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

doi:10.11947/j.AGCS.2026.20250404

Abstract

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

CLC Number:

P228

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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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