A hierarchical estimation of road grade based on tire force observation

Road grade is important for autonomous vehicles, but it is difficult to measure directly. To address this issue, a hierarchical estimation of road grade is suggested based on the observation of tire forces. First, a 7-degree-of-freedom (DOF) dynamics model, including vehicle longitudinal, lateral, and yaw motions together with wheel rotations, is developed while considering the road grade. Subsequently, a dual-layer road grade estimation strategy is proposed based on an unscented Kalman filter (UKF). The lower-layer UKF estimates the longitudinal and lateral tire forces for road grade observation, and the upper-layer UKF is employed to estimate the road grade by considering the vehicle’s lateral acceleration and yaw rate. Finally, CarSim and MATLAB joint simulations and road tests are performed under different conditions to validate the correctness and effectiveness of the proposed estimation method. The results show that the proposed tire force observation-based estimator exhibits a lower mean absolute error and root mean square error on sloping roads and combined curved and sloping roads, and presents a better overall estimation performance on road grade compared with the widely used kinematics and dynamics model-based estimators.