基于自然梯度提升的空间物体轨道状态预测误差不确定性估计方法
作者:
作者单位:

东北大学

作者简介:

通讯作者:

中图分类号:

V448.21

基金项目:

国家自然科学基金项目(面上项目,重点项目,重大项目),国家重点基础研发项目


Uncertainty Estimation Approach in Orbital Prediction Error of Space Objects Based on Natural Gradient Boosting
Author:
Affiliation:

Northeastern University

Fund Project:

The National Natural Science Foundation of China (General Program, Key Program, Major Research Plan),The National Basic Research Program of China

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    摘要:

    针对空间监视环境中基于动力学模型的轨道状态预测方法精度不够、而基于机器学习的误差补偿模型可靠性不足的问题, 以及SSA 应用中对不确定性建模的需求, 将轨道状态预测误差估计问题重新表述为概率预测问题, 提出了一种对物理模型的轨道状态预测误差进行建模的方法, 该方法将轨道状态变量误差的概率分布参数作为梯度提升算法的学习目标, 以量化轨道状态误差估计中的不确定性. 由于参数所对应的概率分布函数位于黎曼空间, 利用基于Fisher 信息矩阵的自然梯度代替标准梯度, 推导了自然梯度的计算公式, 给出了状态预测误差的条件概率分布. 实验结果表明, 与仅采用物理动力学方法的状态预测相比, 采用本文所述的机器学习误差估计方法后, 轨道状态各分量的均方根误差至少降低了约60%, 同时, 与其他常用不确定性估计方法相比, 本文方法可以得到更好的负对数似然值. 因此, 本文方法能够有效估计状态预测误差的不确定性, 提高将机器学习方法用于空间态势感知任务时的可靠性.

    Abstract:

    In view of the insufficient accuracy of the orbital state prediction method based on the physical model in the space surveillance environment, and the insufficient reliability of the error compensation model based on machine learning, as well as the demand for uncertainty modeling in the SSA application, we reformulated orbital state prediction error estimation problem as a probability prediction problem, and proposed a method of using a gradient boosting machine to model the orbital state prediction error distribution. In order to quantify the uncertainty in the state error estimation, the parameters of the conditional distribution of the orbital state error is treated as targets for the gradient boosting algorithm. Since the probability distribution function corresponding to the parameter is located in the Riemann space, the natural gradient based on the Fisher information matrix is used instead of the standard gradient, and the formula of the natural gradient is deduced. As a result, conditional distribution of state prediction error can be calculated. Experiments show that compared with the state prediction method that only uses the physical dynamics, The root mean square error of each component of the orbital state is reduced by at least about 60%. At the same time, compared with other commonly used uncertainty estimation methods, our method can achieve a better negative log likehood. Therefore, our method can effectively estimate the distribution of state prediction errors, and improve the reliability of using machine learning methods for space situational awareness tasks.

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历史
  • 收稿日期:2021-04-25
  • 最后修改日期:2021-08-23
  • 录用日期:2021-08-26
  • 在线发布日期: 2021-09-17
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