## 6 Result Analysis
### Simulation Analysis
#### 6.1.2 The Slalom Simulation
Even so, it is still affected to some extent by the applied Gaussian white noise signal, so there is a certain error in the AGHCKF and the GHCKF curves in Figure 6d. The CKF is relatively weak in handling errors and noise in a nonlinear vehicle dynamics model, resulting in the accumulation and divergence of estimation errors when estimating the longitudinal velocity. When driving at low speeds on the slalom line, the estimation effect of the road adhesion coefficient on the left rear wheel road surface is similar to that of the double-lane change simulation. The response time of AGHCKF in the figure is about 5 s, the response time of GHCKF is 6 s, and the response time of CKF is about 7 s. The curve of the AGHCKF is smoother than that of the CKF. The RMSE values are shown in Table 2, \(\text{AGHCKF}_{\text{RMSE}}<\text{GHCKF}_{\text{RMSE}}<\text{CKF}_{\text{RMSE}}\). So the AGHCKF has the best effect, the GHCKF takes the second place, and the CKF has the worst effect, as shown in Figure 6e,f and Table 2. It can also be seen that the estimated road adhesion coefficient is poor at around 0 to 6 s from the beginning. This is because the vehicle for Figure 6e,f is set to low speed, and the vehicle is in a straight and uniform state around 0 to 3 s. The state variables and measurements are constant, and the state equation and measurement equation of the estimator have not yet started to operate. Effective data are input around 3 s for operation, and convergence begins at 6 s to obtain an effective estimate of the road adhesion coefficient. On the other hand, the road state estimator indirectly uses the estimated values of the vehicle state estimator, and the estimation of road adhesion coefficient lags behind the estimation of the vehicle state; at the same time, the vehicle model and Magic Formula established have inherent errors, and the Duggoff tire model used for estimating the road adhesion coefficient also has errors, which accumulate and cause fluctuations in road adhesion coefficient estimation. In order to improve this problem, on the one hand, it is necessary to improve the mathematical models of the vehicle and tires, modify the structure, parameters, or initial conditions of the models to better match the actual system, and on the other hand, fully optimize the estimator structure and conduct multiple simulations to find the optimal control parameters and improve controller performance. Figure 6g,h show the estimated results for the road adhesion coefficient during high-speed driving. The GHCKF and CKF have good estimates of the high-adhesion coefficient on the left rear wheel side, but cannot estimate the road adhesion coefficient on low-adhesion sections. On the right rear wheel side, it is possible to estimate the adhesion coefficient of high- and low-adhesion road surfaces within a certain range, and the filtering effect of the GHCKF is superior to that of the CKF. The AGHCKF algorithm can estimate the adhesion coefficient of the left and right rear wheel road surfaces within a certain accuracy range, the filtering effect is the best, and the estimation accuracy is the highest, as shown in Table 2. The difficulty in estimating the low adhesion road surface on the left rear wheel side via the GHCKF and CKF is mainly due to severe vehicle slip during high-speed slalom