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

Accurate knowledge of wheel loads is of great value in vehicle design and control. However, a direct measurement of these forces is generally not feasible. This motivates the use of model-based estimation techniques, such as the Kalman filter to obtain operational wheel forces. The general approach in literature is to use simple ad-hoc models (like the bicycle model) in the Kalman filter. In many applications however, including vehicle dynamics, this results in a system that is not observable for all the variables of interest, e.g. the individual tyre forces. In this light, this work proposes the use of general flexible multibody models for Kalman filtering. The introduction of flexible deformations in the model enables the observation of variables which cannot be obtained from a rigid model. This allows the filter to differentiate between the contributions of different input forces. This approach is demonstrated by employing an augmented extended Kalman filter to perform a combined estimation of the current vehicle state and wheel forces of a 2D vehicle model. The system is modeled in a floating-frame-of-reference (FFR) approach and the vehicle body is described by a reduced order finite element model. An observability analysis is performed and the observability conditions for the unknown input forces are derived. The proposed approach is validated numerically and compared to an estimator with a rigid assumption.