GPS/Galileo/BDS overlapping frequencies multipath error analysis and modeling

doi:10.11947/j.AGCS.2025.20240316

Abstract

Abstract:

Multipath error is one of the primary unmodeled errors affecting GNSS precise positioning. Currently, the multipath hemispherical map (MHM) model generated by single system is limited by satellite orbit period and data volume, leading to restricted data coverage and low modeling efficiency. Therefore, this paper constructs an integrated multi-system MHM model by combining overlapping frequency data from GPS, Galileo, and BDS. The effectiveness of the short-term fusion model for multipath correction is evaluated with short-baseline data. The results show that the multipath error of the overlapping frequency for the three systems exhibits consistent spatial distribution characteristics, and the data coverage (the proportion of grids with more than 30 residuals within the total grids) of the three-system fusion model constructed with 4-day data is higher than that of the model built with 10-day data of a single system. The multipath models with overlapping frequency between systems has good interoperability. After using an overlapping grid evaluation method, the inter-system multipath correction rate is approximately 30%~45%. The correction rates of the three-system fusion model for GPS, Galileo, and BDS are approximately 60%、46%, and 48%, respectively. Additionally, the multi-system fusion model, constructed in a short time, can enhance positioning accuracy by approximately 10%~20% compared to single-system models, which is comparable to those of single-system multipath models built with long-term data. However, the difference in the multipath correction effect between the GPS single-system model and the multi-system fusion model is not significant.

Key words: GNSS, multipath error, MHM, overlapping frequencies, multi-frequency

CLC Number:

P228

Yangyi CHEN, Kai ZHENG, Xiaohong ZHANG, Mingkui WU, Pengxu WANG, Wenju FU, Kezhong LIU. GPS/Galileo/BDS overlapping frequencies multipath error analysis and modeling[J]. Acta Geodaetica et Cartographica Sinica, 2025, 54(8): 1427-1438.

