Data-driven Estimation of Tire Cornering Stiffness: A Dynamic Mode Decomposition Approach

Accurate information about tire cornering stiffness is essential for the implementation of advanced vehicular control systems. Data-driven modelling method leverages the availability of high-quality measurement data alone, without vehicle parameters, which provides a tutorial to reconstruct the system dynamics and estimate tire cornering stiffness. As such, we collect the states and inputs of the vehicle to build its state space using the dynamic mode decomposition (DMD) method. Then, based on the entries of the system and input matrix, the tire cornering stiffness can be further identified by solving the linear equations via orthogonal regression with considering the measurement noise. The sufficient and necessary rank condition for the DMD execution is also analyzed. Additionally, we introduce two alternative ways to update the system and input matrices - recursive least squares (RLS) and sliding window (SW). Finally, the simulation tests are conducted by CarSim-Simulink to compare the proposed data-driven solution to the extended Kalman filter (EKF). The validation results indicate that the DMD method is capable of reconstructing vehicle lateral dynamics in linear regions and achieves comparable performance to the EKF without requiring prior tire forces. Specifically, the SW offers the best performance for tracking the time-varying system and input matrices. The RLS, in comparison, demonstrates a slow response with satisfactory numerical stability.