Analytical configuration uncertainty propagation of geocentric interferometric detection constellation

Long-term configuration stability is essential for an interferometric detection constellation (IDC), which is closely related to initial uncertainty. Therefore, it is vital to evaluate the uncertainty and characterize the configuration stability. In this study, an analytical method was developed for the configuration uncertainty propagation of a geocentric triangular IDC. The angular momentum and the argument latitude were found to be significantly affected by the initial uncertainty and were selected as the core variables. By averaging the perturbation in one revolution, an analytical solution was proposed for propagating the core orbital elements in one revolution. Subsequently, the analytical solution of the orbit elements during the mission period is obtained by multiplying the solutions in iterative revolutions. The relationship between the selected orbital elements and the configuration stability parameters was established using an analytical solution. The effects of the initial uncertainty in different directions on the configuration and stable domains were studied. Simulations show that the developed method is highly efficient and accurate in predicting the configuration stability. The relative error with respect to the Monte Carlo simulations was less than 3% with a time consumption of 0.1%. The proposed method can potentially be useful for constellation design and stability analysis.