顾及GNSS卫星姿态的相位缠绕及精密单点定位

doi:10.11947/j.AGCS.2026.20260051

测绘学报 ›› 2026, Vol. 55 ›› Issue (6): 1018-1030.doi: 10.11947/j.AGCS.2026.20260051

• 大地测量学与导航 • 上一篇

顾及GNSS卫星姿态的相位缠绕及精密单点定位

刘学习¹^,²(), 刘广涵¹, 杨超³, 郑南山¹(), 郭福东¹, 张克非¹, 豆世贸¹

^1.中国矿业大学环境与测绘学院，江苏　徐州　221116
^2.湖北珞珈实验室，湖北　武汉　430079
^3.香港理工大学土地测量及地理空间科学系，香港　999077

收稿日期:2026-02-02 修回日期:2026-05-20 发布日期:2026-07-28
通讯作者: 郑南山 E-mail:xuexiliu@cumt.edu.cn;znshcumt@cumt.edu.cn
作者简介:刘学习（1992—），男，博士，副教授，研究方向为GNSS精密数据处理与空间大地测量。E-mail：xuexiliu@cumt.edu.cn
基金资助:
江苏省自然科学基金(BK20231087);国家自然科学基金(42304015; 42274049);江苏省自然资源科技项目(JSZRKJ202510);湖北珞珈实验室开放基金(250100007);中国博士后科学基金(2025T180062);中国博士后科学基金面上项目(2024M753525);江苏省青年科技人才托举工程项目(JSTJ-2024-075);国家自然科学基金重点项目(U22A20569)

Phase Wind-up and precise point positioning considering GNSS satellite attitude

Xuexi LIU¹^,²(), Guanghan LIU¹, Chao YANG³, Nanshan ZHENG¹(), Fudong GUO¹, Kefei ZHANG¹, Shimao DOU¹

^1.School of Environmental and Spatial Informatics, China University of Mining and Technology, Xuzhou 221116, China
^2.Hubei Luojia Laboratory, Wuhan 430079, China
^3.Department of Land Surveying and Geospatial Science, The Hong Kong Polytechnic University, Hong Kong 999077, China

Received:2026-02-02 Revised:2026-05-20 Published:2026-07-28
Contact: Nanshan ZHENG E-mail:xuexiliu@cumt.edu.cn;znshcumt@cumt.edu.cn
About author:LIU Xuexi (1992—), male, PhD, associate professor, majors in GNSS precise data processing and space geodesy. E-mail: xuexiliu@cumt.edu.cn
Supported by:
The Natural Science Foundation of Jiangsu Province(BK20231087);The National Natural Science Foundation of China(42304015; 42274049);Jiangsu Provincial Natural Resources Science and Technology Project(JSZRKJ202510);The Open Fund of Hubei Luojia Laboratory(250100007);China Postdoctoral Science Foundation(2025T180062);General Project of China Postdoctoral Science Foundation(2024M753525);Jiangsu Province Youth Science and Technology Talent Support Project(JSTJ-2024-075);Key Program of the National Natural Science Foundation of China(U22A20569)

摘要/Abstract

摘要：

卫星姿态模型通过影响偏航角（Yaw）的变化，进而改变卫星天线相位中心偏移（PCO）在视线方向的投影以及相位缠绕改正量，最终影响精密单点定位（PPP）的建模与定位结果。在低β角或地影等姿态敏感条件下，此类影响更为明显。本文引入IGS姿态四元数产品（OBX/ORBEX），在统一PPP策略与同源精密产品的约束下，对比名义姿态与4家分析中心（武汉大学分析中心（WUM）、欧洲定轨中心（CODE）、德国地学研究中心（GFZ）、法国国家空间研究中心（GRG））四元数姿态在GPS、BDS、Galileo、GLONASS四系统中的差异，并沿“Yaw—PCO—Wind-up—PPP”链路验证其影响路径。结果表明：姿态偏转窗口内Yaw可发生接近±180°的偏转且不同分析中心在偏转过程与分支选择上存在差异；由姿态差异引起的PCO差异为GPS 2~3 cm、BDS 0.7~0.8 cm、Galileo约1 cm、GLONASS可达10~16 cm；相位缠绕差异在偏转期间同样显著，GPS与BDS可达0.8~1.0周，Galileo与GLONASS相对较弱，差异为0.2~0.4周。3天PPP结果与多测站统计表明，四元数姿态在多数情况下可降低PPP三向RMS，但改善幅度具有明显的系统差异和分析中心差异：GPS整体提升有限，最大为7.96%；BDS改善最为显著，最大可达22.05%；Galileo整体表现较为稳定，最大提升13.39%；GLONASS提升相对较小，最大为7.78%；但个别组合下仍会出现轻微退化，最大为－0.89%。综上，四元数姿态产品能在姿态敏感阶段显著影响PPP精度，但应用中需按系统与分析中心分层评估并进行质量控制。

