## 3 Results
### Experimental Verification
Figure 13: The changes of fault detection function for yaw angles in experiment based on: (**a**) double state chi-square detector; and (**b**) residuals chi-square detector. In Figure 14a, we can see that due to the sensor failure within the time intervals of 5-10 s and 15-50 s the lateral position detected by GPS sensing system is fault signal. In Figure 14b, we can see that the peak lateral position error of GPS sensing system reaches almost 2.5 m, which is extremely large considering the maximum lateral position of vehicle in simulation is about 4 m and width of road lane is 4 m. Therefore, the sensor fault of GPS channel cannot be ignored and needs to be detected and isolated in the experiment. Figure 15 shows the curves of fault detection functions for lateral position in experiment based on chi-square detector. In Figure 15a, we can see that the value of fault detection functions \(\lambda\) for vision and LIDAR sensing systems by using double state chi-square detector remain in the ranges of \(0\sim 5\times 10^{-7}\) and \(0\sim 5\times 10^{-9}\), respectively. However, the peak value of the fault detection functions \(\lambda\) for GPS signal channel reaches \(2\times 10^{-4}\), \(3.8\times 10^{-3}\), \(3.7\times 10^{-3}\), and \(5\times 10^{-4}\) at 5, 10, 15, and 20 s, which correspond with the moments when the fault GPS signal occurs and disappears. In Figure 15b, we can see that there are peaks on the curves of fault detection functions \(\gamma\) for vision and LIDAR signal channels by using residuals chi-square detector, which correspond with the lateral position error curves. It is worth noting that the order of magnitude of fault detection functions \(\gamma\) for vision and LIDAR signal channels are \(10^{-6}\). However, the order of magnitude of fault detection functions \(\gamma\) for GPS signal channels are \(10^{-4}\) within the time intervals of 5-10 and 15-20 s, which means we can easily detect the fault lateral position signals by setting the appropriate threshold. From the above simulation results, we know that directly sending the fault signal to the path tracking controller may seriously affect the driving safety of the autonomous vehicle; therefore, in the experiment, we only compared the performance of FTMPC and FTAMPC, as shown in Figure 16.  
In Figure 16a,b, we can see that the path tracking performances of FTMPC and FTAMPC are obviously different, although both algorithms can control the autonomous vehicle to move along the reference path. During the experiment process, the longitudinal velocity of autonomous vehicle is not a constant. The autonomous vehicle accelerates first and then decelerates; under this circumstance, FTAMPC shows better performance. Figure 16c,d shows that, compared with the tracking results of the lateral position, the tracking performance of yaw angle is relatively poor. This is mainly due to the short longitudinal travel distance and large changes of longitudinal velocity and yaw angle, which make it difficult to accurately yaw angle tracking control. Figure 15: The changes of fault detection function for lateral position in experiment based on: (**a**) double state chi-square detector; and (**b**) residuals chi-square detector.