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References 33

[1]	杨元喜. 北斗卫星导航系统的进展、贡献与挑战[J]. 测绘学报, 2010, 39(1): 1-6.
	YANG Yuanxi. Progress, contribution and challenges of Compass/BeiDou satellite navigation system[J]. Acta Geodaetica et Cartographica Sinica, 2010, 39(1): 1-6.
[2]	凌晴, 张勤, 张静, 等. 融合工程地质资料与GNSS高精度监测信息的黑方台党川黄土滑坡稳定性研究[J]. 测绘学报, 2022, 51(10): 2226-2238. DOI: . doi: 10.11947/.AGCS.2022.20220307
	LING Qing, ZHANG Qin, ZHANG Jing, et al. Stability evaluation of Dangchuan loess landslide in Heifangtai based on integration of engineering geological data and GNSS high-precision monitoring information[J]. Acta Geodaetica et Cartographica Sinica, 2022, 51(10): 2226-2238. DOI: . doi: 10.11947/.AGCS.2022.20220307
[3]	YAO Chaolong, LUO Zhicai, HU Yueming, et al. Detecting droughts in southwest China from GPS vertical position displacements[J]. Journal of Geodesy and Geoinformation Science, 2020, 3(3): 50-58.
[4]	WANG Xiaolei, NIU Zijin, HE Xiufeng, et al. Monitoring of coastal subsidence changes based on GNSS positioning and GNSS-IR[J]. Journal of Geodesy and Geoinformation Science, 2023, 6(2): 71-80.
[5]	王利, 许豪, 舒宝, 等. 滑坡灾害GNSS监测技术研究进展与展望[J]. 导航定位与授时, 2023, 10(1): 12-26.
	WANG Li, XU Hao, SHU Bao, et al. Research progress and prospects of GNSS deformation monitoring technology for landslide hazards[J]. Navigation Positioning and Timing, 2023, 10(1): 12-26.
[6]	HOFMAN-WELLENHO B, LICHTENEGGER H, WASLE E. GNSS-global navigation satellite systems: GPS, GLONASS, Galileo, and more[M]. New York: Springer Science & Business Media, 2007.
[7]	LUO Xiaoguang, MAYER M, HECK B, et al. A realistic and easy-to-implement weighting model for GPS phase observations[J]. IEEE Transactions on Geoscience and Remote Sensing, 2014, 52(10): 6110-6118.
[8]	李岚, 朱锋, 刘万科, 等. 城市分类场景的GNSS伪距随机模型构建及其定位性能分析[J]. 武汉大学学报(信息科学版), 2025, 50(3): 545-553.
	LI Lan, ZHU Feng, LIU Wanke, et al. GNSS pseudorange stochastic model for urban classification scenes and its positioning performance[J]. Geomatics and Information Science of Wuhan University, 2025, 50(3): 545-553.
[9]	SATIRAPOD C, RIZOS C. Multipath mitigation by wavelet analysis for GPS base station applications[J]. Survey Review, 2005, 38(295): 2-10.
[10]	DAI Wujiao, HUANG Dawei, CAI Changsheng. Multipath mitigation via component analysis methods for GPS dynamic deformation monitoring[J]. GPS Solutions, 2014, 18(3): 417-428.
[11]	SU Mingkun, ZHENG Jiansheng, YANG Yanxi, et al. A new multipath mitigation method based on adaptive thresholding wavelet denoising and double reference shift strategy[J]. GPS Solutions, 2018, 22(2): 40.
[12]	LI Wanqing, ZHU Xiangwei, CHEN Zhengkun, et al. Code multipath error extraction based on the wavelet and empirical mode decomposition for Android smart devices[J]. GPS Solutions, 2021, 25(3): 91.
[13]	PAN Yuanxin, MÖLLER G, SOJA B. Machine learning-based multipath modeling in spatial domain applied to GNSS short baseline processing[J]. GPS Solutions, 2023, 28(1): 9.
[14]	SHEN Nan, CHEN Liang, WANG Lei, et al. GNSS site unmodeled error prediction based on machine learning[J]. GPS Solutions, 2023, 27(2): 77.
[15]	HU Mingxian, YAO Yibin, GE Maorong, et al. Random walk multipath method for Galileo real-time phase multipath mitigation[J]. GPS Solutions, 2023, 27(2): 58.
[16]	YE Shirong, CHEN Dezhong, LIU Yanyan, et al. Carrier phase multipath mitigation for BeiDou navigation satellite system[J]. GPS Solutions, 2015, 19(4): 545-557.
[17]	郑凯, 檀灵敏, 刘克中, 等. 多频GNSS非差非组合PPP多径误差修正及定位性能评估[J/OL]. 武汉大学学报(信息科学版). [2024-07-31]. https://doi.org/10.13203/j.whugis20230200.
	ZHENG Kai, TAN Lingmin, LIU Kezhong, et al. Performance of multi-frequency and multi-GNSS undifferenced and uncombined precise point positioning with multipath correction[J/OL]. Geomatics and Information Science of Wuhan University. [2024-07-31]. https://doi.org/10.13203/j.whugis20230200.
[18]	DONG D, WANG M, CHEN W, et al. Mitigation of multipath effect in GNSS short baseline positioning by the multipath hemispherical map[J]. Journal of Geodesy, 2016, 90(3): 255-262.
[19]	WANG Zhiren, CHEN Wen, DONG Danan, et al. Multipath mitigation based on trend surface analysis applied to dual-antenna receiver with common clock[J]. GPS Solutions, 2019, 23(4): 104.
[20]	LU Ran, CHEN Wen, DONG Danan, et al. Multipath mitigation in GNSS precise point positioning based on trend-surface analysis and multipath hemispherical map[J]. GPS Solutions, 2021, 25(3): 119.
[21]	ZHENG Kai, ZHANG Xiaohong, LI Pan, et al. Multipath extraction and mitigation for high-rate multi-GNSS precise point positioning[J]. Journal of Geodesy, 2019, 93(10): 2037-2051.
[22]	TANG Weiming, WANG Yawei, ZOU Xuan, et al. Visualization of GNSS multipath effects and its potential application in IGS data processing[J]. Journal of Geodesy, 2021, 95(9): 103.
[23]	YUAN Haijun, ZHANG Zhetao, HE Xiufeng, et al. Multipath mitigation in GNSS precise point positioning using multipath hierarchy for changing environments[J]. GPS Solutions, 2023, 27(4): 55-62.
[24]	ZHANG Zhetao, DONG Yi, WEN Yuanlan, et al. Modeling, refinement and evaluation of multipath mitigation based on the hemispherical map in BDS2/BDS3 relative precise positioning[J]. Measurement, 2023, 213: 112722.
[25]	WANG Hao, ZHANG Zhetao, DONG Yi, et al. Real-time multipath mitigation based on spatiotemporal correlations in BDS precise point positioning[J]. GPS Solutions, 2023, 28(1): 37.
[26]	LU Ran, CHEN Wen, LI Zhao, et al. An improved joint modeling method for multipath mitigation of GPS, BDS-3, and Galileo overlapping frequency signals in typical environments[J]. Journal of Geodesy, 2023, 97(10): 95.
[27]	GENG Jianghui, LI Pengbo, LI Guangcai. Combining the GPS/Galileo/BDS-3 signals on overlap frequencies for interoperable multipath hemispherical maps[J]. Journal of Geodesy, 2024, 98(4): 32-41.
[28]	LIU Chao, TAO Yuan, XIN Haiqiang, et al. A single-difference multipath hemispherical map for multipath mitigation in BDS-2/BDS-3 short baseline positioning[J]. Remote Sensing, 2021, 13(2): 304.
[29]	TEUNISSEN P J G. The least-squares ambiguity decorrelation adjustment: a method for fast GPS integer ambiguity estimation[J]. Journal of Geodesy, 1995, 70(1): 65-82.
[30]	ZHONG Ping, DING Xiaoli, YUAN Linguo, et al. Sidereal filtering based on single differences for mitigating GPS multipath effects on short baselines[J]. Journal of Geodesy, 2010, 84(2): 145-158.
[31]	REN Hanxin, LI Guangcai, GENG Jianghui, et al. Multipath hemispherical map model with geographic cut-off elevation constraints for real-time GNSS monitoring in complex environments[J]. GPS Solutions, 2023, 27(4): 188.
[32]	FUHRMANN T, LUO Xiaoguang, KNÖPFLER A, et al. Generating statistically robust multipath stacking maps using congruent cells[J]. GPS Solutions, 2015, 19(1): 83-92.
[33]	GENG Jianghui, PAN Yuanxin, LI Xiaotao, et al. Noise characteristics of high-rate multi-GNSS for subdaily crustal deformation monitoring[J]. Journal of Geophysical Research: Solid Earth, 2018, 123(2): 1987-2002.

