Tire-road friction coefficient information is of critical importance for vehicle dynamic control such as yaw stability control, trajectory tracking control, and rollover prevention for both manned and unmanned applications. Existing tire-road friction coefficient estimation approaches often require certain levels of vehicle longitudinal and/or lateral motion excitations (e.g. accelerating, decelerating, and steering) to satisfy the persistence of excitation condition for reliable estimations. Such excitations may undesirably interfere with vehicle motion controls. By utilizing the actuation redundancy, this paper presents a novel, real-time, tire-road friction coefficient estimation method that is independent of vehicle longitudinal motion for ground vehicles with separable control of front and rear wheels. A dynamic LuGre tire model is utilized in this study. An observer is proposed to estimate the internal state in a LuGre tire model. An adaptive control law with a parameter projection mechanism is designed to track the desired vehicle longitudinal motion in the presence of tire-road friction coefficient uncertainties and an actively-injected persistently exciting input signal. An RLS estimator was employed to estimate the tire-road friction coefficient in real-time. Simulation results based on a full-vehicle CarSim^® model show that the system can reliably estimate the tire-road friction coefficient independent of vehicle longitudinal motion.