# Estimation of Intelligent Commercial Vehicle Sideslip Angle Based on Steering Torque
## 5 Conclusions  
The sideslip angle estimation of intelligent commercial vehicles based on steering torque using the EKF algorithm is proposed in this paper. First, the transfer functions between the sideslip angle-torque and sideslip angle-angle are constructed. Then, based on the analysis of transfer functions, it is found that the steering torque signal has an accurate and more direct response due to the hydraulic pressure in the EHPS system. To estimate the vehicle sideslip angle, a state observer derived from the extended Kalman filter (EKF) method is proposed. Both simulation and test bench results show that the sideslip angle estimated based on steering torque has a smaller phase lead and higher accuracy than the sideslip angle estimated based on steering angle in the linear region and nonlinear region. The experimental results show that the accuracy of estimation sideslip angle based on steering torque is improved by 23.9% and 34.6% compared with that based on steering angle under high-adhesion road conditions and low-adhesion road conditions, respectively. However, the proposed method is applied to a bench test in this paper, so its application for a real car test will be studied in the future. In addition, side angle estimation will be very important for autonomous vehicles and connected automated vehicles. It is also interesting to use the automated driving systems data acquisition and analytics platform technology and 3D lidar fusion sensing technology to enhance the performance of side angle estimation.  
Conceptualization, Y.L. and Y.Y.; methodology, Y.L.; software, Y.L.; validation, Y.L., X.W. and Y.Z.; formal analysis, Y.L. and Y.Z.; investigation, Y.L. and C.W.; resources, Y.L., Y.Y. and C.W.; data curation, Y.L.; writing--original draft preparation, Y.L. and Y.Y.; writing--review and editing, Y.L. and Y.Y.; visualization, Y.L., X.W. and Y.Z.; supervision, Y.Y., X.W. and C.W.; project administration, Y.Y., X.W. and C.W.; funding acquisition, Y.Y., X.W. and C.W. All authors have read and agreed to the published version of the manuscript.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Maneuver** & **Method** & **Max Error (°)** & **MAE (°)** & **RMSE (°)** \\ \hline Double line change & Steering torque & \(-0.175\) & \(0.0613\) & \(0.0733\) \\ \(u\) = 50 km/h \(\mu\) = 0.85 & Steering angle & \(-0.3\) & \(0.0805\) & \(0.1112\) \\  & Steering torque & \(-0.26\) & \(0.0822\) & \(0.1032\) \\ \(u\) = 65 km/h \(\mu\) = 0.75 & Steering angle & \(-0.51\) & \(0.1257\) & \(0.1739\) \\  & & & & \\ \end{tabular}
\end{table}
Table 4: The estimation error in different test conditions.  
Figure 12: The errors of sideslip angle between two methods: (**a**) The results at \(u\) = 50 km/h, \(\mu\) = 0.85; (**b**) The results at \(u\) = 65 km/h, \(\mu\) = 0.75.  
**Funding:** This research was funded by the National Natural Science Foundation of China, grant number 52275218 and the National Key Research and Development Program of China, grant number 2021 YFC2801403.  
**Institutional Review Board Statement:** Not applicable.  
**Informed Consent Statement:** Not applicable.  
**Data Availability Statement:** Not applicable.  
**Acknowledgments:** The authors would like to thank the handling editor and the anonymous reviewers for their valuable comments and suggestions.  
**Conflicts of Interest:** The authors declare no conflict of interest.