Unscented Kalman filter for vehicle state estimation

Abstract Vehicle dynamics control (VDC) systems require information about system variables, which cannot be directly measured, e.g. the wheel slip or the vehicle side-slip angle. This paper presents a new concept for the vehicle state estimation under the assumption that the vehicle is equipped with the standard VDC sensors. It is proposed to utilise an unscented Kalman filter for estimation purposes, since it is based on a numerically efficient nonlinear stochastic estimation technique. A planar two-track model is combined with the empiric Magic Formula in order to describe the vehicle and tyre behaviour. Moreover, an advanced vertical tyre load calculation method is developed that additionally considers the vertical tyre stiffness and increases the estimation accuracy. Experimental tests show good accuracy and robustness of the designed vehicle state estimation concept. Keywords: vehicle dynamics controlstate estimationunscented Kalman filtervertical tyre forces Acknowledgements We want to thank Daniel Heyes for the fruitful discussions and the work he has performed during his internship for the vertical tyre force calculation method. We also appreciate the valuable contribution of our alumni internship student Matthias Feld to the Matlab implementations and tests of the discussed Kalman filter variants. A special thanks goes to Peter Ziegler and Stefan Otterbein from Corporate Research of Robert Bosch GmbH for performing vehicle tests as well as for sharing their outstanding expertise. Notes The steering wheel angle sensor belongs to the standard VDC system equipment. Therefore, the steer angles of the front wheels can be calculated out of the known steering wheel angle and the kinematics of the steering system. The accuracy can be additionally increased by introducing a detailed steering system model. These parameters are also referred to as Magic Formula tyre parameters and are only valid for a given velocity, tyre, and road surface. Practically, they are extracted from tyre measurement data by means of an optimisation procedure. Note that the matrix is invertible as long as c t or c c is unequal to zero. Note that the matrix is always invertible for physically consistent vehicle parameters. Note that within one sampling interval T 0 Equation Equation(39a) is an autonomous system, since is constant due to the zero-order-hold assumption. Here and subsequently, the notation x(a|b) relates to the stochastic properties of a given random variable at the discrete time step a, in which only the measurements of the discrete time steps from 0 to b are incorporated. ADMA is a measurement equipment developed by GeneSys GmbH. It is based on combination of an inertial navigation system with a global positioning system (GPS/INS).