## 4 Results
### Characteristics of the Mixed OSB
To more objectively illustrate the performance of Schemes 1 and 2, Table 2 illustrates the statistical results and improvement of Scheme 2 in January 2021. The STD improvement of the undifferenced OSB is 7.5, 68.4, 38.6, 13.3, 60.9, and 22.2%, and the RMS can be improved by 9.4, 66.1, 34.8, 11.8, 56.5, and 20.7% with respect to GPS L5, BDS-3 B1C, B2a, and Galileo E5b, E5, and E6 signals. Moreover, the STD improvement of the ED OSB is 60.0, 80.0, 87.5, 75.0, 50.0, and 75.0%, and the RMS can be improved by 60.0, 83.3, 88.9, 75.0, 66.7, and 80.0%C. There are significant differences in improvement rates among different satellitesystems or frequencies. There are two main reasons: (1) the undifferenced mixed OSB for different satellite systems are frequencies that have different scales, and (2) the number of observations for different signals is different, so there are differences in the improvement. Figure 4: The BDS-3 BIC and B2a mixed OSB on DOY 011, 2021. Figure 3: GPS L5 mixed OSB on DOY 011, 2021. Overall, these discoveries illustrate that the stability and accuracy of the new undifferenced DSB estimation algorithm compared to the ED IFCB algorithm. Figure 5: The Galileo E5b, E5, and E6 mixed OSB on DOY 011, 2021. Figure 6: Amplitudes of the mixed OSB of GPS L5, BIDS-3 B1C, B2a, and Galileo E5b, E5, and E6 signals on DOY 011, 2021. Figure 7: Pseudorange and phase time-variant mixed epoch-differenced (ED) OSB for GPS L5 signal on DOY 011, 2021. Notably, it can be found that there is a systematic periodic bias in the OSB obtained from Scheme 1 at BDS B2a and Galileo E6 signals from Figures 4 and 5. Some of the literature suggests that this systematic periodic bias is related to the number of available observations at the GNSS tracking station. Due to the small number of MGEX stations capable of tracking BDS-3 B2a and Galileo E6 signals, the accuracy and reliability of the estimated OSB are poor [24]. The OSB estimation is affected by the receiver antenna environment and receiver and antenna quality, which results in periodic errors [1]. Unfortunately, these explanations cannot explain this systematic error at the BDS B2a and Galileo E6 signals. However, it can be found that the mixed OSB value obtained from Scheme 2 does not have significant periodic bias. By comparing the two algorithms, it can be seen that the epoch-differenced algorithm is based on the assumption that the IFCB of the same satellite at different stations has good consistency and the receiver phase time-variant OSB can be combined into satellite phase time-variant OSB. However, it is necessary to separate the satellite and receiver phase time-variant OSB in the new algorithm. To confirm that this small periodic bias is caused by some receiver phase time-variant OSB, Figure 10 shows the receiver OSB for all receiver types in the observation network. It can be seen that the JAVAD TRE-3 receiver OSB for BDS-3 B2a and Galileo E6 exhibits significant periodic variations; the OSB of other receivers is relatively stable and does not have significant deviations. Figure 11 further depicts the receiver OSB for multiple stations with the JAVAD TRE-3 receiver. This is just more evidence for the theory that JAVAD TRE-3 receiver hardware delay exhibits periodic variations at the BDS-3 B2a and Galileo E6 signals. Scheme 1 ignores the receiver phase time-variant OSB, which negatively impacts the estimation of the satellite OSB. On the contrary, the new undifferenced method uses zero-mean constraints to separate the satellite and receiver OSB, which effectively solves this problem. Figure 8: Pseudorange and phase time-variant mixed ED OSB for BDS-3 BIC and B2a signals on DOY 011, 2021. Figure 9: Daily satellite pseudorange and phase time-variant mixed OSB for Galileo E5b, E5, and E6 signals on DOY 011, 2021. Figure 11: Daily JAVAAD TRE-3 receiver pseudorange and phase time-variant mixed OSB at BDS-3 B2a and Galileo E6 signals on DOY 011, 2021.