The paper presents an observer design method for estimating the slips and the cornering stiffness of autonomous road vehicles. As a first step, the dynamical one-wheeled bicycle model is reformulated to express directly the slips of the vehicle. In the second step, a polytopic model-based observer is designed which can deal with the variation of the scheduling parameters (longitudinal velocity, cornering stiffness). In order to eliminate the parameter uncertainty an ultra-local model is applied by which the cornering stiffness is estimated. The effectiveness and the operation of the proposed observer method are demonstrated through a complex scenario in the high-fidelity simulation software, CarMaker.