Nonlinear semi-analytical uncertainty propagation of trajectory under impulsive maneuvers

Abstract

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.

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Acknowledgements

The authors acknowledge the financial support from the National Natural Science Foundation of China (Nos. 11222215 and 11572345), the National Basic Research Program of China (973 Program, No. 2013CB733100), and the Program for New Century Excellent Talents in University (No. NCET-13-0159).

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Correspondence to Ya-Zhong Luo.

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Zhen Yang received his B.S., M.S., and Ph.D. degrees in aerospace engineering from National University of Defense Technology, China, in 2011, 2013, and 2018, respectively. He was a visiting scholar of Cranfield University, UK, in 2016. After graduation from doctoral, he joined National University of Defense Technology as a lecturer in 2018. His current research interests include astrodynamics, uncertainty quantification, and space trajectory optimization.

Ya-Zhong Luo received his B.S., M.S., and Ph.D. degrees in aerospace engineering from National University of Defense Technology, China, in 2001, 2003, and 2007, respectively. Since December 2013, he has been a professor in National University of Defense Technology. His current research interests include manned spaceflight mission planning, spacecraft dynamics and control, and evolutionary computation.

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Cite this article

Yang, Z., Luo, YZ. & Zhang, J. Nonlinear semi-analytical uncertainty propagation of trajectory under impulsive maneuvers. Astrodyn 3, 61–77 (2019). https://doi.org/10.1007/s42064-018-0036-7

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Keywords

  • uncertainty propagation
  • state transition tensors (STTs)
  • Gaussian mixture model
  • rendezvous phasing