Nonlinear semi-analytical uncertainty propagation of trajectory under impulsive maneuvers
uncertainty propagation, state transition tensors (STTs), Gaussian mixture model, rendezvous phasing
The usage of state transition tensors (STTs) was proved as an effective method for orbitaluncertainty propagation. However, orbital maneuvers and their uncertainties are notconsidered in current STT-based methods. Uncertainty propagation of spacecraft trajectorywith maneuvers plays an important role in spaceflight missions, e.g., the rendezvous phasingmission. Under the effects of impulsive maneuvers, the nominal trajectory of a spacecraftwill be divided into several segments. If the uncertainty is piecewise propagated using theSTTs one after another, large approximation errors will be introduced. To overcome thischallenge, a set of modified STTs is derived, which connects the segmented trajectoriestogether 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 momentsof navigation and impulsive maneuver uncertainties. The probability density function isobtained by combining STTs with the Gaussian mixture model. The proposed uncertaintypropagator is shown to be efficient and affords good agreement with Monte Carlo simulations.It also has no dimensionality problem for high-dimensional uncertainty propagation.
Tsinghua University Press
Zhen Yang,Ya-Zhong Luo,Jin Zhang,Nonlinear semi-analytical uncertainty propagation of trajectory under impulsive maneuvers.Astrodyn.2019, 3(1): 61–77.