## 3 Results  
### Simulation Verification  
To verify the feasibility and effectiveness of the proposed method, we simulated a driving environment of straight lane with two lanes, as shown in Figure 5a. The details about the system and vehicle platform setup for the simulations follows the parameters of our own developed autonomous vehicle, as shown in Table 1. The single lane width is 4 m and the longitudinal driving speed is 15 km/h. The driving condition chosen in this work is double lane changing path control, which is a very typical and common condition for autonomous vehicle. In Figure 5b, we can see that the curve of the trajectory is relatively smooth, the yaw angle changes within a small range, the longitudinal travel distance is about 190 m, and the initial and ending yaw angles are basically 0 rad. Figure 6a shows the yaw angle changes detected by vision, GPS, and LIDAR sensing systems and Figure 6b shows the errors between the reference yaw angel and the yaw angles obtained by vision, GPS, and LIDAR sensing systems. Figure 5: Double lane changing control simulation: (**a**) driving scenario; and (**b**) reference trajectory. In Figure 6a, we can see that, within the time intervals of 3-5 and 8-10 s, the sensor failure occurs to the GPS sensing system. In Figure 6b, we can see that the yaw angle errors of vision and LIDAR sensing systems maintained in an extremely small range, which are cause by measurement noises. However, since the peak yaw angle error of GPS sensing system reaches 0.07 rad, considering the maximum yaw angle of vehicle in simulation is about 0.1 rad, the sensor fault of GPS channel cannot be ignored and needs to be detected and isolated. The values of fault detection function based double state chi-square detector and residuals chi-square detector can be seen in Figure 7a,b, respectively. Based on the results shown in Figure 7, we can see that the proposed method can easily detect the fault signal. In Figure 7a, the peak value of fault detection function \(\lambda\) for GPS signal channel by \begin{table}
\begin{tabular}{c c} \hline
**Hardware** & **Property** \\ \hline Laser LIDAR: HESAI Pandar 40 & Lines: 40; Range: 200 m; Angular resolution: 0.1\({}^{\circ}\); Updating: 20 Hz; Accuracy: \(\pm\)2 cm \\ \hline Radar: Delphi ESR & Range: 100 m; Viewing field: \(\pm\)10 deg; Updating: 20 Hz; Accuracy: \(\pm\)5 cm, \(\pm\)0.12 m/s, \(\pm\)0.5\({}^{\circ}\) \\ \hline Navigation system: NovAtel SPAN-CPT & Accuracy: \(\pm\)1 cm, 4.002 m/s, \(\pm\)0.05\({}^{\circ}\) (Pick/Roll), 0.1\({}^{\circ}\) (Azimuth); Updating: 10 Hz \\ \hline Camera: SY8031 & Resolution: 3264 \(\times\) 2448; FPS: 15 Viewing field: 65\({}^{\circ}\) (vertical), 50\({}^{\circ}\) (horizontal) \\ \hline Image processor: NVIDIA JTX 2 & CPU: ARM Cortex-A57 (Quad-core, 2 GHz); GPU: Pascal TM (256 core, 1300 MHz); RAM: LPDDR4 (8 G, 1866 MHz, 58.3 GB/s) \\ \hline Controller: ARK-3520P & CPU: Intel Core i5-6440 EQ (Quad-core, 2.8 GHz); RAM: LPDDR4 (32 G, 2133 MHz, 100 GB/s) \\ \hline \end{tabular}
\end{table} 
Table 1: Configurations of autonomous vehicle. Figure 6: The yaw angle changes in simulation: (**a**) detected yaw angle using different sensors; and (**b**) the yaw angle error. Figure 7: The changes of fault detection function for yaw angles in simulation based on: (**a**) double state chi-square detector; and (**b**) residuals chi-square detector. using double state chi-square detector reaches \(5\times 10^{-6}\) and \(4\times 10^{-6}\) at 3 and 5 s, which is the moment 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 \(2\times 10^{-7}\) and \(5\times 10^{-8}\), respectively.