北斗三号卫星多形式码偏差统一估计及改正方法

doi:10.11947/j.AGCS.2026.20250404

测绘学报 ›› 2026, Vol. 55 ›› Issue (6): 1047-1057.doi: 10.11947/j.AGCS.2026.20250404

• 大地测量学与导航 • 上一篇

北斗三号卫星多形式码偏差统一估计及改正方法

赵劲竹¹^,²(), 施闯²^,³, 范磊²^,³(), 郭仕伟²^,³, 张涛¹^,²

^1.北京航空航天大学电子信息工程学院，北京　100191
^2.卫星导航与移动通信融合技术工信部重点实验室，北京　100191
^3.北京航空航天大学空间与地球科学学院，北京　102206

收稿日期:2025-09-28 修回日期:2026-06-01 发布日期:2026-07-28
通讯作者: 范磊 E-mail:jingzhu@buaa.edu.cn;bhflei@buaa.edu.cn
作者简介:赵劲竹（2000—），女，博士生，研究方向为高精度GNSS数据处理。E-mail：jingzhu@buaa.edu.cn
基金资助:
国家自然科学基金(42274041; 42404038; 41931075);中国科协青年人才托举项目(YESS20230249)

Unified estimation and correction method for multi-form code bias using BDS-3 data

Jingzhu ZHAO¹^,²(), Chuang SHI²^,³, Lei FAN²^,³(), Shiwei GUO²^,³, Tao ZHANG¹^,²

^1.School of Electronic and Information Engineering, Beihang University, Beijing 100191, China
^2.Key Laboratory of Navigation and Communication Fusion Technology, Ministry of Industry and Information Technology, Beijing 100191, China
^3.School of Space and Earth Sciences, Beihang University, Beijing 102206, China

Received:2025-09-28 Revised:2026-06-01 Published:2026-07-28
Contact: Lei FAN E-mail:jingzhu@buaa.edu.cn;bhflei@buaa.edu.cn
About author:ZHAO Jingzhu (2000—), female, PhD candidate, majors in GNSS precise data processing. E-mail: jingzhu@buaa.edu.cn
Supported by:
The National Natural Science Foundation of China(42274041; 42404038; 41931075);Young Elite Scientists Sponsorship Program by CAST(YESS20230249)

摘要/Abstract

摘要：

GNSS码偏差主要存在3种主流表征形式：观测量信号偏差（OSB）、差分码偏差（DCB）和频间钟差偏差（IFCB）。精密处理这些码偏差对实现GNSS不同频率观测数据的一致性具有关键意义。然而，受估计模型、误差处理策略、基准引入方式等影响，不同来源、不同表征形式的码偏差产品不一致。针对这一问题，本文推导了用于不同形式码偏差估计兼容统一的函数模型，构建了不同形式码偏差的统一改正方法。利用北斗三号全球卫星导航系统（BDS-3）观测数据，对OSB、DCB与IFCB 3种码偏差进行统一估计与评估。结果显示，非组合BDS-3卫星码偏差估计结果与外部产品存在钟差基准导致的系统偏差；BDS-3卫星OSB、DCB、IFCB 3种码偏差估计结果自洽，相互间差异的均方根（RMS）均在3.0×10^－3 ns以内。进一步将码偏差估计结果应用于精密单点定位中，在钟差层面实现多形式码偏差的统一改正。相较于外部OSB产品，本文所估码偏差在B1I+B2a与B1C+B2a两种组合下，收敛期间三维定位误差RMS分别平均降低4.9%与9.3%。3种形式码偏差在PPP收敛期间与收敛后定位精度均一致。因此，在实际应用中，用户可根据数据条件灵活选用任一形式的码偏差，获得符合一致性的高精度定位结果。

关键词: 观测量信号偏差, 差分码偏差, 频间钟差偏差, 非差非组合, 精密单点定位, BDS-3

Abstract:

