## 6 Result Analysis  
### Simulation Analysis  
#### 6.1.1 The Double-Lane Change Simulation  
The sampling time interval is set to 0.005 s. The initial conditions of the vehicle state estimator are set as follows: the error covariance matrix \(\mathbf{P}_{\mathrm{c}}\) = 0.01 \(\times\) eye(3); process noise covariance matrix \(\mathbf{Q}_{\mathrm{c}}\) = 0.1 \(\times\) eye(3); and the measurement noise covariance matrix \(\mathbf{R}_{\mathrm{c}}\) = 0.1 \(\times\) eye(3).  
The initial conditions of the road adhesion coefficient estimator are set as follows: the error covariance matrix \(\mathbf{P}_{\mathrm{p}}\) = 0.01 \(\times\) eye(4); process noise variance co-matrix \(\mathbf{Q}_{\mathrm{p}}\) = 0.01 \(\times\) eye(4); and the measurement noise covariance matrix \(\mathbf{R}_{\mathrm{p}}\) = 0.1 \(\times\) eye(3). In the simulation diagram, the blue line represents the simulated value, the red line represents the value estimated via GHCKF, the green line represents the value estimated via AGHCKF, and the purple line represents the value estimated via CKF.  
Figure 4: The experiment conditions. (**a**) The new asphalt pavement for the high-speed double-lane change experiment; and (**b**) the asphalt—gravel joint road for the low-speed slalom experiment.  
Figure 3: The experiment principle and equipment.  
To analyze the simulation results: Figure 5a shows the steering wheel angle change curve during the driving process of the vehicle along the double-lane change path. As the yaw rate is both the input of the measurement equation and the output of the state equation, the CKF, GHCKF, and AGHCKF algorithms can accurately track the measurement signal and estimate the yaw rate; however, in terms of the filtering effect and accuracy, as shown in Figure 5b, and the RMSE of the yaw rate, as shown in Table 1, the AGHCKF is better than the GHCKF, and the GHCKF is better than the CKF. As shown in Figure 5c, the value estimated via AGHCKF can accurately track the lateral velocity simulation value, and the minimum RMSE value in the AGHCKF indicates the highest accuracy. However, in comparison with the simulation values, there are some errors in the values estimated via the GHCKF and CKF algorithms, especially at the positions of peaks and valleys. Further comparing the RMSE values of the two algorithms, the GHCKF is more accurate in estimating the lateral velocity than the CKF; as shown in Figure 5d, obviously, the AGHCKF algorithm is the most accurate for estimating the longitudinal velocity, while the GHCKF's estimated value can differ from the simulated value by up to 0.005 m/s, while CKF's estimated value can differ from the simulated value by up to 0.025 m/s; the CKF has the worst accuracy, as also confirmed via the RMSE value. In terms of filtering, the CKF is also the worst algorithm.  
Figure 5: _Cont._  
Compared with the simulation results for the road adhesion coefficient, according to Figure 5e-h, the trend of simulation results is consistent for both high-and low-road adhesion coefficients. The response time of AGHCKF in the figure is about 2 s, the response time of GHCKF is 3-4 s, and the response time of CKF is about 6-8 s. The curve of AGHCKF is smoother than that of GHCKF, and the curve of GHCKF is smoother than that of CKF. The RMSE values are shown in Table 1, \(\text{AGHCKF}_{\text{RMSE}}<\text{GHCKF}_{\text{RMSE}}<\text{CKF}_{\text{RMSE}}\). That is, the AGHCKF has the fastest response, the best filtering effect, and the highest accuracy, followed by the GHCKF, and the CKF shows the worst performance in the three aspects.