星敏感器姿态测量算法研究

doi:10.12305/j.issn.1001-506X.2023.03.24

系统工程与电子技术 ›› 2023, Vol. 45 ›› Issue (3): 822-830.doi: 10.12305/j.issn.1001-506X.2023.03.24

星敏感器姿态测量算法研究

段辉¹^,², 周召发¹^,²^,*, 张志利¹^,², 徐志浩¹^,², 郝诗文¹^,², 曾进³

1. 火箭军工程大学导弹工程学院, 陕西西安 710025
2. 火箭军工程大学兵器发射理论和技术国家重点学科实验室, 陕西西安 710025
3. 飞行自动控制研究所惯性技术航空科技重点实验室, 陕西西安 710065

收稿日期:2021-11-12 出版日期:2023-02-25 发布日期:2023-03-09
通讯作者: 周召发
作者简介:段辉(1996—), 男, 博士研究生, 主要研究方向为惯性、天文组合导航
周召发(1973—), 男, 教授, 博士, 主要研究方向为车载导航、天文导航
张志利(1966—), 男, 教授, 博士, 主要研究方向为车载导航、系统仿真
徐志浩(1994—), 男, 博士研究生, 主要研究方向为车载导航
郝诗文(1996—), 男, 博士研究生, 主要研究方向为车载导航与重力测量
曾进(1989—), 男, 高级工程师, 硕士, 主要研究方向为惯性导航
基金资助:
国家自然科学基金(41174162);航空科学基金(201808U8004)

Study on attitude measurement algorithm of star sensor

Hui DUAN¹^,², Zhaofa ZHOU¹^,²^,*, Zhili ZHANG¹^,², Zhihao XU¹^,², Shiwen HAO¹^,², Jin ZENG³

1. School of Missile Engineering, Rocket Force University of Engineering, Xi'an 710025, China
2. State Key Discipline Laboratory of Armament Launch Theory and Technology, Rocket Force University of Engineering, Xi'an 710025, China
3. Aviation Key Laboratory of Science and Technology on Inertial Technology, Flight Automatic Control Research Institute, Xi'an 710065, China

Received:2021-11-12 Online:2023-02-25 Published:2023-03-09
Contact: Zhaofa ZHOU

摘要/Abstract

摘要：

针对传统矢量定姿方法精度较低的问题，研究了主流的星敏感器多矢量天文定姿算法, 从理论上对奇异值分解(singular value decomposition, SVD)算法、双矢量定姿加研究背景算法、最小二乘(least square, LS)算法、四元数估计(quaternion estimator, QUEST)算法和线性估计算法进行了详细推导。其中, 线性估计算法先将各矢量对的坐标变换等式分散表示, 推导出对应的四元数形式, 再联立所有矢量的坐标变换等式, 基于长方矩阵的Moore-Penrose伪逆运算对二次四元数矩阵方程线性化, 再在此基础上考虑随机噪声的影响对一次四元数矩阵方程进行鲁棒性操作, 具有良好的创新性与实用性。以最小化Wahba损失函数为目标, 对定姿算法的性能进行对比分析。仿真和实验结果表明, 线性估计算法较之于其余4种算法, 具有更快的解算速度、更高的定姿精度。

关键词: 星敏感器, 姿态确定, 线性估计, 多矢量

Abstract:

For the problem of low accuracy of traditional vector fixation method, the mainstreammulti-vector astronomical attitude determination algorithm based on star sensor is studied, and singular value decomposition (SVD) algorithm, double vector fixed attitude algorithm, least square (LS) algorithm, quaternion estimator (QUEST) algorithm and linear estimation algorithm are derived theoretically in detail. The linear estimation algorithm disperses the coordinate transformation equations of each vector pair and deduces the corresponding quaternion form, then combines the coordinate transformation equations of all vectors, and linearizes the quadratic quaternion matrix equation based on the M-P pseudo-inverse operation of rectangular matrix. On this basis, considering the influence of random noise, a robust operation is performed on the quaternion matrix equation with degree 1.The method has good innovation and practicability. With the goal of minimizing the Wahba loss function, the performance of the attitude determination algorithm is compared and analyzed. The simulation and experimental results show that the linear estimation algorithm has faster solving speed and higher accuracy than the other four algorithms.

Key words: star sensor, attitude determination, linear estimation, multi-vector

中图分类号:

V448.22

段辉, 周召发, 张志利, 徐志浩, 郝诗文, 曾进. 星敏感器姿态测量算法研究[J]. 系统工程与电子技术, 2023, 45(3): 822-830.

Hui DUAN, Zhaofa ZHOU, Zhili ZHANG, Zhihao XU, Shiwen HAO, Jin ZENG. Study on attitude measurement algorithm of star sensor[J]. Systems Engineering and Electronics, 2023, 45(3): 822-830.

图/表 6

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算法	噪声标准差
算法	1e-2	1e-3	1e-4	1e-5
双矢量定姿	8.287e-01	6.941e-02	9.671e-03	6.749e-04
SVD	2.108e-01	2.699e-02	2.904e-03	4.185e-04
LS	3.741e-01	3.691e-02	4.311e-03	4.571e-04
QUEST	2.108e-01	2.699e-02	2.904e-03	4.185e-04
线性估计算法	2.108e-01	2.699e-02	2.904e-03	4.185e-04

算法	噪声标准差
算法	1e-2	1e-3	1e-4	1e-5
SVD	6.199e-05	5.748e-05	6.303e-05	6.419e-05
LS	9.484e-05	9.401e-05	9.791e-05	9.488e-05
QUEST	5.594e-05	5.705e-05	5.897e-05	5.419e-05
线性估计算法	3.309e-05	3.504e-05	3.094e-05	3.519e-05

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星敏感器姿态测量算法研究

Study on attitude measurement algorithm of star sensor

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