多矢量姿态测量算法研究综述

吴美平; 刘一麟; 郭妍; 于瑞航

doi:10.13700/j.bh.1001-5965.2022.0325

多矢量姿态测量算法研究综述

doi: 10.13700/j.bh.1001-5965.2022.0325

国防科技大学智能科学学院，长沙 410072

基金项目: 国家自然科学基金面上项目(42276199)；国家自然科学基金青年科学基金(62103424)

详细信息

通讯作者:
E-mail：meipingwu@263.net

中图分类号: V221⁺.3；TB553
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出版历程
- 收稿日期: 2022-05-07
- 录用日期: 2022-09-23
- 网络出版日期: 2022-11-21
- 整期出版日期: 2024-05-29

A review of algorithms for multi-vector attitude synthesis of research

College of Intelligence Science and Technology，National University of Defense Technology，Changsha 410072，China

Funds: General Project of National Natural Science Foundation of China (42276199); Youth Science Fund of National Natural Science Foundation of China (62103424)

More Information

Corresponding author: E-mail：meipingwu@263.net

摘要

摘要:
将矢量测量转化为姿态测量，该问题在姿态估计中被称为Wahba问题。介绍了最小化Wahba问题的损失函数的不同算法，包括最优四元数估计器(ESOQ)、四元数估计器(QUEST)、快速最优姿态矩阵(FOAM)、矩阵的奇异值分解(SVD)等广泛使用的算法，以及基于快速线性四元数姿态估计器（FLAE）、黎曼流形等近年来提出的算法。给出了简单的计算原理与推导过程，并通过计算机仿真对照，归纳各类算法在计算旋转矩阵时的计算精度、鲁棒性。针对姿态测量算法应对当前应用场景的性能需求，简要介绍其在惯性测量单元(IMU)动态对准、协同集群视觉定姿、图像拼接等方面的适用可能和工作原理，并在此基础上简述了姿态测量算法当前的缺陷与未来的发展趋势。
- Wahba问题 /
- 视觉定姿 /
- 图像拼接 /
- 人体动作测量 /
- 协同导航
Abstract:
The transformation of vector measurements into attitude measurements is known as the Wahba problem in the literature of attitude estimation. This review introduces various algorithms for minimizing the Wahba’s loss function, including estimator of the optimal quaternion (ESOQ), quaternion estimator (QUEST), fast optimal attitude matrix (FOAM), singular value decomposition (SVD) as well as new algorithms proposed in recent years such as fast linear quaternion attitude estimator (FLAE) and the algorithm based on Riemannian manifold. The calculation principle and derivation process are briefly introduced. The computational accuracy and robustness of various methods in calculating rotation matrices are summarized through computer simulation. Then, this review outlines the applicability and working principles of these algorithms in inertial measurement unit (IMU) dynamic alignment, collaborative cluster visual attitude determination, and image mosaic in addressing emerging performance requirements in current applications. Finally, we describe the current limitations and development trends of attitude algorithms in the future.
- Wahba problem /
- visual attitude determination /
- image mosaic /
- human motion measurement /
- cooperative navigation

HTML全文

图 1 星光成像几何示意图^[26]

Figure 1. Geometric diagram of starlight imaging^[26]

下载: 全尺寸图片幻灯片

图 2 卫星姿态确定原理^[33]

Figure 2. Principle of satellite attitude determination^[33]

下载: 全尺寸图片幻灯片

图 3 人体加速度计算模型^[40]

Figure 3. Calculation model of human body acceleration^[40]

下载: 全尺寸图片幻灯片

图 4 基于共视目标的双机姿态约束^[46-47]

Figure 4. Dual-aircraft attitude constraints based on common viewing targets^[46-47]

下载: 全尺寸图片幻灯片

图 5 航天器相对姿态描述涉及的坐标系^[48]

Figure 5. Coordinates involved in relative attitude description of spacecraft^[48]

下载: 全尺寸图片幻灯片

表 1 信噪比100 dB时失准角误差

Table 1. Misalignment angle error corresponding to signal-to-noise ratio of 100 dB 10⁻⁶

向量	QUEST	SVD	ESOQ	FLAE	FOAM	Davenport
1	9.4	9.6	9.85	9.41	9.53	9.39
2	10.3	10.1	10.15	10.52	NaN	10.24
3	9.56	9.55	9.91	9.65	9.57	9.38
4	10.14	10.18	10.23	10.44	NaN	10.20
5	10.0	10.0	10.0	10.29	NaN	10.43
注：NaN表示算法解算未收敛到解的可行域。

下载: 导出CSV

表 2 信噪比100 dB时损失函数

Table 2. Loss function with signal-to-noise ratio of 100 dB 10⁻⁶

向量	QUEST	SVD	ESOQ	FLAE	FOAM	Davenport
1	6.78	6.76	7.32	6.76	6.76	6.83
2	5.49	5.40	5.28	5.41	NaN	5.41
3	6.69	6.84	6.91	6.82	6.75	6.72
4	5.44	5.33	5.48	5.38	NaN	5.45
5	5.41	5.38	5.42	5.38	NaN	5.43
注：NaN表示算法解算未收敛到解的可行域。

下载: 导出CSV

表 3 信噪比20 dB时失准角误差

Table 3. Misalignment angle error corresponding to Signal-to-Noise Ratio of 20 dB

向量	QUEST	SVD	ESOQ	FLAE	FOAM	Davenport
1	0.154	0.09	0.349	0.147	0.152	0.09
2	0.103	0.101	0.102	0.104	NaN	0.102
3	0.154	0.09	0.349	0.136	0.151	0.09
4	0.102	0.103	0.103	0.102	NaN	0.101
5	0.101	0.102	0.102	0.103	NaN	0.104
注：NaN表示算法解算未收敛到解的可行域。

下载: 导出CSV

表 4 信噪比20 dB时损失函数

Table 4. Loss function with signal-to-noise ratio of 20 dB

向量	QUEST	SVD	ESOQ	FLAE	FOAM	Davenport
1	0.0874	0.0680	0.1836	0.0927	0.0899	0.0675
2	0.0542	0.0541	0.0532	0.0539	NaN	0.530
3	0.0887	0.0670	0.1841	0.088	0.0939	0.0675
4	0.0543	0.0535	0.0539	0.0542	NaN	0.0544
5	0.0544	0.0530	0.0539	0.0542	NaN	0.0530
注：NaN表示算法解算未收敛到解的可行域。

下载: 导出CSV

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