## 4 Results and Discussion
### Comparative Performance Analysis  
Using the IMU and OD data collected by the train's onboard equipment as well as the digital track map, we validated the proposed SINS/OD algorithm assisted by digital track map matching. First, the combined SINS/OD navigation algorithm presented in Section 3 was utilized for OD-assisted inertial navigation solving, because the initial attitude needed to be determined using the initial alignment algorithm prior to the combined navigation. The initial alignment was not the focus in this paper, so the initial attitude solution provided by the truth value was used. Because the train was strictly constrained on the track, when assisted by the forward speed of the OD, we simultaneously made a nonholonomic constraint (NHC): the eastward and upward speeds of the train were set to zero in order to obtain more accurate solving results. Secondly, because the attitudes used in the SINS/OD combination process were derived from the inertial guidance solving results, the SINS attitudes were slowly dispersed due to the lack of absolute position correction, and in addition, due to wheel diameter's wear and tear, thermal expansion and contraction, etc., there were errors in the OD scale factor that resulted in the dispersion of the navigation position of the SINS/OD combination navigation results with the increase in navigation mileage and navigation time. Therefore, the SINS/OD combination navigation results were corrected by using the digital track map-matching algorithm mentioned in Section 3. The results of the OD-assisted inertial guidance trajectory and the ground truth superimposed results are shown in Figure 11. As can be seen from the figure, after a big sharp curve, the SINS/OD-solved trajectories ceased to be overlapped and then began to slowly diverge at the end of the navigation 80 km, and after 59 min, the error in the east direction reached 5998.65 m, and the error in the north direction reached 3407.05 m, and the detailed results are shown in Table 2. \begin{table}
\begin{tabular}{c c c c c} \hline \multirow{2}{*}{**Distance (km)**} & **SINS/OD** & **SINS/OD** & **SINS/OD/MM** & **SINS/OD/MM** \\  & **North Position Error (m)** & **East Position Error (m)** & **North Position Error (m)** & **East Position Error (m)** \\ \hline
5 & 86.55 & 13.55 & \(-\)3.22 & 0.91 \\
10 & 301.15 & 18.15 & \(-\)5.95 & 0.05 \\
15 & 411.25 & 452.40 & \(-\)5.42 & 5.48 \\
20 & 663.70 & 673.50 & \(-\)6.65 & 5.46 \\
25 & 976.05 & 921.65 & \(-\)6.66 & 5.18 \\
30 & 1366.75 & 1152.50 & \(-\)7.20 & 1.61 \\
35 & 1833.05 & 1249.45 & \(-\)5.72 & 2.93 \\
40 & 2226.80 & 1554.95 & \(-\)0.13 & 3.01 \\
45 & 2310.40 & 2390.90 & 0.15 & \(-\)0.63 \\
50 & 2624.35 & 2811.90 & 5.07 & \(-\)2.64 \\
55 & 2826.25 & 3404.05 & 0.67 & \(-\)10.72 \\
60 & 2899.32 & 4120.80 & 5.34 & \(-\)13.35 \\
65 & 3110.30 & 4696.25 & 6.91 & \(-\)17.24 \\
70 & 3215.46 & 4948.55 & \(-\)3.22 & 0.918 \\
75 & 3326.50 & 5282.60 & 8.39 & \(-\)21.24 \\
80 & 3407.05 & 5998.65 & 3.13 & \(-\)23.82 \\ \hline \end{tabular}
\end{table} 
Table 2: Statistical results of SINS/DO solving and SINS/OD/MM solving for onboard train tests. The latitude and longitude of the SINS/OD combination and the latitude and longitude provided by the ground truth were superimposed as shown in Figure 12, and the result of plotting the east-to-north position errors of the combined navigation is shown in Figure 13, which shows that the train's position error is constantly dispersing without positional assistance and the dispersion speed is becoming faster and faster.