## 3 Experiment and Analysis
### Analysis of AMG Combined Cycle Slip Detection Results  
In order to test the detection capability of the AMG combination for cycle slips in a severe multipath environment, both frequencies of the MEO C38 and IGSO C40 satellites of different constellations were added with 1-8 cycles of scattered small cycle slips in a severe multipath environment. The added cycle slips combinations are shown in Table 2.  
Figure 8: Pseudorange residuals predicted by AR model: (**a**) C38 P1 predicted residual; (**b**) C38 P5 predicted residual; (**c**) C40 P1 predicted residual; (**d**) C40 P5 predicted residual. Figure 9: PRN38 and PRN40 cycle slips estimated value based on AR model assistance. Figure 10 shows the cycle slips' detection result of the traditional MW + GF combination. Figure 11 shows the cycle slips detection result of the AMG model, and the comparison of the completeness detection is shown in Figure 12. The repair results are shown in Table 3. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Epoch** & **700** & **900** & **1300** & **1700** & **2000** & **2300** \\ \hline cycle slips & \(1\) & \(2\) & \(8\) & \(1\) & \(-1\) & \(5\) \\  & \(1\) & \(4\) & \(6\) & \(-2\) & \(1\) & \(3\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Size and position of simulated cycle slips. Figure 10: Cycle slip detection results of PRN38 and PRN40 MW + GF combinations in a multipath environment: (**a**) PRN38 cycle slips estimated value; (**b**) PRN40 cycle slips estimated value. Figure 11: Cycle slips detection results of PRN38, PRN40 AMG combinations in a multipath environment: (**a**) PRN38 cycle slips estimated value; (**b**) PRN40 cycle slips estimated value. As shown in Figure 11, the results indicate that, on the one hand, for the carrier phase observations at B1c and B2a with the same period of small cycle slips (e.g., at 700 epochs), the MW combination does not detect the cycle slips successfully, but the GF method clearly detects them, because the MW combination cannot detect the same cycle slips at the same epoch for both frequencies. On the other hand, for the cycle slips (8,6) of the frequencies B1c and B2a at 1300 epoch, the GF combination cannot detect accurately, because the cycle slips' ratio in the carrier phase observation values of the B1C and B2A frequencies is very close to the ratio of the two frequencies. In a weak multipath environment, the GF + MW model can detect most types of cycle slips, but in a severe multipath environment, if there are special cycle scale situations (such as: 1300 epoch), the GF combination is unable to detect cycle slips due to the existence of some kind of detection blind spots. Furthermore, the MW combination can detect if cycle slips occurred, but the result is not accurate. This is because the multipath effect seriously affects the pseudorange accuracy and leads to the failure of the MW + GF model. At this time, the MW + GF combination fails in the severe multipath environment. In contrast, the AMG combination is not affected by the pseudorange multipath, and cycle slips can still be accurately detected and successfully  
Figure 12: Comparison of cycle slips completeness detection in multipath environment.