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Spacecraft attitude control employs quaternion representation to avoid singularity issues and obtain global maneuver stability. However, it has redundancy associated, resulting in dual equilibrium points. The attitude control may confront the unwinding phenomenon due to the presence of the equilibria. In this paper, an anti-unwinding controller for spacecraft stabilization in the presence of external disturbances and inertial uncertainties, angular velocity limit, actuator saturation and faults is presented. Specifically, a modified extended state observer (ESO) is designed to obtain total disturbance estimates of the rigid-body spacecraft. Auxiliary parameters are added in the design to avoid initial high estimates in the proposed ESO design resulting in faster convergence. The proposed disturbance observer is to release the assumption that requires the estimated disturbance to be constant or varying at slow rates. Using the ESO estimates, a particular back-stepping-SMC (ESO-BTSMC) controller is devised to formulate anti-unwinding control law for spacecraft stabilization. Lyapunov stability theory is employed to prove closed-loop stability of system and estimation error convergence. Comparative simulations are performed to demonstrate the performance of the proposed control scheme. It is found that the proposed control scheme gives smooth and precise control performance along with faster transient response. Additionally, it also alleviates the chattering phenomenon. [ABSTRACT FROM AUTHOR]