## 5 Case Study of Combined Positioning in Tunnels
### Comparison of Three Positioning Methods  
Figure 7 shows the positioning trajectories of three positioning methods in the tunnel. The green points represent the GNSS/INS combined positioning results, the yellow points represent the GNSS/INS/OD combined positioning results, the red points represent the GNSS/INS/OD combined positioning results constrained by lateral distance and lane lines, and the blue points represent the actual lane lines. From the figure, it can be seen that the GNSS/INS combination deviates the most from the lane lines, with the largest positioning error. The GNSS/INS/OD combination follows; although it shows significant improvements compared to the GNSS/INS combination, the positioning deviation is still considerable over long distances. The GNSS/INS/OD combination with lateral distance lane line constraints provides the best positioning results.  
Due to the moving status of vehicles in the tunnel and the lack of means for high-precision dynamic positioning assessment on the roadside, it is difficult to quantitatively evaluate the absolute positioning accuracy in the tunnel. Therefore, in this study, in the open area outside the tunnel, the positioning data were compared with the RTK positioning  
Figure 7: Comparison of the positioning trajectories of three positioning methods in a tunnel.  
results obtained at the same time as the first fixed solution to calculate the positioning accuracy when the vehicle exits the tunnel. Figures 8-10 show the first positioning results outside the tunnel in the opposite direction. The yellow points represent the first fixed RTK results outside the tunnel, which serve as a reference due to the centimeter-level accuracy of RTK's fixed solutions; the red points represent the positioning points that are extended from the tunnel positioning method (excluding the GNSS signals received when exiting the tunnel). The distances between corresponding points (at the same time) in the figures represent the errors between the tunnel positioning points and the RTK reference points. Table 2 provides the corresponding error statistics for two tunnel driving scenarios. It can be seen from the table that in the two sets of experiments, the positioning errors of GNSS/INS and GNSS/INS/OD combinations at the RTK fixed points outside the tunnel are over 100 m, indicating that relying solely on INS, odometers, and other dead reckoning sensors in severe GNSS-denied environments in long tunnels makes it difficult to maintain high-precision positioning and navigation capabilities. The GNSS/INS/OD combination with lateral distance and lane markings constraints provides positioning results that are closest to the RTK results, with a horizontal positioning accuracy between 1.2 m and 1.5 m.  
Figure 8: Comparison of GNSS/INS combination results with the first fixed RTK point positioning after exiting the tunnel (reverse 1, yellow circle represents RTK position and red circle represents GNSS/INS position).  
Figure 9: Comparison of GNSS/INS/OD combined results with the first fixed RTK point positioning after exiting the tunnel (reverse 1, yellow circle represents RTK position and red circle represents GNSS/INS/OD position).