## 3 Results and Discussion
Therefore, the elevation-dependent SICB correction model cannot be applied to these satellites. A further investigation of SICB modeling as a function of elevations and azimuths for these satellites is needed. In Figure 18, there are approximately 0.18 and 0.16 million epoch-wise MP values for C33 and C34, respectively. For the single-frequency PPP technology, the GROup And PHase Ionospheric Correction (GRAPHIC) [24], namely the ionospheric-free observable formed by the carrier phase and code observations on a single frequency, is usually used. Single-frequency PPP processing can be employed to further validate the effectiveness of our SICB correction model. Only BDS-2 IGSO and MEO satellites are adopted because the precise products are currently not available for the BDS-3S satellites. Another valid reason is that the SICB model works in the BDS-2 IGSO and MEO satellites, and the RMS MP combinations decrease compared with the uncorrected data, as shown in Figures 12 and 13. The single-frequency PPP models developed by [PERSON] et al. [25] are employed. The epoch-wise  
Figure 16: Distribution of corrected MP combination time series with the traditional SICB correction model for BDS-2 IGSO and MEO satellites. single-frequency PPP solutions without SICB corrections and with SICB corrections derived from the traditional and improved SICB correction models at station ANMG on 15 August 2016 are shown in Figure 19. When using the uncorrected observations, we find a significant systematic bias of approximately 0.8 m in the vertical direction. There are no such biases for the position solutions in the two horizontal directions. After considering the SICB corrections with the traditional or improved SICB correction models, the systematic biases almost completely vanish. The single-frequency PPP solutions using the improved SICB correction model show slightly better performance in terms of convergence time and positioning accuracy compared with those applying the traditional SICB correction model. The datasets from 21 stations for 15 August-15 September 2016 are used for the accuracy statistics. The BDS service of the Asia-Pacific area covers the selected stations. We calculate the RMSs of position errors over the last 15 min for each 24-h session. The average values of the RMSs over all the selected stations and days are listed in Table 2. On the basis of average RMSs over all the sessions, the positioning accuracies of the single-frequency PPP using the uncorrected observations are 3.3, 1.6 and 79.4 cm in the east, north and vertical directions, respectively. Taking the SICB corrections into account with the improved SICB correction model, the positioning accuracies can be improved by 24%, 19% and 89% to 2.5, 1.3 and 9.1 cm in the three directions, respectively. When using the code observations with SICB corrections derived from the traditional SICB correction model, the positioning accuracies are 2.7, 1.4 and 9.7 cm in the three directions, respectively, which are significantly better than those ignoring SICB corrections, but slightly worse than those using our improved SICB correction model. The accuracy improvements for the single-frequency PPP applying the improved SICB correction model over the case using the traditional SICB correction model are 7%, 7% and 6% in the three directions, respectively. Figure 17: Distribution of uncorrected and corrected MP combination time series for BDS-3S IGSO satellites. Figure 19: Single-frequency PPP positioning errors at station ANMG on 15 August 2016. Figure 18: Distribution of uncorrected and corrected MP combination time series for BDS-3S MEO satellites.