This paper addresses the study of observer-based two-stage extended Kalman filter (TSEKF) estimation problem for the satellite attitude control system (ACS) in the presence of unknown time-varying actuator faults. In the traditional TSEKF methods, the considered faults always refers to constant signal in the propagation of the filter estimation, even though time-varying faults are taken into account in simulation demonstrations. In order to promote the accuracy of the TSEKF algorithm, a nonlinear observer is designed to obtain the fault dynamics and the state estimation with consideration of the nonlinear nature of the satellite ACS, and its estimation results are treated as exogenous signals used for linearizing the nonlinear ACS model. Then based on the observed fault information and the linearized ACS model, the TSEKF estimator is designed to obtain the exogenous filtering scheme, which can simultaneously reconstruct the state and faults accurately. Finally, by using the so called two-stage exogenous Kalman filter (TSXKF), simulation results show that when a time-varying fault occurs, more ideal estimation results can be obtained than those of TSEKF and better dynamic performance can be achieved than that of nonlinear observers.