## 4 Simulation Results
### Analysis of Positioning Errors for Static Points  
According to Reference [31], the RMSE for the pseudorange observation of the GPS L1 signal on the Redmi K60 Ultra phone (Xiaomi, Nanjing, China) is within 0.94 m, and for the BDS B1I signal, it is within 0.78 m. At this level of pseudorange observation error, 100 times independent simulation experiments were conducted for four positions in the tunnel coordinate system: (20,2), (20,8), (40,2), and (40,8). The static point positioning results before and after VEM correction are shown in Figures 12 and 13, respectively. The figures show that the STD of the positioning results is similar before and after VEM correction, but there is a significant error between the uncorrected positioning results and the true positions. Figure 11: HDOP variation with radiation angle in dual V-shaped and combined LCX cable layouts. Figures 14 and 15 demonstrate that the VEM effectively corrects the observation errors in the GNSS signal transmission distance within the LCX as measured by the receiver. To study the impact of pseudorange observation errors on the positioning results, 100 times independent static point positioning simulations were conducted at the tunnel coordinate position (25 m, 5 m) under pseudorange observation errors of approximately 1 m, 3 m, 5 m, and 7 m. Figures 16-19 show the static point positioning results under different levels of pseudorange observation errors. This figure indicates that as the pseudorange observation error increases, the STD of the positioning results gradually increases, but the overall distribution of the positioning results remains within the normal range. Table 1 presents the maximum, minimum, mean, and STD of the deviations in the static point positioning results. The table shows that as the noise variance increases, the positioning errors in both the horizontal and vertical directions gradually increase. However, the overall positioning error remains less than 10 m, achieving meter-level accuracy. Figure 19: Static point positioning map (pseudorange observation error approximately 73 m). \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Pseudorange** & **Error Type** & **Max Error (m)** & **Min Error (m)** & **Mean Error (m)** & **STD (m)** \\ \hline BDS 0.9722 & X & 1.0929 & 0.0184 & 0.4480 & 0.3505 \\ GPS 1.0795 & Y & 1.4819 & 0.0182 & 0.5045 & 0.3837 \\ GLO 0.6484 & Total & 2.0168 & 0.0371 & 0.7407 & 0.4192 \\ \hline BDS 3.2459 & X & 2.4078 & 0.0151 & 0.6759 & 0.5633 \\ GPS 3.2108 & Y & 2.9131 & 0.0091 & 0.8029 & 0.6357 \\ GLO 3.1798 & Total & 3.5101 & 0.1577 & 1.1428 & 0.7175 \\ \hline BDS 5.0781 & X & 3.0942 & 0.0151 & 0.8653 & 0.7515 \\ GPS 5.4541 & Y & 5.0393 & 0.0091 & 1.0308 & 0.8855 \\ GLO 4.7849 & Total & 5.0552 & 0.1577 & 1.4647 & 1.0057 \\ \hline BDS 6.7853 & X & 4.0102 & 0.0151 & 0.9749 & 0.8346 \\ GPS 6.2355 & Y & 5.0393 & 0.0047 & 1.0851 & 0.9648 \\ GLO 7.9101 & Total & 5.0552 & 0.1577 & 1.6142 & 1.0700 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Error statistics of static point positioning. Figure 18: Static point positioning map (pseudorange observation error approximately 5 m). Figures 20-23 show the CDF of positioning errors under different pseudorange observation error levels.