## 2 Elevation-Dependent Modeling of Satellite-Induced Code Bias
### Traditional SICB Modeling  
In traditional SICB modeling, the float phase ambiguities in Equation (3) are roughly determined as the average values of the MP combination time series over each continuous tracking arc [5; 9]. After subtracting the estimated phase ambiguities from the MP combination time series, the remaining series are used to model the long-term changes, namely SICB, based on the relationship with elevation angles. When employing this method, only MP variations over continuous ambiguity blocks, rather than absolute MP values, can be acquired. Both the different tracking of a satellite at different stations and cycle slips can affect the absolute level of the remaining MP series. The consistency of different ambiguity blocks cannot be ensured. This is because the true integer phase ambiguities and hardware delay terms cannot be obtained. Additional biases will be brought in by the alignment of different MP combination time series with a removal of average values. The additional biases will degrade the modeling accuracy of SICB.  
Figure 2 illustrates the MP combination time series of B1 signal with and without cycle slips at 500 consecutive epochs for BDS-2 MEO satellite C12 at station SGG1 on 13 July 2016. We artificially add a cycle slip at the 250 th epoch so that its effects on SICB modeling can be analyzed. For the three continuous ambiguity arcs, the respective float phase ambiguities are calculated. It is clearly seen that there are constant differences between the absolute MP values with and without cycle slips. The MP differences reach \(-0.251\) and \(0.251\) m before and after the cycle slip occurs, respectively. For further analysis, Figure 3 shows the MP combination time series as a function of elevations. The third-order polynomial fitting is conducted for the MP series, and these results are also provided in Figure 3. The MP fitting values with and without cycle slips show significant differences at elevation angles lower than \(50^{\circ}\) and higher than \(70^{\circ}\), which will negatively affect the elevation-dependent modeling of SICB.  
Figure 4 presents the MP combination time series of B1 signal at 800 consecutive epochs for BDS-2 MEO satellite C14 at stations ASCG (7.92\({}^{\circ}\)S, 14.33\({}^{\circ}\)W) and NKLG (0.35\({}^{\circ}\)N, 9.67\({}^{\circ}\)E) on 19 August 2016. The tracking time of C14 is different at the two stations located in different longitude and latitude regions. Figure 5 shows the dependence of the MP combination time series on the elevation angles. The third-order polynomial fitting is also carried out for these MP series. The MP fitting values at stations ASCG and NKLG show differences at both ends of elevations, but the MP differences with a level of several centimeters are much smaller than those caused by the cycle slips shown in Figure 3. The different tracking of a satellite at different stations also has navigate effects on the SICB modeling.  
Figure 3: Dependence of MP combination time series of B1 signal with and without cycle slips on elevations for BDS-2 MEO satellite C12 at station SGG1 on 13 July 2016.  
Figure 2: MP combination time series of B1 signal with and without cycle slips at 500 consecutive epochs for BDS-2 MEO satellite C12 at station SGG1 on 13 July 2016.  
The results shown in Figures 2-5 indicate that both the cycle slips and the different tracking of a satellite at different stations can negatively affect the SICB modeling due to the inconsistency of the absolute level of MP combinations caused by the calculation of float phase ambiguities, which is a severe flaw for the traditional SICB modeling approach. This flaw will degrade the modeling accuracy, and must be carefully repaired.