## 5 Simulation and Discussion
### Split Road Driving Simulation  
In the split road driving scenario, the adhesion coefficient on the left side is set to 0.18 for compacted snow and 0.5 for slippery asphalt on the right side. The reference speed accelerates from 0 km/h to 70 km/h within 10 s, with the optimal slip ratio set to 0.12 on the left side and 0.18 on the right side. The estimation results and errors of the adhesion coefficients on both sides of the split road are shown in Figure 5. Analysis shows that the adhesion coefficients converge to values close to the true values within 1 s of vehicle start-up. Since the right-side adhesion \begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameters** & **Symbol** & **Value (Unil)** \\ \hline Vehicle mass & \(m\) & 1998 kg \\ Distance from center of mass to front axis & \(Lf\) & 1.4 m \\ Distance from center of mass to rear axis & \(Lr\) & 1.85 m \\ Height of the center of mass & \(Hg\) & 0.795 m \\ Wheel track & \(B\) & 1.7 m \\ Effective radius of tire & \(R\) & 0.385 m \\ Moment of inertia about the yaw axis & 1 & 5757 kg - m\({}^{2}\) \\ Wheel inertia & J & 1.5 kg - m\({}^{2}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Basic vehicle parameters. coefficient is smaller, it converges to the true value faster and remains stable around it. The error graph shows that the adaptive improvement of the UKF significantly enhances the estimation accuracy of the adhesion coefficients on both sides and makes them stable. In contrast, the traditional UKF algorithm cannot mitigate the impact of process noise, resulting in large estimation errors that increase as the vehicle progresses. To quantitatively analyze the errors, we use the mean absolute error (MAE) to measure the estimation performance:  
\[MAE=\frac{1}{n}\sum abs(\mu_{est}-\mu_{\text{real}}\,) \tag{52}\]  
The statistical results are shown in Table 2. From the table, it can be seen that the AUKF algorithm significantly outperforms the UKF in estimating adhesion coefficients on split roads, with estimation accuracy improvements of 63% and 84% for the left and right sides, respectively, while maintaining stability. Figure 6 shows the simulation results of the split road scenario. It can be seen that after the vehicle starts, all wheels quickly slip. The right rear wheel, being on the side with relatively better adhesion and having a slightly larger vertical force than the front wheel, experiences a delay in slip time. When the vehicle detects wheel slip, CESMC and DASMC start to intervene to control the slip of each wheel. From the slip ratio curves shown in Figure 6b,c, it can be seen that as the vehicle starts and accelerates, the slip ratio \begin{table}
\begin{tabular}{c c c} \hline \hline
**Estimation Strategy** & **Condition1 (L)** & **Condition1 (R)** \\ \hline UKF & 0.0468 & 0.0437 \\ AUKF & 0.0173 & 0.0068 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Average estimation error on split roads. Figure 5: Simulation estimation results for split road. (**a**) Left-side adhesion coefficient estimation results. (**b**) Right-side adhesion coefficient estimation results. (**c**) Estimation error. under CESMC control exhibits relatively severe overshoot and response delay, with a steady-state time of 3 s and an overshoot of 0.32. Under DASMC control, the slip ratio quickly responds and reaches the desired slip ratio value in less than 1 s. The improved response steady-state time is reduced by 66.6%, and the overshoot is decreased by 0.26. The average overshoot for each wheel control is only about 0.06 above the desired value, and both the left and right wheels fully utilize the road adhesion, significantly improving the control effect. This indicates that the DASMC control algorithm has good robustness and response speed. According to Figure 6d,e, which show the output torque of each wheel, it can be seen that after the vehicle starts to slip, the motor output torque directly reaches the maximum limit. Although the torque under traditional control can also reach a stable effective value, there is noticeable severe chattering.