Use of flexible models in extended Kalman filtering for vehicle body force estimation

The forces acting on a vehicle are an important area in vehicle dynamics research. A direct measurement of these forces, however, is not feasible for mass-produced vehicles. This has motivated the use of model-based estimation techniques such as the Kalman filter. In this work the discrete-time augmented extended Kalman filter is employed to perform a combined estimation of the current vehicle state and the input forces, such as the tyre forces. Currently, the general approach is to use simplified ad-hoc models for the Kalman filter. In vehicle dynamics applications this can lead to an unobservable system which makes it impossible to estimate the individual tyre forces. In order to solve this issue, this work proposes to take the flexibility of the vehicle body into account in the model for the Kalman filter. This adds an effect to the model that allows to differentiate between the contributions of all the different input forces. The model is derived according to the floating frame of reference formulation and a reduced order finite element model is used to describe the flexibility of the vehicle body. An exponential integrator is applied to time-discretize the equations of motion. An observability analysis is performed and the observability conditions for the unknown input forces are derived. Furthermore, it is shown that no position-level measurements are required if only the forces are of interest. The proposed approach is numerically validated and compared to the current general approach. The validation demonstrates that the proposed approach provides superior estimation results.status: publishe