# Enconv1d Model Based on Pseudolite System for Long-Tunnel Positioning
## 4 Experiment and Result Analysis
### Analysis of Experimental Result
This indicates that, in terms of overall localization performance, the Enconv1d model significantly improves the localization accuracy for all points across the four test paths. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Test Path** & **\# 1** & **\# 2** & **\# 3** & **\# 4** \\ \hline Number of locating points & 13,622 & 10,678 & 11,231 & 10,595 \\ LSTM & 2.27 & 1.54 & 2.84 & 2.19 \\ Conv1d & 2.60 & 2.13 & 3.11 & 2.87 \\ Encoder & 1.80 & 1.30 & 1.80 & 1.73 \\ Enconv1d & 1.19 & 0.75 & 1.44 & 1.21 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The MAE (m) of the localization results for the four models across different test paths. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Test Path** & **\# 1** & **\# 2** & **\# 3** & **\# 4** \\ \hline Number of locating points & 13,622 & 10,678 & 11,231 & 10,595 \\ LSTM & 1.81 & 1.68 & 2.39 & 1.79 \\ Conv1d & 2.13 & 2.20 & 2.61 & 2.52 \\ Encoder & 1.38 & 1.39 & 1.50 & 1.49 \\ Enconv1d & 0.90 & 0.96 & 1.09 & 0.95 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The Mean Distance Error (m) of the localization results for the four models across different test paths. Figure 7d shows the cumulative distribution function (CDF) of the Distance Error calculated using different localization models across the four test paths. The graph shows that the Enconv1d model, represented by the red curve, achieves 80% distance error within 1.36 m. In comparison, the encoder model reaches 80% within 2 m, while both the LSTM and Conv1d models have 80% Distance Errors exceeding 2 m. To further illustrate the effectiveness of the Enconv1d model in reducing outliers and optimizing overall accuracy, we compiled the percentage distribution of distance errors for the four localization models across different test paths, as shown in Table 5.  
In Test path 1, the percentage of localization errors less than 1 m for Enconv1d is 67.54%, and errors greater than 3 m account for only 0.10%. For the encoder model, 29.74% of errors are less than 1 m, while 0.93% exceed 3 m. The Conv1d model shows 26.37% errors less than 1 m and 22.10% greater than 3 m. Meanwhile, the LSTM model achieves 34.94% of errors less than 1 m, with 13.84% exceeding 3 m. In test path 2, the percentage of localization errors less than 1 m for the Enconv1d model is 64.31%, and errors greater than 3 m account for only 0.45%. Moreover, none of the localization points have errors exceeding 4 m. For the encoder model, 42.42% of errors are less than 1 m, while 5.79% exceed 3 m. The Conv1d model shows 26.37% of errors less than 1 m, with 26.63% exceeding 3 m. The LSTM model achieves 42.47% of errors less than 1 m, with 12.42% exceeding 3 m. In test path 3, the percentage of localization errors less than 1 m for the Enconv1d model is 54.49%, and errors greater than 3 m account for only 1.34%. For the encoder model, 40.82% of errors are less than 1 m, while 9.05% exceed 3 m. The Conv1d model shows 28.53% of errors less than 1 m, with with 33.37% exceeding 3 m. The LSTM model achieves 37.61% of errors less than 1 m, with 15.14% exceeding 3 m. In test path 4, the percentage of localization errors less than 1 m for the Enconv1d model is 61.62%, and errors greater than 3 m account for only 0.24%. For the Encoder model, 41.40% of errors are less than 1 m, while 10.19% exceed 3 m. The Conv1d model shows 31.18% of errors less than 1 m, with 32.39% exceeding 3 m. The LSTM model achieves 40.02% of errors less than 1 m, with 12.45% exceeding 3 m. Overall, across the four test paths, the proportion of errors greater than 3 m for the Enconv1d model does not exceed 1.5%, significantly lower than the other three models. Furthermore, the proportion of errors less than 1 m is substantially higher for the Enconv1d model than the others. This  
\begin{table}
\begin{tabular}{c c c c  
demonstrates that the proposed model effectively limits outliers and significantly enhances overall localization accuracy. Figure 8 illustrates the distribution of distance errors for different models across the four test paths.