## 3 Results
### Experimental Verification  
We also conducted a path tracking control experiment using self-developed autonomous vehicle. The details about the sensor system and autonomous vehicle platform setup are shown in Table 1.  
The driving condition is double lane changing. Figure 10(a) shows the autonomous vehicle and the equipped sensing system, including the vision, GPS, and LIDAR sensing systems. The width of lane is about 4 m. Figure 10(b) shows the vehicle trajectory of double lane changing obtained by GPS sensing system with manual driving mode. We use the record yaw angle and lateral position as reference in the following autonomous path tracking process. As shown in Figure 10(b), the trajectory of double lane changing is not perfect; the final yaw angle is not 0 rad and the longitudinal travel distance is about 70 m.  
Figure 11(a) shows the yaw angle changes detected by vision, GPS, and LIDAR sensing systems in the autonomous path tracking process and Figure 11(b) shows the errors between the reference yaw angel and the measured yaw angles. In Figure 11(a), we can see that the total travel time is about 23 s, and, within the time intervals of 5-10 and 15-20 s, the sensor failure occurs to the GPS sensing system. In Figure 11(b), we can see that the yaw angle errors of vision and LIDAR sensing systems are maintained in an extremely small range and the peak of yaw angle error is less than 0.03 rad, which may cause by measurement noises or too few feature points for LIDAR and vision algorithms. However, the peak value of yaw angle  
Figure 11: The experimental scene: (**a**) self-developed autonomous vehicle; and (**b**) trajectory of double lane changing obtained by GPS sensing system. Figure 12: The yaw angle changes in experiment: (**a**) detected yaw angle using different sensors; and (**b**) the yaw angle error. error of GPS sensing system reaches 0.22 rad at 7 s; considering the maximum yaw angle of vehicle in the experiment is about 0.3 rad, the sensor fault of GPS channel cannot be ignored and needs to be detected and isolated. The values of fault detection function for yaw angle in our experiment based on double state chi-square detector and residuals chi-square detector are shown in Figure 13a,b, respectively. Based on the results shown in Figure 13, we can see that the fault signal can be exactly detected by using the proposed method. In Figure 13a, the peak values of fault detection function \(\lambda\) for GPS signal channel by using double state chi-square detector reaches \(2\times 10^{-6}\), \(2\times 10^{-6}\), \(2\times 10^{-5}\), and \(1\times 10^{-6}\) at 5, 10, 15, and 20 s, which are the moments when the yaw angle error of GPS signal reaches its peak. However, the peak values of fault detection function \(\lambda\) for vision and LIDAR sensing system reach no more than \(1\times 10^{-8}\) and \(2\times 10^{-8}\), respectively. In Figure 13b, the value of fault detection function \(\gamma\) for GPS signal channel by using residuals chi-square detector remains in the order of magnitude of \(10^{-6}\), and this value is proportional to the absolute value of the yaw angle error within the time intervals of 5-10 and 15-20 s. However, the order of magnitude of the fault detection function \(\gamma\) for vision and LIDAR sensing systems remain at \(10^{-7}\). Through the above analysis, we obtained similar results as in the simulation process, which means that the fault signals can be detected by our proposed method with setting the appropriate threshold. Figure 14a shows the lateral position changes detected by vision, GPS, and LIDAR sensing systems and Figure 14b shows the errors between the reference lateral position and the lateral position obtained by vision, GPS, and LIDAR sensing systems. Figure 14: The lateral position changes in experiment: (**a**) lateral position detected by using different sensors; and (**b**) the lateral position error.