimal solution is derived to correct the estimation parameters. The spacecraft orbit, together with the magnitude, direction, and time of the impulsive maneuver, are simultaneously estimated in an iterative framework. The performance of the proposed method is validated in a low-Earth-orbit case and a high-Earth-orbit case. Simulations show that the proposed method outperforms its linear version in terms of convergence, accuracy, and uncertainty quantification capacity. Its maneuver reconstruction and orbit estimation errors are one order of magnitude less than those of competitive methods. Moreover, the proposed method can handle severe conditions and is robust to initial guesses.