Improved anti-lock brake systems (ABS) employed on aircraft and land vehicles and methods of operating same employing a sliding mode observer (SMO) incorporated into an ABS algorithm requiring only measurement of wheel speed to regulate the application of braking torque are disclosed. Braking is optimized simply by maintaining an SMO estimate of differential wheel torque (road/tire torque minus applied brake torque) derived from wheel speed at an extremum via applying or releasing the brakes as the extremum is passed through.