Extended Kalman Filter for Vehicle Dynamics Determination Based on a Nonlinear Model Combining Longitudinal and Lateral Dynamics

The vehicle body sideslip angle (VBSSA) is a key variable in vehicle dynamics indicating critical driving situations. It is, e.g., essential in vehicle dynamics control concepts. Since it cannot be measured with standard sensors, it has to be determined via a model based approach. Thereto an Extended Kalman Filter will be presented that is capable of describing the VBSSA with high accuracy. The filter design is based on a nonlinear double track model combining the longitudinal and lateral dynamics. Starting point is a double track model with three state variables, that are the velocity in the center of gravity, the VBSSA and the yaw rate. Then, the longitudinal dynamics are incorporated, yielding the velocity and the longitudinal forces at the individual wheels. The resulting nonlinear state space model only requires information that is provided by the standard sensors available in series production vehicles.

On basis of this nonlinear model an Extended Kalman Filter is derived. Utilizing the individual wheel speeds, the longitudinal and lateral acceleration as well as the yaw rate, the Extended Kalman Filter is capable of describing the lateral dynamics with high accuracy. Additionally, dealing with parameter variations is demonstrated by the example of a yaw rate offset. This offset between true and measured yaw rate is explicitly incorporated into the filter design and the resulting filter properly determines not only constant but also slowly drifting offsets. Accordingly, the estimation results for the VBSSA are not affected by the presence of yaw rate sensor offsets.