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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 the front and rear wheels. The tire-road friction coefficient information is of critical importance for vehicle dynamic control systems and intelligent autonomous vehicle applications. In this paper, the vehicle longitudinal-motion-independent tire-road friction coefficient estimation method consists of three main components: 1) an observer to estimate the internal state of a dynamic LuGre tire model; 2) an adaptive control law with a parameter projection mechanism to track the desired vehicle longitudinal motion in the presence of tire-road friction coefficient uncertainties and actively injected braking excitation signals; and 3) a recursive least square estimator that is independent of the control law, to estimate the tire-road friction coefficient in real time. Simulation results based on a high-fidelity CarSim full-vehicle model show that the system can reliably estimate the tire-road friction coefficient independent of vehicle longitudinal motion.