Estimation of Road Friction Coefficient for Distributed Electric Vehicles Based on a Sliding Mode Observer and a Square-Root Cubature Kalman Filter

For distributed drive electric vehicles, accurate estimation of the road friction coefficient is essential for torque allocation, stability control, and full utilization of tire force potential, since each wheel is independently actuated and directly constrained by the tire–road interaction. To address this issue, a robust road friction coefficient estimation method based on a sliding mode observer (SMO) and a square-root cubature Kalman filter (SRCKF) is proposed. The SMO is first designed to estimate the longitudinal and lateral tire forces using measurable vehicle states, providing reliable force information under conditions of modeling uncertainties and external disturbances. Based on the estimated tire forces, the SRCKF is then employed to fuse nonlinear tire model information and obtain an accurate and numerically stable estimate of the road friction coefficient. The proposed method is evaluated through simulation studies under various driving conditions. At a vehicle speed of 20 km/h, the friction coefficient estimation error converges from 0.01 to zero within 1.3 s; at 60 km/h, the estimation error converges from 0.6 to zero within only 0.005 s. The simulation results demonstrate that the proposed estimator can accurately track changes in road friction and provide reliable inputs for motion control and torque distribution in distributed drive vehicles.