Accurate control of high-speed mobile robots moving off-road constitutes a challenging robotic issue: numerous time-varying dynamic phenomena (and first of all, sliding effects) are no longer negligible and must explicitly be taken into account in control design, in order to ensure high accuracy path tracking. Since these phenomena are hardly measurable at a reasonable cost, they have to be estimated on-line. A multi-model based observer is here proposed, in order to supply on-line tire cornering stiffnesses (i.e. grip conditions) as well as mobile robot sideslip angles. It takes part of the complementarity between kinematic and dynamic mobile robot models, in order to significantly decrease the number of required robot inertial parameters (since their values are sometimes difficult to obtain). Full scale experiments demonstrate that the proposed observer can supply reactive and reliable sideslip angle estimates, so that high accuracy path tracking can still be achieved, whatever grip conditions and vehicle velocity.