## 5 Conclusions  
In this paper, we adopt MCSRCKF, which has solved the driving state estimation problems for distributed nonlinear vehicles in a non-Gaussian noise environment. After comparing and analyzing the results of simulated experiments in the Double-lane change condition and serpentine condition at high speed, it is demonstrated that this algorithm is accurate in estimating the driving state of the nonlinear vehicle system under a heavy-tailed non-Gaussian noise influence. Firstly, an electric vehicle model with distributed driving is built by combining a 7-DOF vehicle dynamic model, an electric motor model, and the Dugoff tire model. Secondly, the vehicle's longitudinal speed, lateral speed, yaw rate, and four-wheel rotation speed are accurately observed on the basis of the MCSRCKF algorithm, and the estimated values at each moment are fed back to the vehicle model for the next moment of calculation, forming a closed-loop system through mutual exchange of information and mutual correction. Analyzing the experimental data obtained from the simulation, from the values of RMSE and MAE, it can be clearly seen that the estimation error of MCSRCKF has been reduced significantly compared to both CKF and SCKF, and from the simulation curve, it can be seen that the estimation result of MCSRCKF at the peak of the curve is more closely fit to the real value, especially in the limiting conditions, because MCC reduces the influence of the outliers in the non-Gaussian noise environment on the estimation accuracy. We can sufficiently confirm that the MCSRCKF performs well in noise immunity, can better estimate the longitudinal, lateral, and yaw, can maintain small fluctuations in extreme working conditions, has strong robustness, and ultimately converges to its value by providing real-time and accurate information of key vehicle  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Index** & **Parameters** & **CKF** & **SCKF** & **MCSCKF** \\ \hline \multirow{3}{*}{MAE} & \(v_{x}\)(m/s) & 1.2343 & 2.4148 & 0.0605 \\  & \(v_{y}\)(m/s) & 1.0560 & 2.0644 & 0.4690 \\  & \(r\)(rad/s) & 0.0689 & 0.1121 & 0.0129 \\ \hline \multirow{3}{*}{RMSE} & \(v_{x}\)(m/s) & 1.7582 & 3.3601 & 0.0740 \\  & \(v_{y}\)(m/s) & 1.4914 & 3.3601 & 0.5911 \\ \cline{1-1}  & \(r\)(rad/s) & 0.1114 & 0.1524 & 0.0209 \\ \hline \hline \end{tabular}
\end{table}
Table 4: MAE and RMSE of various algorithms under the serpentine condition.  
parameters for the control system, which provides high applied value for the development of intelligent vehicles.  
In the subsequent research, we will attempt to apply the method to real vehicle tests and consider more dimensions of vehicle motion to obtain further improvements in estimation accuracy and real-time performance.  
Conceptualization, P.G. and C.Z.; methodology, C.Z.; software, T.Z. and L.G.; validation, P.G. and Q.X.; resources, P.G.; writing--original draft preparation, C.Z. and Q.X.; writing--review and editing, P.G.; funding acquisition, P.G. and L.G. All authors have read and agreed to the published version of the manuscript.  
This research was supported by the National Natural Science Foundation of China, grant numbers 52175078 and 51975089, and the Fundamental Research Funds for the Central Universities, grant number DUT22 QN248, and the National Key Research and Development Program of China, grant number 2022 YF82602305.  
Not applicable.  
The authors declare no conflict of interest.