To deal with inconsistency between Global Navigation Satellite System (GNSS) multi-frequency data and International GNSS Service (IGS) clock product, we propose a unified model for GNSS satellite inter-frequency clock bias (IFCB) estimation and correction based on the IGS clock datum. The proposed model is rigorously derived by three sequential steps. First, by means of accurate modeling of the time-variant part of satellite phase-based IFCB (PIFCB) and introducing a zero-mean condition for satellite code-based IFCB (CIFCB), a set of independent satellite IFCBs are estimated in a full-rank multi-frequency uncombined model where IGS orbit and clock products are taken as input. The independent satellite IFCB refers to hardware delay difference between a specified frequency and two reference frequencies that are used for generating the IGS product. In the second step, a linear equation between satellite IFCBs from any three frequencies and the independent satellite IFCB estimates is derived. Based on this equation, the third step aims to establish a general satellite IFCB correction model which is used to align data on any two frequencies to the IGS clocks. The proposed model is implemented and validated using one month of multi-frequency data from BeiDou regional system (BDS-2) and BeiDou global system (BDS-3), i.e., B1I, B2I, B3I, B1C, B2a and B2b. By choosing B1I and B3I as reference frequencies, periodic analysis results suggest that a second-order periodic function is suitable for modeling BDS-2 independent satellite PIFCB variations. Yet there is no need to introduce periodic function into BDS-3 independent satellite PIFCB variations at all frequencies. For observation types of 1X (B1C), 5X (B2a) and 7Z (B2b), the standard deviation (STD) of three independent CIFCB estimates at each BDS-3 new frequency (i.e., B1C, B2a and B2b) and one CIFCB from the three new frequencies for all BDS-3 satellites are 3.14, 0.09, 0.12 and 0.09 ns, while those for the observation types of 1P (B1C), 5P (B2a) and 7D (B2b) are 2.52, 0.08, 0.08 and 0.04 ns, respectively. A major reason for the large noise of the independent satellite CIFCB at frequency B1C is that the frequency value of B1C is very close to that of B1I. Using the satellite IFCB estimates as corrections, the average RMS of kinematic precise point positioning (PPP) errors using ionosphere-free combination of BDS-3 multi-frequency data is 2.7 and 5.0 cm on horizontal and up directions, respectively, showing a same level with that of B1I/B3I-based PPP. In comparison, the accuracy of PPP is decreased by several millimeters during convergence when the differential code bias (DCB) product is used for correction.

针对全球导航卫星系统（GNSS）多频数据与国际GNSS服务（IGS）时钟产品不一致的问题，我们提出了一种基于IGS时钟的GNSS卫星异频时钟偏差（IFCB）估计和校正的统一模型基准。所提出的模型是通过三个连续步骤严格推导出来的。首先，通过对基于卫星相位的IFCB（PIFCB）的时变部分进行精确建模，并为基于卫星码的IFCB（CIFCB）引入零均值条件，对一组独立的卫星IFCBs进行完整的估计。 -rank 多频未组合模型，其中 IGS 轨道和时钟产品作为输入。独立卫星 IFCB 是指指定频率与用于生成 IGS 产品的两个参考频率之间的硬件延迟差。在第二步中，推导出来自任意三个频率的卫星 IFCB 与独立卫星 IFCB 估计值之间的线性方程。基于该方程，第三步旨在建立通用卫星IFCB校正模型，用于将任意两个频率上的数据与IGS时钟对齐。使用来自北斗区域系统（BDS-2）和北斗全球系统（BDS-3）即 B1I、B2I、B3I、B1C、B2a 和 B2b 的一个月多频数据实施和验证了所提出的模型。通过选择 B1I 和 B3I 作为参考频率，周期分析结果表明二阶周期函数适用于对 BDS-2 独立卫星 PIFCB 变化进行建模。然而，没有必要在所有频率的 BDS-3 独立卫星 PIFCB 变化中引入周期函数。对于 1X (B1C)、5X (B2a) 和 7Z (B2b) 的观测类型，每个 BDS-3 新频率（即 B1C、B2a 和 B2b）的三个独立 CIFCB 估计的标准偏差 (STD) 和来自所有BDS-3卫星的三个新频率为3.14、0.09、0.12和0.09 ns，而1P（B1C）、5P（B2a）和7D（B2b）观测类型的三个新频率分别为2.52、0.08、0.08和0.04 ns ， 分别。独立卫星CIFCB在B1C频率噪声较大的一个主要原因是B1C的频率值与B1I的频率值非常接近。使用卫星IFCB估计作为修正，使用无电离层组合BDS-3多频数据的运动精确点定位（PPP）误差的平均RMS在水平和向上方向分别为2.7和5.0 cm，显示相同水平基于 B1I/B3I 的 PPP。