## 4 Conclusions  
An improved elevation-dependent SICB piecewise linear correction model with an elevation node separation of \(1^{\circ}\) in consideration of the consistency of the MP combinations is proposed in this study. We obtain effective SICB corrections for the code observations from BDS-2 IGSO and MEO satellites on B1, B2 and B3 frequencies, as well as the code observations from BDS-3S IGSO satellites on B1 and B3 frequencies. The correction parameters are estimated for each frequency and for each satellite. The traditional SICB correction model is also established for the purpose of comparison.  
Significant differences can be observed for the elevation-dependent SICB corrections among the orbit types and frequency bands. The SICB variations have much more effect on the BDS-2 MEO satellites than the BDS-2 IGSO satellites. For BDS-2 satellites, the code observations on the B2 frequency are less affected by the SICB than those on the B1 frequency, while the B3 signal has the smallest SICB corrections. Elevation-dependent code biases are successfully removed after adding the SICB corrections to the code observations. After applying the improved SICB correction model, the RMS values of MP combination time series are reduced from 0.447, 0.381, and 0.406 m to 0.417, 0.360 and 0.398 m, and from 0.523, 0.405, and 0.382 m to 0.431, 0.348 and 0.363 m, on the B1, B2 and B3 frequencies for the BDS-2 IGSO and MEO satellites, respectively. With the traditional SICB correction model, the corresponding RMS MP combinations are 0.422, 0.364 and 0.400 m, and 0.448, 0.355 and 0.364 m on the three frequencies for the BDS-2 IGSO and MEO satellites, respectively, which are smaller than those of uncorrected MP series, but slightly larger than those of corrected MP series using the improved SICB correction model. Single-frequency PPP processing using BDS-2 IGSO and MEO satellites is carried out to validate the effectiveness and correctness of our improved model. The positioning accuracies of single-frequency PPP considering SICB corrections derived from the improved model are improved by 24%, 19% and 89%, and 7%, 7% and 6% compared with the case neglecting the SICB effects and the case using the SICB corrections computed by the traditional SICB correction model in east, north and vertical directions, respectively. Only centimeter-level SICB variations can be observed for all the signals of BDS-3S satellites. After applying the SICB corrections derived from the improved SICB correction model, the RMSs of MP series for B1 and B3 signals of BDS-3S IGSO satellites C31 and C32 are reduced from 0.505 and 0.433 m to 0.484 and 0.420 m, and from 0.499 and 0.397 m to 0.483 and 0.394 m, respectively.  
Currently, the BDS-3 is under construction. As of 29 March 2018, there have been eight BDS-3 satellites. According to the performance of the code systematic biases for BDS-3S satellites, it is reasonable to infer that SICB variations at centimeter level will still exist in the code observations from BDS-3 satellites. Our approach can be well used to establish the SICB correction models for the BDS-3 satellites in the future.  
[PERSON] and [PERSON] conceived and designed the experiments; [PERSON] performed the experiments, analyzed the data and wrote the paper; [PERSON] and [PERSON] reviewed the paper. This research was funded by the National Natural Science Foundation of China (Grant Nos. 41774034 and 41404006) and National Key Research and Development Program of China (Grant Nos. 2016 YFB0501803 and 2017 YFB0503402). The contribution of data from IGS and iGMAS is appreciated. The authors declare no conflict of interest.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Direction** & **Uncorrected** & **Corrected (Improved SICB Model)** & **Corrected (Traditional SICB Model)** \\ \hline East (cm) & 3.3 & 2.5 & 2.7 \\ North (cm) & 1.6 & 1.3 & 1.4 \\ Up (cm) & 79.4 & 9.1 & 9.7 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Average positioning accuracy of single-frequency PPP with and without SICB corrections for all 24-h sessions.