关键词: 卫星姿态, 四元数, 偏航角, 相位缠绕, 天线相位中心改正, 精密单点定位

Abstract:

Satellite attitude models influence variations in the Yaw angle, thereby changing the line-of-sight projection of the satellite antenna phase center offset (PCO) and the phase Wind-up correction, and ultimately affecting the modeling and positioning results of precise point positioning (PPP). Such effects become more pronounced under attitude-sensitive conditions, such as low-β angles and eclipse periods. In this study, attitude quaternion products (OBX/ORBEX) released by the International GNSS Service (IGS) are introduced. Under a unified PPP processing strategy and with consistent precise products from the same analysis center, differences between the nominal attitude model and quaternion-based attitude products from four analysis centers—Wuhan University (WUM), the Center for Orbit Determination in Europe (CODE), the German Research Centre for Geosciences (GFZ), and the Groupe de Recherche de Géodésie Spatiale (GRG)—are compared for four GNSS constellations: GPS, BDS, Galileo, and GLONASS. Their impact path is further investigated along the “Yaw-PCO-Wind-up-PPP” chain. The results show that, within attitude maneuver windows, Yaw angles can undergo rotations close to±180°, and different analysis centers exhibit discrepancies in maneuver evolution and branch selection. The attitude-induced PCO differences are 2~3 cm for GPS, 0.7~0.8 cm for BDS, about 1 cm for Galileo, and up to 10~16 cm for GLONASS. Phase wind-up differences are also significant during maneuver periods, reaching 0.8~1.0 cycles for GPS and BDS, while being relatively smaller for Galileo and GLONASS, at 0.2~0.4 cycles. Three-day PPP results and multi-station statistics indicate that quaternion-based attitude products can reduce the three-component PPP RMS in most cases, but the improvement exhibits clear system-dependent and analysis-center-dependent characteristics. Specifically, the improvement for GPS is limited, with a maximum of 7.96%; BDS shows the most significant improvement, reaching up to 22.05%; Galileo performs relatively stably, with a maximum improvement of 13.39%; and GLONASS shows relatively small improvement, with a maximum of 7.78%. Slight degradation may still occur in a few combinations, with a maximum of about－0.89%. In summary, quaternion-based attitude products can significantly affect PPP accuracy during attitude-sensitive periods, but their practical application still requires system-specific and analysis-center-specific evaluation and quality control.

Key words: satellite attitude, quaternion, Yaw angle, phase Wind-up, phase center offset, precise point positioning

中图分类号:

P228

刘学习, 刘广涵, 杨超, 郑南山, 郭福东, 张克非, 豆世贸. 顾及GNSS卫星姿态的相位缠绕及精密单点定位[J]. 测绘学报, 2026, 55(6): 1018-1030.

Xuexi LIU, Guanghan LIU, Chao YANG, Nanshan ZHENG, Fudong GUO, Kefei ZHANG, Shimao DOU. Phase Wind-up and precise point positioning considering GNSS satellite attitude[J]. Acta Geodaetica et Cartographica Sinica, 2026, 55(6): 1018-1030.

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项目	设置
观测值	GPS：L1/L2； Galileo：E1/E5a； BDS：B1I/B3I； GLONASS：G1/G2
采样间隔	30 s
精密轨道/钟差	与姿态产品一致的同源分析中心精密产品
ERP	IERS发布的地球自转参数产品
PCO/PCV	igs20_2290.atx
相位缠绕	模型改正
对流层延迟	Saastamoinen模型
对流层投影函数	GMF（global mapping function）
湿延迟估计策略	随机游走参数模型
电离层延迟	非差非组合估计
接收机钟差	白噪声参数
系统间偏差ISB	随机游走参数
截止高度角	7°
观测定权	高度角定权
固体潮/海洋潮/极潮	模型改正
模糊度	动态浮点解
参数估计	Kalman滤波
周跳探测	MW和GF组合

系统	分析中心	提升/（%）
系统	分析中心	E方向	N方向	U方向
GPS	WUM	0.27	7.96	6.98
	CODE	6.74	3.52	1.85
	GFZ	2.71	4.44	1.26
	GRG	2.11	1.91	0.01
BDS	WUM	20.44	9.24	19.49
	CODE	21.87	12.43	22.05
	GFZ	19.10	14.07	21.36
	GRG	－0.09	－0.07	0.29
Galileo	WUM	3.43	1.54	2.24
	CODE	10.80	7.94	1.68
	GFZ	6.62	3.57	0.92
	GRG	13.39	8.68	7.08
GLONASS	WUM	7.78	7.66	0.65
	CODE	4.99	1.70	0.09
	GFZ	－0.89	0.19	－0.82
	GRG	5.28	2.16	0.21

顾及GNSS卫星姿态的相位缠绕及精密单点定位

Phase Wind-up and precise point positioning considering GNSS satellite attitude

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