• Extended Kalman Filter
• Moving Horizon Estimation
• data post-processing
• system identification
• online estimation algorithms

The aim of this work, which is the result of a research carried out at Fraunhofer-Institute for Structural Durability and System Reliability LBF in Darmstadt (Germany), is to present some techniques for the estimation of the vehicle wheel forces.
Over the years, knowledge of vehicle wheel loads has become an aspect of considerable interest to automotive companies. One of the most interesting engineering aspects is related to the fatigue field, in order to assess the "durability" and "reliability" of components closely connected to the wheels, such as suspension components. The best solution would be to measure directly the forces, but the problem is that sensors such as Wheel Force Transducers" (WTF) are expensive, and thus far from the demands of large-scale mass production. So, tire forces must be observed or estimated from measurements already available in modern vehicles. Therefore, this identification is reduced to a problem of estimating states, and this approach is called “Virtual tyre sensor”.

After bibliographic research of the state of the art of state estimation, online state estimators like Moving Horizon Estimation (MHE) and Extended Kalman Filter (EKF) are presented. In order to estimate the forces, it is necessary to describe the vehicle dynamics. To this aim, two different vehicle dynamics models are used in this work. Specifically, a “single-track model” coupled with “rotating wheel dynamics” was used to estimate longitudinal forces and lateral axle forces. Instead, a 7 DOF ride model coupled with a planar roll and pitch sub-models is used to estimate the vertical forces also when longitudinal and lateral inertial forces are present. The estimators process the signals available as a result of different maneuvers performed on a virtual reference vehicle in MSC. Adams, which in turn serves to evaluate the accuracy of the results obtained by the algorithms. The estimators were then evaluated on different maneuvers, such as performance, handling, and ride. The results are presented by comparing the estimated signals with the force signals directly available from the reference vehicle measurements. The Root Mean Square Error (RMSE) and relative damage are among the most important parameters used to assess the goodness of the estimates obtained. In addition, a sensitivity analysis was performed to show how the accuracy of the results depends on a good choice of control parameters of the estimators available to the user.