Gradient Descent based Iterative Observer for Lateral-Yaw Dynamics and Tire Stiffness Estimation in EVs

Abstract

In Electric Vehicles (EVs), the behavior of lateral slip and yaw motion is governed by lateral-yaw dynamics, and the information of stiffness coefficients determines how efficiently the vehicle transforms the driver's inputs into lateral forces. The unbiased real-time information of these traits improves the vehicle’s lateral-yaw stability and responsiveness across diverse driving environments. The conventional vehicle stability systems depend on the fixed tire road parameters and basic sensor readings, which often fail to handle the abrupt tire-road conditions under aggressive maneuvering. Therefore, in this paper, a Gradient Descent-based Iterative Observer (GDIO) framework is proposed to continuously observe the changes in tire-road conditions and estimate the lateral-yaw dynamics to enhance the yaw and handling stability. The GDIO framework minimized the error-based objective functions through iterative gradient descent updates and corrected the estimated lateral-yaw accelerations and stiffness coefficients in real-time. The effectiveness of the proposed framework is validated on two distinct simulated test environments: Test–1, which is performed on S-Turn reference steering input, whereas Test–2 is carried out on Sine Sweep reference steering input at variable steering frequency. The GDIO is furthermore examined for qualitative performance analysis over four (04) different sets of initial conditions, cornering stiffness and learning rate , for . Finally, the simulation and RMSE results exhibited that the GDIO with , configuration delivered an overall maximum improvement for lateral acceleration estimation and , yaw acceleration and , followed by front stiffness and , and rear stiffness and in comparison with other initial configurations in Test-1 and Test-2, respectively. Thus, the GDIO framework provides a reliable and mathematically rigorous mechanism for enhancing the lateral-yaw stability and handling responsiveness of EVs.Electric Vehicles (EVs), the behavior of lateral slip and yaw motion is governed by lateral-yaw dynamics, and the information of stiffness coefficients determines how efficiently the vehicle transforms the driver's inputs into lateral forces. The unbiased real-time information of these traits improves the vehicle’s lateral-yaw stability and responsiveness across diverse driving environments. The conventional vehicle stability systems depend on the fixed tire road parameters and basic sensor readings, which often fail to handle the abrupt tire-road conditions under aggressive maneuvering. Therefore, in this paper, a Gradient Descent-based Iterative Observer (GDIO) framework is proposed to continuously observe the changes in tire-road conditions and estimate the lateral-yaw dynamics to enhance the yaw and handling stability. The GDIO framework minimized the error-based objective functions through iterative gradient descent updates and corrected the estimated lateral-yaw accelerations and stiffness coefficients in real-time. The effectiveness of the proposed framework is validated on two distinct simulated test environments: Test–1, which is performed on S-Turn reference steering input, whereas Test–2 is carried out on Sine Sweep reference steering input at variable steering frequency. The GDIO is furthermore examined for qualitative performance analysis over four (04) different sets of initial conditions, cornering stiffness and learning rate , for . Finally, the simulation and RMSE results exhibited that the GDIO with , configuration delivered an overall maximum improvement for lateral acceleration estimation and , yaw acceleration and , followed by front stiffness and , and rear stiffness and in comparison with other initial configurations in Test-1 and Test-2, respectively. Thus, the GDIO framework provides a reliable and mathematically rigorous mechanism for enhancing the lateral-yaw stability and handling responsiveness of EVs.