• 论文 •

### UKF参数估计在三体Lambert问题中的应用

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

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.