Most of active devices focused on vehicle stability concerns on-road cars and cannot be applied satisfactorily in an off-road context, since the variability and the non-linearities of the tire/ground contact are often neglected. In previous work, a rollover indicator devoted to light ATVs, accounting for these phenomena has been proposed. It is based on the prediction of the lateral load transfer. Such an indicator requires the online knowledge of the tire cornering stiffness, initially selected from a ground classes network. In this paper, an adapted backstepping observer, making only use of yaw rate measurement, is designed to improve specifically tire cornering stiffness estimation. Capabilities of such an observer are demonstrated and discussed through both advanced simulations and actual experiments.