北京航空航天大学学报 ›› 2015, Vol. 41 ›› Issue (2): 228-233.doi: 10.13700/j.bh.1001-5965.2014.0120

• 论文 • 上一篇    下一篇

UKF参数估计在三体Lambert问题中的应用

张洪礼1, 罗钦钦2, 韩潮1   

  1. 1. 北京航空航天大学 宇航学院, 北京 100191;
    2. 北京空天技术研究所, 北京 100074
  • 收稿日期:2014-03-12 出版日期:2015-02-20 发布日期:2015-03-12
  • 通讯作者: 韩潮(1960—), 男, 北京人, 教授, hanchao@buaa.edu.cn, 主要研究方向为航天器动力学与控制、航天器导航、制导与控制、航天系统动力学仿真等. E-mail:hanchao@buaa.edu.cn
  • 作者简介:张洪礼(1988—), 男, 山东威海人, 博士生, zhanghongli@buaa.edu.cn
  • 基金资助:

    载人航天预研资助项目(010103)

Application of UKF parameter estimation in the three-body Lambert problem

ZHANG Hongli1, LUO Qinqin2, HAN Chao1   

  1. 1. School of Astronautics, Beijing University of Aeronautics and Astronautics, Beijing 100191, China;
    2. Beijing Aerospace Technology Institute, Beijing 100074, China
  • Received:2014-03-12 Online:2015-02-20 Published:2015-03-12

摘要:

为了快速精确地求解三体Lambert问题,提出了一种新的基于无损卡尔曼滤波(UKF)参数估计的数值求解算法,该算法由初值猜测和精确解求解两部分组成.首先,基于地月系统二体模型,通过简单迭代求解三体Lambert问题的初值.然后,将三体Lambert问题对应的两点边值问题转化为参数估计问题,通过UKF滤波算法求解,可得到收敛的精确解.该算法是基于概率估计理论的,不仅避免了传统数值方法推导相关梯度矩阵的复杂性,而且降低了三体Lambert问题对初值精确度的要求,从而显著降低了三体Lambert问题求解的难度.数值仿真表明,该方法求解效率较高,具有良好的鲁棒性,与微分修正算法、二阶微分修正算法对比具有更大的收敛域.

关键词: 三体系统, Lambert问题, 两点边值问题, 无损卡尔曼滤波, 参数估计

Abstract:

A new algorithm based on unscented Kalman filter (UKF) parameter estimation was proposed for the fast and efficient solution of the three-body Lambert problem. The algorithm was divided into two steps, guessing the initial solution and searching the exact solution. The initial solution of the three-body Lambert problem was generated using the two-body model of the Earth-Moon system. Then the two-point boundary value problem corresponding to the original three-body Lambert problem was converted to a parameter estimation problem. Through solving the converted problem using UKF, the converged exact solution was found. The algorithm was based on the theory of probability, so the derivation of the gradient matrixes required by traditional numerical methods was omitted. Moreover, the demand for the accuracy of the initial solutions for the three-body Lambert problem was modified. Therefore, the difficulty of solving the three-body Lambert problem was greatly reduced. Numerical examples indicate that the algorithm is of high efficiency and robustness and obtains a larger convergence domain compared with the differential-correction method and the second order differential-correction method.

Key words: three-body systems, Lambert problem, two-point boundary value problem, unscented Kalman filter, parameter estimation

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