## 5 Conclusions  
In this paper, we propose an interacting multiple model based on square root cubature Kalman filter algorithm and apply the algorithm to distributed drive electric vehicle observation. Experimental validation of the algorithm was carried out using double-lane change condition with a sinusoidal condition and sinusoidal steering combined with a braking condition, which can perform accurate estimation of vehicle state based on less on-board sensor information and can effectively resist the effect of noise. The  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Simulation Condition** & **Parameters** & **UKF** & **SCKF** & **IMM-SCKF** \\ \hline \multirow{3}{*}{Double-lane change condition} & Yaw rate & 0.0137 & 0.0088 & 0.0007 \\  & Longitudinal & 0.0792 & 0.0622 & 0.0276 \\  & velocity & 0.0303 & 0.0298 & 0.0107 \\  & Yaw rate & 0.0039 & 0.0005 & 0.0003 \\ \multirow{3}{*}{Sinusoidal steering condition} & Longitudinal & \multirow{3}{*}{0.0052} & \multirow{3}{*}{0.0007} & \multirow{3}{*}{0.0002} \\  & velocity & & & \\  & Lateral velocity & 0.0117 & 0.0099 & 0.0041 \\ \multirow{3}{*}{Sinusoidal steering combined with braking condition} & Yaw rate & 0.0012 & 0.0011 & 0.0007 \\  & Longitudinal & \multirow{3}{*}{0.0364} & \multirow{3}{*}{0.0245} & \multirow{3}{*}{0.0128} \\  & velocity & & & \\  & Lateral velocity & 0.4052 & 0.3729 & 0.1308 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Comparison of RMSE values under two simulation conditions.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Simulation Condition** & **UKF** & **SCKF** & **IMM-SCKF** \\ \hline Double-lane change condition & 6.74 s & 4.12 s & 3.69 s \\ Sinusoidal steering condition & 5.02 s & 3.21 s & 2.87 s \\ Sinusoidal steering combined with braking condition & 7.32 s & 3.88 s & 3.67 s \\ \hline \hline \end{tabular}
\end{table}
Table 3: Comparison of the actual computing time consumed by various algorithms.  
model was designed based on the 3-DOF vehicle dynamics and nonlinear brush tire model. The interacting multiple model approach allows multiple observers with different noise covariance matrices to interact with one another, improving the overall algorithm's performance against noise uncertainty to some extent, and the observer can always choose the sub-model with smaller errors for the state output. The co-simulation results show that the IMM-SCKF algorithm can estimate the vehicle longitudinal, lateral, and transverse sway motion states well, and its estimated information can provide accurate and reliable information for the active safety control system.  
Future research could include developing a hardware-in-the-loop simulation platform for vehicle state observation, studying vehicle models with more degrees of freedom and parameter estimation, and conduct hardware-in-the-loop simulation and real-vehicle tests to further evaluate the algorithm in terms of real-time and accuracy.  
[PERSON] conceived this paper, designed the experiments, and analyzed the data; [PERSON] revised the paper and provided some valuable suggestions; [PERSON] carried out the investigation, [PERSON] has provided support in software. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the National Natural Science Foundation of China, grant number 61663042.  
Data Availability StatementData sharing is not applicable. No new data were created or analyzed in this study.  
The authors declare no conflict of interest.