## 3 Experiment and Analysis
### Analysis of Influence of Multipath Environment on Cycle Slips Detection  
The dual-frequency data of 2000 epoch static observations of PRN38 and PRN40 satellites for BDS-3 MEO and IGSO constellations collected in Experiment 1 are analyzed. The method in reference [38] was used to calculate the multipath effect and its variation between epochs, as shown in Figures 3 and 4.  
According to Figures 3 and 4, in the severe multipath environment, the pseudorange multipath effect of the two frequency points is at the meter level. The change amplitude of the multipath effect is similar for the B1c _and_ B2a frequency, and the maximum values of the multipath effects between the B1c and B2a frequency epoch were C38 (1.202 m and 1.314 m) and C40 (1.234 m and 1.242 m), respectively. According to the above multipath variation, a similar multipath effect is simulated in 500 to 2500 epoch of the Experiment  
Figure 4: The multipath effect of PRN40 satellite: (**a**) multipath effect situation; (**b**) residuals between multipath epochs.  
Figure 3: The multipath effect of PRN38 satellite: (**a**) multipath effect situation; (**b**) residuals between multipath epochs.  
2 data. The cycle slips estimation of the MW combination after simulating the multipath effect is shown in Figure 5.  
Based on the above amount of variation, the cycle slips' estimation of the two frequency points can be set to \(M_{1}=1\) m and \(M_{2}=1\) m, respectively. As shown in Table 1, when the system is seriously affected by the pseudorange multipath, the false detection rate reaches 64% and the missed detection rate reaches 42%. This is because the multipath effect leads to abnormal fluctuations in the pseudorange in the MW combination, the overall narrow-lane combination becomes smaller, and the cycle slips' estimation becomes larger, so the pseudorange multipath effect is misdetected as cycle slips. Especially for the short wavelength of the dual-frequency signal combination, the false detection and missing detection are even more serious.  
Figures 6 and 7 give the cycle slips estimations of the PRN38 and PRN40 satellite observations under the multipath effect using the dual-frequency MW and GF detection models. The MW combination (at 500-2500 epochs) shows a trend term that is clearly affected by the multipath, with the cycle slips' estimations of multiple epochs exceeding 0.4 cycles. The false detection rate is 64%, which is very serious; while on the contrary, the GF combination is not affected by the pseudorange multipath influence and still maintains a good detection capability. The results indicate that the traditional MW detection model fails in a severe multipath environment.  
\begin{table}
\begin{tabular}{c c c c c c} \hline
**Different** & **Detection** & **PRN** & **PF** & **PM** & \(\sigma_{\Delta\text{N}_{\text{gi,wk}}}\)**/Cycles** \\
**Environments** & **Combinations** & & & & \\ \hline No multipath & & C38 & 0.27\% & 0.01\% & 0.2895 \\ environment & & C40 & 0.27\% & 0.01\% & 0.2895 \\ \hline \multirow{3}{*}{
\begin{tabular}{c} Severe multipath \\ environment \\ \end{tabular} } & MW & C38 & 64.83\% & 42.04\% & 1.9042 \\ \cline{2-6}  & & C40 & 64.83\% & 42.04\% & 1.9042 \\ \cline{2-6}  & & C38 & 0.29\% & 0.01\% & 0.2919 \\ \cline{1-1} \cline{2-6}  & & C40 & 0.29\% & 0.01\% & 0.2920 \\ \hline \end{tabular}
\end{table}
Table 1: False detection rate and missed detection rate statistics.  
Figure 5: Simulated cycle slips detection of multipath phenomenon.