Analytical long-term evolution and perturbation compensation models for BeiDou MEO satellites

The current paper establishes the analytical models of the long-term evolution and perturbation compensation strategy for Medium Earth Orbits (MEO) shallow-resonant navigation constellation, with application to the Chinese BeiDou Navigation Satellite System (BDS). The long-term perturbation model for the relative motion is developed based on the Hamiltonian model, and the long-term evolution law is analyzed. The relationship between the control boundary of the constellation and the offset of the orbital elements is analyzed, and a general analytical method for calculating the offset of the orbit elements is proposed. The analytical model is further improved when the luni-solar perturbations are included. The long-term evolutions of the BDS MEO constellation within 10 years are illustrated, and the effectiveness of the proposed analytical perturbation compensation calculation approach is compared with the traditional numerical results. We found the fundamental reason for the nonlinear variations of the relative longitude of ascending node and the mean argument of latitude is the long-periodic variations of the orbital inclination due to the luni-solar perturbations. The proposed analytical approach can avoid the numerical iterations, and reveal the essential relationship between the orbital element offsets and the secular drifts of the constellation configuration. Moreover, there is no need for maintaining the BDS MEO constellation within 10 years while using the perturbation compensation method.