# Characterization of GNSS Signals Tracked by the iGMAS Network Considering Recent BDS-3 Satellites
## 3 Methodology and Results
### Inter-Frequency Clock Bias  
With the availability of three-frequency signals for GPS Block IIF satellites, inter-frequency clock bias (IFCB) was found, which was defined as the difference of the satellite clock offsets determined from two different ionosphere-free (IF) linear combinations of L1/L2 and L1/L5 carrier phase observations, and could most likely be attributed to inconsistency among frequency-dependent phase biases within a satellite [24; 25]. According to previous studies, the IFCB between the BDS-2 B1/B2 and B1/B3 ionosphere-free satellite clocks showed a peak-to-peak amplitude of about 4 cm and, more noticeably, 10-40 cm for GPS Block IIF satellites [26; 27]. In contrast, no apparent IFCB variations could be identified for the three signals of Galileo and QZSS satellites [28]. The presence of such IFCB makes it inappropriate to use one set of satellite clock products for data processing across all frequency bands, which complicates the implementation of triple-frequency PPP [29; 30]. Thus, some approaches have been developed to estimate IFCBs [24; 31]. The estimated IFCBs exhibit a time dependency and can be modeled. [PERSON] et al. [31] and [PERSON] et al. [32] investigated the modeling of IFCBs for describing their characterization and predicting their values in advance. Figure 7: MP combinations as a function of elevation for four BDS-3 satellites on five frequencies of signals observed at three iGMAS stations equipped with different antennas (RINT-8 CH CETD/LEIAR25.R4 LEIT/GNSS-750) during DOY 150-152, 2018. The five rows from top to bottom represent five BDS-3 signals: B1, B3I, B1C, B2a, and B2b; the four columns from left to right represent four selected BDS-3 satellites: C19, C21, C28, and C30. As discussed in previous publications, the IFCB is directly observable from the triple-frequency carrier phase combination, which is the difference of two different carrier phase IF combinations, as follows:  
\[ \begin{array}{ll}DIF(\varphi_{1},\varphi_{2},\varphi_{3})&=IF(\varphi_{1}, \varphi_{2})-IF(\varphi_{1},\varphi_{3})\\ &=\left(\frac{f_{1}^{2}}{f_{1}^{2}-f_{2}^{2}}-\frac{f_{1}^{2}}{f_{1}^{2}-f_{3} ^{2}}\right)\cdot\varphi_{1}-\left(\frac{f_{2}^{2}}{f_{1}^{2}-f_{2}^{2}}\right) \cdot\varphi_{2}+\left(\frac{f_{3}^{2}}{f_{1}^{2}-f_{3}^{2}}\right)\cdot\varphi _{3}\end{array}  \tag{2}\]  
where \(\varphi_{1},\varphi_{2},\varphi_{3}\) are carrier phase observations (in meters) on three distinct frequencies \(f_{i}\) (with \(f_{1}>f_{2}>f_{3}\)). In addition to observing the IFCB variations, the triple-frequency carrier phase combination is usually used to assess carrier phase errors, since it is both geometry-free and ionosphere-free and reflects a weighted sum of the carrier phase multipath and noise on the respective frequencies after removing the constant ambiguity. Numerical values of the coefficients for several triple-frequency carrier phase combinations shown in this study are listed in Table 4. For BDS-2 satellites, the iGMAS stations can only receive double-frequency signals of B1I and B3I, and thus cannot form the combination. For BDS-3, some stations are capable of receiving five frequencies of signals, which provide more choices to form the triple-frequency carrier phase combination. In this study, (B1I, B3I, B2b) and (B1C, B2b, B2a) triple-frequency combinations of BDS-3 are chosen as typical examples for analysis. The triple-frequency carrier phase combinations for GPS Block IIF and Galileo satellites, which have been revealed in previous research, are further confirmed in our experiment, as shown in Figure 8, which plots the results of triple-frequency combinations for G08 and E07 satellites at station WHU1. As expected, obvious IFCB variations are recognized in the GPS Block IIF satellite and are confined to peak amplitudes of about 5 cm, while a good E1/E5b/E5a consistency and no significant bias variations can be seen in Galileo satellites.