Wheel forces estimation with an Augmented and Constrained Extended Kalman Filter applied on a nonlinear multi-body model of a half vehicle

The design of a vehicle suspension requires the knowledge of wheel loads due to road unevenness. These loads can be identified from measurements acquired during vehicle rolling on roads or tracks. Different off-line methods are used to identify them. Most of these methods use some transfer functions between points of measurements and hypothesis of linear dynamic behaviour of the vehicle. This leads to miss-estimation of end-tail load probability distribution. We propose here an approach based on a nonlinear multi-body model of the half-vehicle and an Augmented and Constrained Extended Kalman Filter for the data fusion with accelerometers, gyrometer, tachometer and GPS measurements. This half vehicle model lies in a 2D plane and allow the description of pitch behavior but not the yaw neither the roll behavior. The specificities of our work are that 1) the Kalman state vector is composed of positions and velocities of each solid in the multi-body system, 2) the state model of the multi-body system is based on the Newmark explicit integration scheme, 3) the road/tracks loads are unknown and 4) the state prediction is constrained by kinematic links between bodies. Finally, this method provides an estimation of wheel center forces for a multi-body car model.