Yaw attitude modeling of GLONASS-K and GLONASS-M+ satellites and its impact on satellite clock estimation and precise point positioning

doi:10.11947/j.AGCS.2025.20250091

Abstract

Abstract:

Accurate satellite attitude modeling significantly influences both precise satellite clock estimation and precise point positioning (PPP). This work elucidates the mathematical relationships between satellite attitude, antenna phase center correction and phase wind-up effects, following by a comparative analysis of attitude modeling discrepancies between GLONASS-M+ and GLONASS-K satellites. Finally, six-month observations in 2024 are utilized to evaluate the impacts of three attitude strategies on GLONASS satellite clock accuracy and PPP positioning performance. It reveals that the eclipsing GLONASS-K satellites last for 5~6 days on average, substantially shorter than GLONASS-M+ satellites. Currently, GLONASS-K satellite attitude quaternions in IGS analysis centers continue to employ the legacy model or nominal attitude model. When the sun angle above the satellite orbital plane approaches 0°, maximum yaw angle discrepancies reach 90° for the legacy model and 180° for the nominal model. In contrast to the correct attitude model, the nominal and GLONASS-M+ satellite model degrade GLONASS satellite clock accuracy by 29.6% and 3.7%, respectively, with corresponding PPP positioning precision reductions of 15.4% and 3.7%.

Key words: GLONASS-M+, GLONASS-K, yaw attitude, satellite clock estimation, precise point positioning

CLC Number:

P228

Shoujian ZHANG, Xinyun CAO, Yulong GE, Fei SHEN. Yaw attitude modeling of GLONASS-K and GLONASS-M+ satellites and its impact on satellite clock estimation and precise point positioning[J]. Acta Geodaetica et Cartographica Sinica, 2025, 54(12): 2142-2152.

