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  

Uncertainty estimation approach in orbital prediction error of space objects based on natural gradient boosting

作　　者：陈慕羿 王大玲 冯时 张一飞 CHEN Mu-yi;WANG Da-ling;FENG Shi;ZHANG Yi-fei(College of Computer Science and Engineering,Northeastern University,Shenyang 110169,China;School of Automation and Electrical Engineering,Shenyang Ligong University,Shenyang 110159,China)

机构地区：[1]东北大学计算机科学与工程学院,沈阳110169 [2]沈阳理工大学自动化与电气工程学院,沈阳110159

出　　处：《控制与决策》2022年第12期3289-3296,共8页Control and Decision

基　　金：国家自然科学基金项目(61772122,61872074);国家重点研发计划项目(2018YFB1004702);辽宁省教育厅科学研究项目(LG201932)。

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,基于机器学习的误差补偿模型可靠性不足,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,推导自然梯度的计算公式,并给出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,采用所提出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约60%.同时,与其他常用不确定性估计方法相比,所提出方法可以得到更好的负对数似然值,因此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.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 reformulate the orbital state prediction error estimation problem as a probability prediction problem, and propose 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, the proposed method can achieve a better negative log likehood. Therefore, the method can effectively estimate the distribution of state prediction errors, and improve the reliability of using machine learning methods for space situational awareness tasks.

关 键 词：空间态势感知 不确定性 机器学习 自然梯度 Fisher信息矩阵 梯度提升 

分 类 号：V448.21[航空宇航科学与技术—飞行器设计]