## 3 Results
### Characteristics of ISB Estimates
It implies that the receiver types are replaced when the curves turn into dotted lines. As the station UNSA is located in South America (outside the service regions of BDS-2), the daily ISBs between BDS-2 and GPS at this station are unavailable. It is seen that the daily ISBs between Galileo and GPS at both BRUX and UNSA stations as well as those between GLONASS and GPS at UNSA station do not present step changes when encountering the replacement of receiver types. However, the step changes can be up to 13, 9, and 10 ns for the daily ISBs between GLONASS and GPS, between BDS-2 and GPS, and between BDS-3 and GPS at BRUX station, and to 17 ns for the daily ISBs between BDS-3 and GPS at UNSA station when the receiver types are replaced, respectively. Thus, the effects of receiver types on the ISB estimation cannot be neglected. For the purpose of analyzing the short-term stability of ISB, Figure 5 depicts the distribution of STDs of epochwise ISB estimates over a day based on the data sets from 120 stations spanning a month. The single-day STDs of epochwise ISBs with a value smaller than 1, 2, 3, and 4 ns account for 0.0%, 26.4%, 90.7%, and 99.7% for those between GLONASS and GPS, for 16.5%, 97.9%, 99.8%, and 100.0% for those between Galileo and GPS, for 5.9%, 72.6%, 96.2%, and 99.4% for those between BDS-2 and GPS, and for 3.5%, 91.5%, 98.1%, and 99.2% for those between BDS-3 and GPS, respectively. The average results over all the employed stations and days are also provided in each panel. As we can see, the ISBs between Galileo and GPS achieve the best short-term stability with an average STD statistic of 1.262 ns, followed by those between BDS-3 and GPS, the average STDs of which are 1.532 ns. The short-term stability of ISBs between BDS-2 and GPS is worse than that between BDS-3 and GPS, and the corresponding STDs are increased to 1.741 ns. Among the four groups of ISBs, the one between GLONASS and GPS has the lowest short-term stability with an average STD statistic of 2.335 ns. Figure 3: Time series of daily ISBs at 29 stations (characterized by the change of receiver firmware versions). To investigate the effects of receiver types on the short-term stability of ISBs, we calculate the average value of STDs of epochwise ISB estimates over a day for all the  
Figure 4: Time series of daily ISBs at BRUX (red) and UNSA (blue) stations (characterized by the replacement of receiver types). Figure 5: Distribution of STDs of epochwise ISB estimates over a day based on the data sets from 120 stations spanning a month. stations equipped with the same type of receivers using the data sets from DOY 41 to 70 in 2020, and the results for each receiver type are given in Figure 6. It is seen that, except for the ISB results between BDS-3 and GPS for TRIMBLE ALLOY receiver, the JAVAD TRE_G3 TH receiver achieves worse short-term stability for all the four groups of ISBs. However, the difference of the short-term stability of ISBs among different receiver types is not very significant, which is confined to approximately 0.5, 0.2, 1.0, and 0.5 ns for the ISBs between GLONASS and GPS, between Galileo and GPS, between BDS-2 and GPS, and between BDS-3 and GPS, respectively. To explore the relationship between the numerical values of ISB (i.e., the magnitude of ISB) and the receiver types, Figure 7 presents the time series of daily ISBs (i.e., the average value of the epochwise ISB estimates over a day) for each station on DOY 41-70, 2020. Different colors refer to different receiver types, and some ones are with marks (dots) for clarity. The two stations encountering the receiver replacement, namely BRUX and UNSA, are not included in the analysis here. As can be seen, the daily ISBs are roughly consistent for the stations equipped with the same type of receivers, except for those between GLONASS and GPS at station CEDU.