Most active devices focused on vehicle stability concern on-road cars and cannot be applied satisfactorily in an off-road context, since the variability and the non-linearities of tire/ground contact are often neglected. In previous work, a rollover indicator devoted to light all-terrain vehicles accounting for these phenomena has been proposed. It is based on the prediction of the lateral load transfer. However, such an indicator requires the on-line knowledge of the tire cornering stiffness. Therefore, in this paper, an adapted backstepping observer, making use only of yaw rate measurement, is designed to estimate tire cornering stiffness and to account for its non-linearity. The capabilities of such an observer are demonstrated and discussed through both advanced simulations and actual experiments.