Real-Time Estimation of Center of Gravity Position for Lightweight Vehicles Using Combined AKF–EKF Method

In this paper, a real-time center of gravity (CG) position estimator, which is based on a combined adaptive Kalman filter-extended Kalman filter (AKF-EKF) approach, for lightweight vehicles (LWVs) is proposed. Accurate knowledge of the CG longitudinal location and the CG height in the vehicle frame is helpful to the control of vehicle motions, particularly for LWVs, whose CG positions can be substantially varied by the payloads on board. The proposed estimation method, taking advantage of the separate front/rear torque control capability available in numerous LWV prototypes, only requires that the vehicle be excited longitudinally and/or vertically, thus avoiding potentially dangerous excitation of the vehicle lateral/yaw/roll motions. Moreover, additional parameters, such as vehicle moments of inertia, suspension parameters, and the tire/road friction coefficient (TRFC), are not necessary. A three-degree-of-freedom (3-DOF) vehicle dynamics model, taking the vehicle longitudinal velocity, the front-wheel angular speed, and the rear-wheel angular speed as states, is employed in the filter formulation. The designed estimator consists of two parts: an AKF for filtering noisy states and an EKF for estimating parameters. To minimize the effects of undesirable oscillation and bias in the filtered states, the optimization-based AKF judiciously tunes the suboptimal process noise covariance matrix in real time. Meanwhile, the EKF utilizes the filtered states from the AKF and takes the parameters as random walks. Simulation results exhibit the advantages of the AKF over the standard KF with fixed covariance matrices. Experimental results obtained from vehicle road tests show that the proposed estimator is capable of estimating the CG position with acceptable accuracy. Moreover, an investigation of the two-layer persistent excitation (PE) condition reveals that, although the CG height estimation largely depends on the excitation level in the maneuver, the CG longitudinal location can be always estimated via the input torque injections.