Figures/Tables 12

Fig. 1

Fig. 2

Tab. 1

Fig. 3

Fig. 4

Fig. 5

Fig. 6

Fig. 7

Fig. 8

Fig. 9

Fig. 10

Tab. 2

References 27

[1]	BAR-SEVER Y E. A new model for GPS yaw attitude[J]. Journal of Geodesy, 1996, 70(11): 714-723.
[2]	MONTENBRUCK O, SCHMID R, MERCIER F, et al. GNSS satellite geometry and attitude models[J]. Advances in Space Research, 2015, 56(6): 1015-1029.
[3]	KUANG D, RIM H J, SCHUTZ B E, et al. Modeling GPS satellite attitude variation for precise orbit determination[J]. Journal of Geodesy, 1996, 70(9): 572-580.
[4]	ZHAO Qile, WANG Chen, GUO Jing, et al. Precise orbit and clock determination for BeiDou-3 experimental satellites with yaw attitude analysis[J]. GPS Solutions, 2017, 22(1): 4.
[5]	CHEN Qiuli, YANG Hui, CHEN Zhonggui, et al. Solar radiation pressure modeling and application of BDS satellites[J]. Journal of Geodesy and Geoinformation Science, 2020, 3(2): 45-52.
[6]	CAO Xinyun, ZHANG Shoujian, KUANG Kaifa, et al. The impact of eclipsing GNSS satellites on the precise point positioning[J]. Remote Sensing, 2018, 10(1): 94.
[7]	LI Xingxing, YUAN Yongqiang, ZHU Yiting, et al. Improving BDS-3 precise orbit determination for medium earth orbit satellites[J]. GPS Solutions, 2020, 24(2): 6109-6131.
[8]	YANG Nannan, XU Aigong, XU Zongqiu, et al. Effect of WHU/GFZ/CODE satellite attitude quaternion products on the GNSS kinematic PPP during the eclipse season[J]. Advances in Space Research, 2025, 75(1): 1-15.
[9]	KOUBA J. A simplified yaw-attitude model for eclipsing GPS satellites[J]. GPS Solutions, 2009, 13(1): 1-12.
[10]	DILSSNER F. GPS IIF-1 satellite antenna phase center and attitude modeling[J]. Inside GNSS, 2010, 5(6): 59-64.
[11]	DAI Xiaolei, GE Maorong, LOU Yidong, et al. Estimating the yaw-attitude of BDS IGSO and MEO satellites[J]. Journal of Geodesy, 2015, 89(10): 1005-1018.
[12]	HAUSCHILD A. GNSS yaw attitude estimation: results for the Japanese quasi-zenith satellite system Block-Ⅱ satellites using single- or triple-frequency signals from two antennas[J]. Navigation, 2019, 66(4): 719-728.
[13]	刘天骏, 陈渠森, 姜卫平, 等. 地影期间卫星姿态四元数产品对北斗精密单点定位的影响分析[J]. 测绘学报, 2023, 52(4): 550-558. DOI: . doi: 10.11947/j.AGCS.2023.20220245
	LIU Tianjun, CHEN Qusen, JlANG Weiping, et al. Effect of satellite attitude quaternions on BeiDou precise point positioning during the eclipse season[J]. Acta Geodaetica et Cartographica Sinica, 2023, 52(4): 550-558, DOI: . doi: 10.11947/j.AGCS.2023.20220245
[14]	ZAMINPARDAZ S, TEUNISSEN P J G, KHODABANDEH A. GLONASS-only FDMA+CDMA RTK: performance and outlook[J]. GPS Solutions, 2021, 25(3): 96.
[15]	侯鹏宇, 张宝成, 刘腾, 等. CDMA+FDMA非差非组合区域PPP-RTK[J]. 测绘学报, 2023, 52(2): 183-194. DOI: . doi: 10.11947/j.AGCS.2023.20210422
	HOU Pengyu, ZHANG Baocheng, LIU Teng, et al. Regional PPP-RTK with CDMA+FDMA data at undifferenced and uncombined level[J], Acta Geodaetica et Cartographica Sinica, 2023, 52(2): 183-194. DOI: . doi: 10.11947/j.AGCS.2023.20210422
[16]	DILSSNER F, SPRINGER T, GIENGER G, et al. The GLONASS-M satellite yaw-attitude model[J]. Advances in Space Research, 2011, 47(1): 160-171.
[17]	DILSSNER F, SPRINGER T. GLONASS-K attitude: rapid turning maneuvers and other deviations from ideal yaw steering[J]. GPS Solutions, 2024, 28(3): 144.
[18]	STEIGENBERGER P, MONTENBRUCK O, HAUSCHILD A. Antenna and attitude modeling of modernized GLONASS satellites[J]. Advances in Space Research, 2024, 74(7): 3045-3059.
[19]	YUAN Yongqiang, LI Xingxing, YAO Yibin, et al. Estimation of phase center corrections for BDS satellites aligned to the IGS20 frame[J]. GPS Solutions, 2024, 28(2): 63.
[20]	CAO Xinyun, KUANG Kaifa, GE Yulong, et al. An efficient method for undifferenced BDS-2/BDS-3 high-rate clock estimation[J]. GPS Solutions, 2022, 26(3): 66.
[21]	LAGLER K, SCHINDELEGGER M, BÖHM J, et al. GPT2: empirical slant delay model for radio space geodetic techniques[J]. Geophysical Research Letters, 2013, 40(6): 1069-1073.
[22]	乔晨昊, 王利, 舒宝, 等. GNSS天线相位中心模型更新对PPP的影响分析[J]. 导航定位学报, 2024, 12(4): 45-57.
	QIAO Chenhao, WANG Li, SHU Bao, et al. Analysis of differences between GNSS antenna phase center correction models and their effects on precise point positioning[J]. Journal of Navigation and Positioning, 2024, 12(4): 45-57.
[23]	PETIT G, LUZUM B. IERS conventions (2010) Bureau International des Poids et Mesures Sevres[EB/OL]. [2025-07-05]. https://www.iers.org/IERS/EN/Publications/TechnicalNotes/tn36.html.
[24]	WU J, WU S, HAJJ G, et al. Effects of antenna orientation on GPS carrier phase[C]//Proceedings of 1992 AAS/AIAA Astrodynamics Conference. San Diego: IEEE, 1992.
[25]	耿涛, 赵普, 谢新, 等. GPS/BDS-3卫星姿态产品评估及对精密数据处理的影响[J]. 武汉大学学报(信息科学版)[2025-03-01]. http://doi.org/10.13203/j.whugis20240155.
	GENG Tao, ZHAO Pu, XIE Xin, et al. Evaluation of GPS/BDS-3 satellite attitude products and impact on precise data processing[J]. Geomatics and Information Science of Wuhan University[2025-03-01]. http://doi.org/10.13203/j.whugis20240155.
[26]	耿江辉, 闫哲, 温强. 多系统GNSS卫星钟差和偏差产品综合：IGS第3次重处理[J]. 武汉大学学报(信息科学版), 2023, 48(7): 1070-1081.
	GENG Jianghui, YAN Zhe, WEN Qiang. Multi-GNSS satellite clock and bias product combination: the third IGS reprocessing campaign[J]. Geomatics and Information Science of Wuhan University, 2023, 48(7): 1070-1081.
[27]	LIU Tianjun, CHEN Hua, CHEN Qusen, et al. Characteristics of phase bias from CNES and its application in multi-frequency and multi-GNSS precise point positioning with ambiguity resolution[J]. GPS Solutions, 2021, 25(2): 58.

模型与误差	钟差估计策略	PPP策略
估计模型	钟差非差模型	无电离层组合模型
滤波器	迭代Kalman滤波^[20]
卫星轨道	CODE精密轨道产品
卫星钟差	模拟实时估计	采用估计的钟差
先验对流层模型	GPT2+VMF投影函数^[21]
PCO	IGS20^[22]
潮汐改正	固体潮+海潮+极潮^[23]（IERS 2010）
相位缠绕	模型改正^[24]
测站坐标	固定为IGS周解	动态白噪声估计
卫星姿态	策略S1：GLONASS-M/M+和GLONASS-K分别采用各自姿态模型
	策略S2：所有卫星均采用GLONASS-M/M+姿态模型
	策略S3：所有卫星均采用名义姿态模型

钟差姿态	PPP姿态	时段1			时段2			时段3
钟差姿态	PPP姿态	N	E	U	N	E	U	N	E	U
S1	S1	4.37	6.89	11.14	3.99	6.24	10.80	4.72	7.49	11.67
S1	S2	4.46	6.98	11.37	4.05	6.47	10.96	4.75	7.52	11.91
S1	S3	5.00	7.83	12.82	4.51	7.10	12.46	5.36	8.27	13.43
S2	S2	4.38	6.93	11.25	4.04	6.50	10.95	4.73	7.53	11.95
S3	S3	4.86	7.77	12.67	4.55	7.20	12.16	5.28	8.22	13.50