系统组合	1 575.42 MHz	1 176.45 MHz	模型
GPS	L1	L5	MHM_G
Galileo	E1	E5a	MHM_E
BDS	B1C	B2a	MHM_C
GPS/Galileo/BDS	L1/E1/B1C	L5/E5a/B2a	MHM_GEC

系统组合	L1/E1/B1C		L5/E5a/B2a
系统组合	Mean	STD	Mean	STD
GPS	-16.0	7.8	15.5	5.7
Galileo	-12.5	7.1	16.4	9.3
BDS	-12.4	7.2	17.8	6.7
GPS/Galileo/BDS	-14.5	7.7	16.1	6.8

模型	GPS		Galileo		BDS
模型	L1	L5	E1	E5a	B1C	B2a
MHM_G	99.1	99.0	36.2	24.1	37.4	21.2
MHM_E	70.5	69.9	61.4	61.3	68.8	68.6
MHM_C	74.7	74.9	71.2	71.2	74.9	75.0
MHM_GEC	99.7	99.7	88.7	87.7	91.4	90.2

模型	GPS			Galileo			BDS			GEC
模型	E	N	U	E	N	U	E	N	U	E	N	U
MHM_G	90.6	88.5	92.6	33.2	23.1	28.9	30.5	16.2	17.3	52.6	35.8	30.6
MHM_E	56.7	54.4	56.9	57.8	45.4	57.7	57.3	46.4	41.2	63.4	51.7	42.9
MHM_C	63.2	59.8	50.5	63.1	49.6	65.9	63.4	57.3	44.3	68.4	53.3	40.8
MHM_GEC	87.9	83.8	86.6	79.7	66.9	75.5	64.5	62.0	64.3	84.2	74.9	69.2