## 3 Experiment and Discussion
### Experiment of the Corrected Model  
During driving, due to the unbalanced load, turning, road bump, and other factors, a vehicle does not move in a stable condition. In this study, the inclination angle has great influence on the lateral distance recognition. By constructing a vehicle dynamics correction model, the relationship between the inclination angle and the recognition distance error that is shown in Equation (23) is obtained. Therefore, only by measuring the inclination angle of the vehicle can the recognition error that is caused by the inclination angle in real time be corrected.  
The experiment was carried out in Chongqing Intelligent Vehicle Integrated System Test Area (i-VISTA) and part of time series were selected to analyze the method efficiency. The inclination angle of the vehicle was obtained by a gyroscope and the noise that was subjected to normal distribution was filtered out by Gaussian [47; 48]. It is defined that the vehicle's inclination angle is 0 at equilibrium, and the positive was to the left and the negative was to the right. After the completion of the test, the sequence of inclination angle and recognition result is obtained. To evaluate the validity of the dynamic correction model, a sequence in the test process was selected for analysis and the ground truth was manually labelled by the time-slice method. As shown in Figure 12, the range of the inclination angle is generally small, fluctuating in the interval \([-4,4]\).  
The result of recognition by LatDisLanes with a high recognition accuracy was consistent with the ground truth, and the average errors on the left and right sides were 0.871 and 0.865 cm, respectively. As shown in Figure 12(a),c, in the vicinity of the 6000 th, 8600 th, and 9400 th frames, the inclination angle was greater than \(3^{\circ}\), which caused a big error. After the error was rectified by the dynamic correction model, the result was closer to the ground truth, as shown in Figure 12(b),d. Meanwhile, the average errors on the left and right sides decreased to 0.791 and 0.765 cm.  
Figure 11: The data set classified within certain error bounds \(|\,e_{\mathrm{i}}-t_{\mathrm{i}}\,|<k\) with \(k\in[0,\dots,5]\). The image row containing the lane marking can be predicted in 97.26% within a precision of 1 pixel, and in 99.94% of the cases with 5-pixel precision in (**a**). (**b**) shows the evaluation result of \(e_{\mathrm{i}}-t_{\mathrm{i}}\) in test images.  
Figure 12: Inclination angle of vehicle.  
Figure 13: The red line is the ground truth. The black in (**a,b**) is the output of DisLanes, wherein the black line away from the red that means larger error in the circle. The black line fluctuates in a small range compared to the red after the correct model in (**c,d**).  
However, the model was based on machine vision and was highly sensitive to light brightness. In the nighttime situation, since the illuminating light was located in front of the vehicle, the side light was extremely weak. It was difficult for the model to detect accurately without supplementary light source. In order to test the performance of the system at night, we have added the test in the circular highway at night with the conditions of streetlights, no streetlights, and a lateral supplementary light. The average error was still as the criteria to evaluate the performance of the model. The test results are shown in Table 4. Obviously, the detection result was better when there is an auxiliary light source, which was basically consistent with the result in the daytime. However, when there was only the street light, the average error fell to 4.296 cm. If there is no street light, then the average error drops to 53.472 cm, which made the detection meaningless. Therefore, in order to ensure the accuracy of the model, a lateral supplementary light source is necessary.