## 3 Results
### ISB Estimates Derived from Smartphones  
Smartphones with built-in low-cost GNSS chipsets and linearly polarized GNSS antenna have been widely applied to the SPP processing in recent years. The ISB estimates derived from the smartphones are characterized in this section. As shown in Figure 15, two Xiaomi Mi8 smartphones, which are identified by Xiaomi Mi8 (1) and Xiaomi Mi8 (2), are used to conduct the SPP experiment, and both of them can support GPS, GLONASS, Galileo, BDS-2, and BDS-3 satellites. The SPP experiment was carried out within the main campus of the Central South University in Changsha, China, on DOY 319 to 320 of 2020, and lasted for approximately 5 h and 20 min for each day, namely from 9:20 to 14:40 (GPS Time) for the first day and from 8:55 to 14:14 (GPS Time) for the second day. The two smartphones with a distance of several decimeters were set up on the roof of the Mining Building of the Central South University, and the multi-GNSS data were collected at a sampling interval of 1 s. After the data collection with smartphones, a Trimble NetR9 receiver with a TRM57970.00 antenna was set up on the almost identical places to help determine the reference coordinates of the two smartphones using the double-differenced RTK approach. For the RTK processing, a base station with the same type of receiver and antenna was also set up on the roof of the Mining Building and was only several meters away from the smartphones. Figure 14: Epochwise positioning errors of GPS/GLONASS integrated SPP with and without a priori ISB constraints using the low-cost u-blox M8T receiver under a cutoff elevation of 30\({}^{\circ}\) on DOY 305 of 2021. Figure 16 presents the epochwise ISB estimates for GLONASS, Galileo, BDS-2, and BDS-3 with respect to GPS derived from the four-system integrated SPP with the two Xiaomi Mi8 smartphones under a cutoff elevation of 10\({}^{\circ}\) on DOY 319 and 320 of 2020. In conjunction with the ISB results obtained with the geodetic receiver and the low-cost u-blox M8T receiver (see Figures 2 and 13), the fluctuations are much more dramatic for those derived from the smartphones, which can be up to approximately 45 ns for the epochwise ISBs between Galileo and GPS, between BDS-2 and GPS, and between BDS-3 and GPS and approximately 120 ns for the epochwise ISBs between GLONASS and GPS, respectively. The epochwise ISB estimates at some epochs between BDS-3 and GPS on DOY 319 of 2020 for Xiaomi Mi8 (1) and on DOY 320 of 2020 for Xiaomi Mi8 (2) and between BDS-2 and GPS on DOY 319 of 2020 for Xiaomi Mi8 (2) have larger varying range, which can be attributed to the limited visible BDS-3 or BDS-2 satellites with a number of only two. The epochwise ISBs at partial epochs on DOY 320 of 2020 between BDS-3 and GPS for the two smartphones and between Galileo and GPS for Xiaomi Mi8 (1) are absent due to the availability of only a BDS-3 or Galileo satellite. The average value and STD statistic of epochwise ISBs over all the available epochs for each session for the two smartphones are listed in Table 7. The epochwise ISBs between GLONASS and GPS have the worst short-term stability, with a STD statistic of 17.135-19.357 ns, while the corresponding statistics are 5.994-7.896, 6.670-7.966, and 6.768-12.185 ns for those between Galileo and GPS, between BDS-2 and GPS, and between BDS-3 and GPS, respectively. The average value of epochwise ISBs is taken as the daily ISB. Regarding the Xiaomi Mi8 (1) smartphone, the single-day prediction accuracy of daily ISB is 6.643, 0.811, 3.389, and 3.732 ns for GLONASS, Galileo, BDS-2, and BDS-3 with respect to GPS, respectively, while the corresponding prediction accuracy is improved to 2.090, 1.357, 1.435, and 0.814 ns for the four groups of daily ISBs for the Xiaomi Mi8 (2) smartphone, respectively, which is still worse than that with the geodetic devices (see Figure 9).