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Nonlinear orbital uncertainty propagation with differential algebra and Gaussian mixture model

  • Zhen-Jiang Sun
  • Ya-Zhong LuoEmail author
  • Pierluigi di Lizia
  • Franco Bernelli Zazzera
Article
  • 42 Downloads

Abstract

Nonlinear uncertainty propagation is of critical importance in many application fields of astrodynamics. In this article, a framework combining the differential algebra technique and the Gaussian mixture model method is presented to accurately propagate the state uncertainty of a nonlinear system. A high-order Taylor expansion of the final state with respect to the initial deviations is firstly computed with the differential algebra technique. Then the initial uncertainty is split to a Gaussian mixture model. With the high-order state transition polynomial, each Gaussian mixture element is propagated to the final time, forming the final Gaussian mixture model. Through this framework, the final Gaussian mixture model can include the effects of high-order terms during propagation and capture the non-Gaussianity of the uncertainty, which enables a precise propagation of probability density. Moreover, the manual derivation and integration of the high-order variational equations is avoided, which makes the method versatile. The method can handle both the application of nonlinear analytical maps on any domain of interest and the propagation of initial uncertainties through the numerical integration of ordinary differential equation. The performance of the resulting tool is assessed on some typical orbital dynamic models, including the analytical Keplerian motion, the numerical J2 perturbed motion, and a nonlinear relative motion.

Keywords

nonlinear orbit uncertainty propagation differential algebra Gaussian mixture model taylor expansion 

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Copyright information

© Science China Press and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • Zhen-Jiang Sun
    • 1
  • Ya-Zhong Luo
    • 1
    Email author
  • Pierluigi di Lizia
    • 2
  • Franco Bernelli Zazzera
    • 2
  1. 1.College of Aerospace Science and EngineeringNational University of Defense TechnologyChangshaChina
  2. 2.Department of Aerospace Science and TechnologyPolitecnico di MilanoMilanoItaly

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