We present a switched adaptive observer for the estimation of the tyre extended braking stiffness (XBS) during ABS 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. Global asymptotic stability of the estimation error is established provided that certain dwell-time and persistency of excitation conditions hold. The approach is validated under constant road conditions with experimental data from a tyre-in-the-loop test rig, and under varying road conditions via numerical simulations on a two-axle vehicle model that includes dynamic load transfer and tyre relaxation length.