Nonlinear Analytical Uncertainty Propagation for Relative Motion near -Perturbed Elliptic Orbits

Abstract

A nonlinear analytical uncertainty propagation method using state transition tensors is developed for satellite relative motion near -perturbed elliptic orbits. The improved state transition tensors are derived by adding a correction factor into the original state transition tensors for propagating relative state. A new set of transitive state transition tensors is further derived to propagate uncertainties for relative motion with abrupt state jumps such as an impulsive maneuver. The nonlinear analytical solution for propagating the first two moments and the probability density function are formulated by combining the state transition tensors 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. Moreover, because the state transition tensors can be analytically computed and account for the perturbation, the proposed uncertainty propagator can be potentially useful for conjunction analysis of formulation flying satellites.