## 6 Result Analysis
### Simulation Analysis
#### 6.1.2 The Slalom Simulation  
The initial conditions of the vehicle state estimator and the road adhesion coefficient estimator are set the same as those in the double-lane change simulation, and the line type setting of the simulation diagram is also the same as in the double-lane change simulation. To analyze the simulation results: Figure 6a shows the steering wheel angle change curve during the driving process of the vehicle along the slalom path. Similar to the double-lane change simulation, the simulated yaw rate is used as the input of the measurement equation and the output of the state equation at the same time. Therefore, Figure 6b shows that the values estimated via the AGHCKF, CHCKF, and CKF algorithms are very accurate. It can also be seen from the locally enlarged image that the filtering effect of the AGHCKF is the best, and that the CKF has the worst filtering effect; from Figure 6c, we can see that three algorithms can also estimate the lateral velocity. We can further observe the locally enlarged image, at the peaks and valleys of the lateral velocity curve, there are certain errors in the values estimated via GHCKF and CKF, but the error of the GHCKF is smaller than the error of the CKF. This result is consistent with the RMSE values for the lateral \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Estimated Value** & \(\mathbf{AGHCKF}_{\text{RMSE}}\) & \(\mathbf{GHCKF}_{\text{RMSE}}\) & \(\mathbf{CKF}_{\text{RMSE}}\) \\ \hline The longitudinal velocity & 0.0010 & 0.0039 & 0.0216 \\ \hline The lateral velocity & 0.0011 & 0.0034 & 0.0051 \\ \hline The yaw rate & 0.0001 & 0.0003 & 0.0015 \\ \hline The left rear wheel adhesion coefficient (\(\mu_{rl}\) = 0.8) & 0.3373 & 0.3394 & 0.4336 \\ \hline The right rear wheel adhesion coefficient (\(\mu_{rl}\) = 0.8) & 0.3375 & 0.3759 & 0.4414 \\ \hline The left rear wheel adhesion coefficient (\(\mu_{rl}\) = 0.5) & 0.1921 & 0.2218 & 0.2492 \\ \hline The right rear wheel adhesion coefficient (\(\mu_{rl}\) = 0.5) & 0.2010 & 0.2880 & 0.3365 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The RMSE of the double-lane change simulation. Figure 5: The results of the double\(-\)lane change simulation. (**a**) The steering angle; (**b**) the yaw rate; (**c**) the lateral velocity; (**d**) the longitudinal velocity; (**e**) the left rear wheel road adhesion coefficient with a high\(-\)adhesion road surface; (**f**) the right rear wheel road adhesion coefficient with a high\(-\)adhesion road surface; (**g**) the left rear wheel road adhesion coefficient with a low\(-\)adhesion road surface; and (**h**) the left rear wheel road adhesion coefficient with a low\(-\)adhesion road surface. velocity in Table 2. According to Figure 6d, both the AGHCKF and GHCKF algorithms undergo a process of divergence before stabilization when estimating the longitudinal velocity. The maximum error of the estimated value of the AGHCKF algorithm is about 0.06 m/s, while that of the CHCKF algorithm is about 0.08 m/s, and the RMSE value of the AGHCKF is smaller than the RMSE value of the GHCKF, meaning that the AGHCKF algorithm is superior to the CHCKF algorithm in terms of the estimation accuracy and filtering effect. The RMSE value of the CKF is smaller than the GHCKF, mainly because the CKF algorithm in the figure has been diverging, passing through the simulation curve, with many unstable approach points, leading to the CKF's estimation of the longitudinal velocity being unreliable. Figure 6: The results of the slalom simulation on a joint road. (**a**) The steering angle; (**b**) the yaw rate; (**c**) the lateral velocity; (**d**) the longitudinal velocity; (**e**) the left rear wheel adhesion coefficient at low speed; (**f**) the right rear wheel adhesion coefficient at low speed; (**g**) the left rear wheel adhesion coefficient at high speed; and (**h**) the right rear wheel adhesion coefficient at high speed. The AGHCKF and the GHCKF can handle high-order nonlinear characteristics and uncertainties in system dynamics, thereby achieving a higher filtering accuracy.