Real-time estimation of longitudinal tire stiffness considering dynamic characteristics of tire

To enhance the effectiveness of active safety control, the tire–road friction coefficient (TRFC) must be precisely estimated, and the longitudinal tire stiffness coefficient is an important vehicle dynamic parameter to estimate TRFC. In this research, we present an observer that improves the performance of longitudinal tire stiffness coefficient estimation by applying tire dynamics that were previously applied in the lateral direction to the longitudinal direction. To begin, we model longitudinal tire dynamics using the relaxation length concept and validate the model using vehicle braking tests. We develop an observer that estimates the longitudinal tire stiffness coefficient by integrating the proposed tire dynamics and vehicle dynamics. The observer, which is based on an extended Kalman filter, can be applied to nonlinear systems and successfully removes noise from wheel speed measurement. The observer’s estimation performance is verified using CarSim simulation and vehicle tests, and the results are compared to existing approaches that do not account for longitudinal tire dynamics. Even in the transient section when the vehicle begins accelerating, the difference between the estimate and the reference value is about 0.3% using the proposed method, but if tire dynamics are not taken into account, the estimate is 6.5% lower than the reference value.