Nonlinear analytical uncertainty propagation for relative motion near J2 -perturbed elliptic orbits

An analytical uncertainty propagation method based on state transition tensors (STTs) has been developed for satellite relative motion near J2-perturbed, elliptic orbits. The STTs used to propagate the relative state uncertainty are derived by adding a correction into the original STTs for propagating relative state. A new set of transitive STTs is further derived in order to propagate uncertainties for relative motion with abrupt state jumps, e.g. impulsive maneuvers executing on any of the two satellites. The nonlinear analytical solution for propagating the first two moments and the probability density function are formulated by combining the STTs with a Gaussian mixture model. Numerical results show that the proposed method outperforms the linear covariance method and provides good agreement with Monte Carlo simulations on nonlinear, non-Gaussian uncertainty propagation. Moreover, as the STTs can be analytically computed and account for the J2-perturbation, the proposed uncertainty propagator is computationally efficient, which will be potentially useful for onboard conjunction analysis in satellites formulation flying mission