## 5 Experiment
### Experimental Verification and Analysis
#### 5.2.2 Continuous Interruption Test  
In urban environments, vehicles passing through tunnels often face continuous interruptions of GNSS signals, posing significant challenges to high-precision navigation. To evaluate the performance of the proposed algorithm in such continuously interrupted environments, we consider two types of road sections: continuously interrupted curved road sections and continuously interrupted long straight road sections. The continuously interrupted curved road section is 3.06 km long with a duration of 400 s (0-400 s), including a curved tunnel section of 1.5 km with continuous interruptions lasting 144 s. The continuously interrupted long straight road section is 3.12 km long with a duration of 400 s (400-800 s), including a straight tunnel section of 1.37 km with continuous interruptions lasting 108 s. Interruption times are detailed in Table 4.  
From the solution trajectories of the three algorithms shown in Figure 12, in cases of continuous GNSS interruptions, the trajectory of FGO gradually deviates from the reference trajectory, and this deviation increases over time. According to the eastward error curve in Figure 13 and the northward error curve in Figure 14, we can clearly see that the error of FGO is significant. Although the errors of LSTM-FGO and CNN-GRU-FGO also increase, they are significantly smaller compared to FGO. This significant reduction in error is mainly attributed to the LSTM-FGO and CNN-GRU-FGO algorithms' ability to more effectively utilize past data to predict GNSS positions, especially in the absence of real-time GNSS data, ensuring the robustness of the integrated navigation. \begin{table}
\begin{tabular}{c c c c c} \hline
**Start Time (s)** & **Interruption Duration (s)** & **Start Time (s)** & **Interruption Duration (s)** & **Start Time (s)** & **Interruption Duration (s)** \\ \hline
44 & 144 & 432 & 6 & 789 & 4 \\
285 & 4 & 469 & 5 & & \\
310 & 8 & 534 & 108 & & \\ \hline \end{tabular}
\end{table} 
Table 4: GNSS interruption time statistics for Section 2. \begin{table}
\begin{tabular}{c c c c c} \hline
**Section 1** & **Algorithm** & **Orientation** & **RMSE (m)** & **Maximum Error (m)** \\ \hline \multirow{4}{*}{winding road} & FGO & east & 3.06 & 14.91 \\  & & north & 3.54 & 13.19 \\ \cline{2-5}  & LSTM-FGO & east & 0.62 & 3.41 \\  & & north & 0.90 & 4.48 \\ \cline{2-5}  & CNN-GRU-FGO & east & 0.27 & 1.81 \\  & & north & 0.40 & 1.92 \\ \hline \multirow{4}{*}{long straight road} & FGO & east & 0.38 & 0.99 \\  & & north & 1.35 & 3.67 \\ \cline{2-5}  & LSTM-FGO & east & 0.26 & 0.85 \\  & & north & 0.19 & 0.80 \\ \cline{2-5}  & CNN-GRU-FGO & east & 0.05 & 0.19 \\  & & north & 0.12 & 0.56 \\ \hline \multirow{4}{*}{all road} & FGO & east & 2.34 & 14.91 \\  & & north & 2.84 & 13.19 \\ \cline{1-1}  & LSTM-FGO & east & 0.50 & 3.41 \\ \cline{1-1}  & & north & 0.70 & 4.48 \\ \cline{1-1} \cline{2-5}  & CNN-GRU-FGO & east & 0.21 & 1.81 \\ \cline{1-1}  & & north & 0.31 & 1.92 \\ \hline \end{tabular}
\end{table} 
Table 3: Position error statistics for Section 1. Figure 14: Section 2 north error. Figure 12: Continuously interrupted section solution trajectories. Figure 13: Section 2 east error. In environments with continuous GNSS interruptions, according to the error statistics in Table 5, there is a significant difference in the precision performance of the three algorithms in handling positioning issues. Specifically, the CNN-GRU-FGO and LSTM-FGO algorithms show a substantial improvement in accuracy compared to the traditional FGO method. The eastward and northward RMSEs of FGO are as high as 4.16 m and 36.55 m, respectively, demonstrating the severe inadequacy of the traditional factor graph algorithm in positioning accuracy in complex environments with continuous GNSS interruptions.