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Orbital Uncertainty Propagation Using Positive Weighted Compact Quadrature Rule

机译：使用正加权紧凑正交规则的轨道不确定性传播

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摘要

In space surveillance, long-term orbital propagation is often required to track space objects when the measurement updates are scarce. It is a challenging uncertainty propagation problem and can be addressed by many different numerical integration rules, such as the unscented transformation, the Gauss-Hermite quadrature rule, and the cubature rule. The conventional cubature rule and the unscented transformation are only the third-degree numerical rules that may not be precise enough for the long-term uncertainty propagation. The Gauss-Hermite quadrature rule is accurate to arbitrary degrees. However, it suffers the curse-of-dimensionality problem. To balance the computational complexity and accuracy, the high-degree sparse-grid quadrature rule and the high-degree spherical-radial cubature rule have been proposed in recent years. Unfortunately, the weights of these two rules may become negative, which can lead to a negative-definite covariance matrix and degrade the performance of uncertainty propagation. In this paper, two new compact quadrature rules together with an adaptive Gaussian-mixture model are proposed to propagate the uncertainty through the nonlinear orbital dynamics, which can achieve high degrees of propagation accuracy while maintaining all positive weights. High-Earth-orbit propagation and low-Earth-orbit propagation examples are used to demonstrate the superb performance of the proposed compact quadrature rules.
机译：在空间监视中，在缺乏测量更新的情况下，经常需要长期轨道传播来跟踪空间物体。这是一个具有挑战性的不确定性传播问题，可以通过许多不同的数值积分规则来解决，例如无味变换，高斯-赫尔姆特正交定律和孵化规则。常规的容积法则和无味的变换仅是三次数值法则，对于长期不确定性传播可能不够精确。高斯-赫尔姆特正交定律可精确到任意程度。但是，它遭受了尺寸诅咒问题。为了平衡计算的复杂性和准确性，近年来提出了高稀疏网格正交规则和高球形辐射半径定律。不幸的是，这两个规则的权重可能变为负值，这可能导致负定协方差矩阵并降低不确定性传播的性能。本文提出了两个新的紧凑正交规则以及自适应高斯混合模型，以通过非线性轨道动力学传播不确定性，可以在保持所有正权重的同时实现较高的传播精度。高地球轨道传播和低地球轨道传播示例被用来证明所提出的紧凑正交规则的卓越性能。

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  • 来源
    《Journal of Spacecraft and Rockets》 |2017年第3期|683-697|共15页
  • 作者

    Jia Bin; Xin Ming;

  • 作者单位

    Intelligent Fus Technol Inc, Germantown, MD 20876 USA;

    Univ Missouri, Dept Mech & Aerosp Engn, Columbia, MO 65211 USA;

  • 收录信息 美国《科学引文索引》(SCI);美国《工程索引》(EI);
  • 原文格式 PDF
  • 正文语种 eng
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