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浙江大学学报(工学版)
浙江大学学报(工学版)  2022, Vol. 56 Issue (12): 2514-2522    DOI: 10.3785/j.issn.1008-973X.2022.12.021
航空航天技术     
多矢量信息下的星敏感器三轴旋转角求解方法
段辉(),张志利,周召发*(),徐泽乾,赵芝谦,王韶迪
火箭军工程大学 导弹工程学院，陕西 西安 710025
Three-axis rotation angle solving method of star sensor under multi-vector information
Hui DUAN(),Zhi-li ZHANG,Zhao-fa ZHOU*(),Ze-qian XU,Zhi-qian ZHAO,Shao-di WANG
School of Missile Engineering, Rocket Force University of Engineering, Xi’an 710025, China
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摘要：

为了提高星敏感器的实时性能与解算精度，基于多矢量信息，提出四元数表示形式下的星敏感器三轴旋转角求解方法，从理论上对所提方法进行详细推导. 基于单个星光矢量在天球系与星敏系中的三维坐标，将方向余弦阵变换形式转变成四元数变换形式. 降次二次四元数变换形式，以便后续求解. 考虑不同星光矢量的权重，联立所有星光矢量的信息求解星敏感器三轴旋转角，给出解决三轴旋转角求解过程中的迭代不确定性和四元数矢量方向奇异性的具体方案. 将所提方法与传统方法的性能进行对比分析. 仿真结果表明，相比传统方法，所提方法具有更快的解算速度和更高的三轴旋转角求解精度.
关键词： 旋转角;  星敏感器;  四元数;  奇异性;  实时性    
Abstract:

In order to improve the real-time performance and solution accuracy of star sensor, based on multi-vector information, a quaternion representation method for solving three-axis rotation angle of star sensor was proposed, and the method was derived in detail theoretically. Based on the three-dimensional coordinates of a single starlight vector in celestial coordinate system and star sensor coordinate system, the direction cosine matrix transformation form was transformed into quaternion transformation form. The quadratic quaternion transformation form was reduced in order to facilitate the subsequent solution. Considering the weight of different starlight vectors, the information of all starlight vectors was combined to solve the three-axis rotation angle of the star sensor. A specific solution was given, aiming at the iteration uncertainty and the direction singularity of quaternion vector in the process of solving three-axis rotation angle, The performance of the proposed algorithm was compared with that of the traditional algorithm. Simulation results show that the proposed algorithm has faster solving speed and higher accuracy in solving three-axis rotation angle than the traditional algorithm.
Key words: rotation angle    star sensor    quaternion    singularity    real time
收稿日期: 2021-12-29 出版日期: 2023-01-03
CLC:  V 448.22  
基金资助: 航空科学基金资助项目（201808U8004）
通讯作者: 周召发     E-mail: 1020423896@qq.com;3199148797@qq.com
作者简介: 段辉（1996—），男，博士生，从事组合导航研究. orcid.org/0000-0003-3886-654X. E-mail： 1020423896@qq.com
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段辉
张志利
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赵芝谦
王韶迪

引用本文:

段辉,张志利,周召发,徐泽乾,赵芝谦,王韶迪. 多矢量信息下的星敏感器三轴旋转角求解方法[J]. 浙江大学学报(工学版), 2022, 56(12): 2514-2522.

Hui DUAN,Zhi-li ZHANG,Zhao-fa ZHOU,Ze-qian XU,Zhi-qian ZHAO,Shao-di WANG. Three-axis rotation angle solving method of star sensor under multi-vector information. Journal of ZheJiang University (Engineering Science), 2022, 56(12): 2514-2522.

链接本文:

https://www.zjujournals.com/eng/CN/10.3785/j.issn.1008-973X.2022.12.021    或    https://www.zjujournals.com/eng/CN/Y2022/V56/I12/2514

图 1  星光矢量成像示意图
图 2  1.0×10−3噪声标准差下不同算法的三轴姿态角误差曲线
算法 σA/(°)
σs=1.0×10?2 σs=1.0×10?3 σs=1.0×10?4 σs=1.0×10?5
SVD 2.071×10?1 2.751×10?2 3.084×10?3 4.055×10?4
LS 3.679×10?1 3.794×10?2 4.286×10?3 4.622×10?4
QUEST 2.071×10?1 2.751×10?2 3.084×10?3 4.055×10?4
本研究 2.071×10?1 2.751×10?2 3.084×10?3 4.055×10?4
表 1  不同噪声标准差下不同算法的姿态角误差标准差
图 3  1.0×10−3噪声标准差下不同算法的时间消耗曲线
算法 t/s
σs=1×10?2 σs=1×10?3 σs=1×10?4 σs=1×10?5
SVD 6.021×10?5 5.971×10?5 6.153×10?5 6.568×10?5
LS 9.354×10?5 9.219×10?5 9.612×10?5 9.674×10?5
QUEST 5.721×10?5 5.671×10?5 5.953×10?5 5.368×10?5
本研究 3.284×10?5 3.322×10?5 3.268×10?5 3.109×10?5
表 2  不同噪声标准差下不同算法的耗时表
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