We present a switched adaptive observer for the estimation of the tyre extended braking stiffness (XBS) during braking scenarios. The design of the observer is based on Burckhardt's friction model, and on a model of the wheel dynamics in which the XBS appears as one of the state variables. Asymptotic stability of the estimation error is established on the basis of dwell-time and persistency of excitation conditions. The approach is validated via numerical simulations considering realistic perturbations on the system's measured output.