Global navigation satellite system (GNSS) code biases are primarily characterized by three forms: observation-specific signal bias (OSB), differential code bias (DCB), and inter-frequency clock bias (IFCB). Precise processing of these code biases is critical for achieving consistency in observation data across different GNSS frequencies. However, due to differences in estimation models, error handling strategies, and reference definition, code bias products from different sources and in different forms exhibit inconsistencies. To address this issue, this study derives a compatible and unified functional model for estimating different forms of code biases and establishes a unified correction method for these code bias forms. Using global observation data from the BeiDou-3 Global System (BDS-3), the three forms of code bias (OSB, DCB and IFCB) are estimated and the results are evaluated. Results demonstrate that systematic biases exist between the code biases estimated from the uncombined model and external products, which are attributed to inconsistencies in the clock datum. Additionally, high consistency is observed among the OSB, DCB, and IFCB estimates, with root mean square (RMS) differences all within 3.0×10^－3 ns. The estimated code biases are further applied to precise point positioning (PPP), achieving unified correction of multi-form code biases at the clock offset level. Experimental results demonstrate that, compared with using external OSB products, the code biases estimated in this study led to average reductions in the RMS of 3D positioning errors during the convergence period by 4.9% and 9.3% for the B1I/B2a and B1C/B2a frequency combinations, respectively. All three code bias forms demonstrated consistent positioning performance during both convergence period and after convergence. Therefore, in practical applications, users can flexibly select any form of code bias according to their data conditions to achieve consistent and high-precision positioning results.

Key words: observation-specific signal bias, differential code bias, inter-frequency clock bias, undifferenced and uncombined, precision point positioning, BDS-3

中图分类号:

P228

赵劲竹, 施闯, 范磊, 郭仕伟, 张涛. 北斗三号卫星多形式码偏差统一估计及改正方法[J]. 测绘学报, 2026, 55(6): 1047-1057.

Jingzhu ZHAO, Chuang SHI, Lei FAN, Shiwei GUO, Tao ZHANG. Unified estimation and correction method for multi-form code bias using BDS-3 data[J]. Acta Geodaetica et Cartographica Sinica, 2026, 55(6): 1047-1057.

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链接本文: http://xb.chinasmp.com/CN/10.11947/j.AGCS.2026.20250404

http://xb.chinasmp.com/CN/Y2026/V55/I6/1047

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参考文献 35

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项目	内容
观测值	C2I、C6I、C1X、C5X原始观测值
卫星个数	BDS-3 23颗MEO卫星和3颗IGSO卫星
截止高度角	7°
处理弧长	24 h
处理间隔	300 s
天线相位中心误差	采用IGS提供的ANTEX（antenna exchange format）文件（igs20.atx）进行卫星和接收机天线相位中心误差改正
卫星轨道钟差	通过WHU发布的精密产品改正
站坐标	估计为常数并由IGS天解紧约束
接收机钟差	估计为随机游走噪声
对流层延迟	使用Vienna Mapping Functions 1（VMF1）映射函数^[35]；对流层梯度估计为24 h内常数；对流层湿延迟估计为1 h内常数并估计为随机游走噪声
模糊度	估计为弧段内浮点常数
电离层延迟	使用电离层单层映射函数；使用CODE发布的GIM产品改正的同时将改正残余量估计为白噪声
卫星码偏差	估计为24 h内常数；采用所有可用卫星的零均值约束；根据估计码偏差类型不同分别加入对应约束
接收机码偏差	估计为24 h内常数
参数估计器	加权最小二乘估计，原始伪距与相位观测值先验精度分别设置为0.2 m和0.002 m，采用高度角e相关的加权策略，即当e≥30°时采用等权，否则权重设为2sine

频率	方向	CAS	WHU	OSB	DCB	IFCB
B1I+B2a	北向	6.81	6.46	6.22	6.22	6.22
	东向	10.43	11.37	10.63	10.63	10.63
	高程	13.94	12.88	12.59	12.59	12.59
	3D	18.70	18.36	17.62	17.62	17.62
B1C+B2a	北向	5.82	6.66	5.62	5.62	5.62
	东向	8.95	10.60	8.62	8.62	8.62
	高程	11.53	13.43	11.41	11.41	11.41
	3D	15.71	18.36	15.36	15.36	15.36

频率	方向	CAS	WHU	OSB	DCB	IFCB
B1I+B2a	北向	1.78	1.70	1.70	1.70	1.70
	东向	2.37	2.27	2.27	2.27	2.27
	高程	4.74	4.48	4.49	4.49	4.49
	3D	5.59	5.31	5.31	5.31	5.31
B1C+B2a	北向	1.67	1.75	1.67	1.67	1.67
	东向	2.23	2.34	2.19	2.19	2.19
	高程	4.47	4.72	4.49	4.49	4.49
	3D	5.27	5.55	5.26	5.26	5.26

北斗三号卫星多形式码偏差统一估计及改正方法

Unified estimation and correction method for multi-form code bias using BDS-3 data

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码偏差	系数	约束	与对应关系
OSB
DCB
IFCB