## 3 Combined Positioning of Tunnel Vehicles Constrained by Lane Lines and Lateral Distance  
1. Determine the starting point of the mileage constraint. Before entering the tunnel, according to the GNSS Real-Time Kinematic (RTK) positioning results of the satellite, the corresponding lane line points are geometrically matched in the vertical direction and are recorded as the starting point of the mileage constraint.
2. Calculate accumulated vehicle mileage. According to the wheel speedometer, the cumulative calculation of vehicle mileage is accumulated by the encoder pulse count of the cumulative mileage meter. Assuming that the cumulative number of pulses of the odometer at a certain time is \(n\), the total cumulative mileage at this time is as follows: \[S=n\times l\times(1+\gamma)\] (10)  
Figure 4: Distance scheme for special situations.  
where \(l\) denotes the circumference of the wheel (prior value, unit: m), and \(\gamma\) represents the perimeter error coefficient in the process of vehicle travel, which is estimated via real-time joint solution calculation with GNSS RTK/INS.
3. Calculate the distance between the vehicle and the lane line. In the tunnel, assuming that the distance between the lane line and the tunnel wall remains unchanged (there will be a small change in reality), this is \(\Delta d\), as shown in Figure 5. The distance between the vehicle and the lane line can be obtained as follows: \[\widetilde{d}=d-\Delta d\] (11) (4) Determine the matching points. As shown in Figure 5, the method of matching the corresponding points of lane lines according to the total mileage \(S\) is as follows: \[\left\{\begin{aligned} p1=S/b+p_{0}\\ p2=S/b+p_{0}+1\end{aligned}\right.\] (12) where \(p1\) indicates the previous recent spot number of the match and \(p2\) indicates the nearest point of the latter match; \(b\) indicates the distance between lane line points (the value in this paper is fixed at 1 m) and \(p_{0}\) indicates the start dot number.
5. Calculate the coordinates of vertical points. According to the principle of distance division, the coordinates of vertical point \(pv\) can be obtained as follows: \[\left\{\begin{aligned} x_{pv}=x_{p1}+\beta\cdot\left(x_{p2}-x_{p1} \right)\\ y_{pv}=y_{p1}+\beta\cdot\left(y_{p2}-y_{p1}\right)\end{aligned}\right.\] (13) where \(\beta=S-floor(S),floor(\cdot)\) indicates the hole down.
6. According to the lateral distance of the vehicle from the lane line and the azimuth of the point tangent line, the coordinates of the vehicle point \(v\) (\(x_{v},y_{v}\)) are obtained, as shown in Figure 6 and Formula (14). \[\left\{\begin{aligned} x_{v}=x_{pv}-\widetilde{d}\cdot\sin(360- \alpha)\\ y_{v}=y_{pv}-\widetilde{d}\cdot\cos(360-\alpha)\end{aligned}\right.\] (14)  
Figure 5: Nearest lane lines’ matching points.  
According to the above mileage matching and lane line constraint positioning method, a higher lateral positioning accuracy can be obtained. However, in the longitudinal direction, due to odometer calibration errors, it is easy to produce mileage accumulation errors when driving for a long time, so in long-distance applications, it is necessary to fully consider the impact of odometer calibration errors. Therefore, this paper proposes a potential positioning for further location combinations of mileage matching positioning results and INS/OD. In other words, the above positioning results are further integrated with the INS/OD combination, and the mileage matching positioning results are used to correct and feedback the INS zero bias errors and odometer scale errors. The odometer calibration error feedback calculated by the INS/OD combination corrects the matching positions of the odometer and lane line, and realizes the mutual correction and complementary advantages of sensors and different positioning means.