Nonlinear semi-analytical uncertainty propagation of trajectory under impulsive maneuvers

The usage of state transition tensors (STTs) was proved as an effective method for orbital uncertainty propagation. However, orbital maneuvers and their uncertainties are not considered in current STT-based methods. Uncertainty propagation of spacecraft trajectory with maneuvers plays an important role in spaceflight missions, e.g., the rendezvous phasing mission. Under the effects of impulsive maneuvers, the nominal trajectory of a spacecraft will be divided into several segments. If the uncertainty is piecewise propagated using the STTs one after another, large approximation errors will be introduced. To overcome this challenge, a set of modified STTs is derived, which connects the segmented trajectories together and allows for directly propagating uncertainty from the initial time to the final time. These modified STTs are then applied to analytically propagate the statistical moments of navigation and impulsive maneuver uncertainties. The probability density function is obtained by combining STTs with the Gaussian mixture model. The proposed uncertainty propagator is shown to be efficient and affords good agreement with Monte Carlo simulations. It also has no dimensionality problem for high-dimensional uncertainty propagation.