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

doi:10.11947/j.AGCS.2026.20260051

Abstract

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

CLC Number:

P228

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