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An extended Luenberger observer for estimating vehicle sideslip angle and road–friction coefficient is proposed in this paper. The observer is designed based on local linearisation and the Routh–Hurwitz criterion. The vehicle is described by a simple nonlinear bicycle model and the road friction is manifested by a random–walk model. It is explicitly proved that road friction will be completely unobservable if all of the tyres operate in the linear range and observability of the vehicle sideslip angle will greatly deteriorate and even get lost when all the tyre forces are saturated. A gain–schedule strategy is proposed for estimation of road friction when the tyres operate in a transition state between linear range and lateral force saturation. The effectiveness and robustness of the proposed observer are evaluated in a simulation environment using a high–fidelity vehicle dynamics. The simulation results clearly verify that the proposed observer–based methodology has sufficient accuracy for estimation and strong robustness to parameter variation.
Ding et al. (2014) studied this question.