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In this paper, we used a non-singular backstepping terminal sliding mode control approach to the unmanned aerial vehicle (quadrotor). In the first step, the governing dynamical equations were obtained based on the quadrotor considering all the effective parameters. The controller objective is limited to obtaining proper tracking of the desired positions (x, y, z) and the yaw angle (ψ), as well as maintaining the stability of the roll and pitch angles despite the presence of external disturbances. Controlling methods require complete information about system states that may be limited in practice. Even if all system conditions are available, it is interfered by noise, and also large number of applier sensors to measure states, makes the entire system more complex and costly. For this purpose, the Extended Kalman Filter (EKF) has been used as an observer. The extended Kalman filter is used as a speed observer and estimator of external disturbances such as wind force. Therefore, the use of a controller-observer is suggested to estimate the effects of external disturbances in order to compensate for them. The design method is based on the stability of Lyapunov. Simulation results show the promising performance and suitability of the observer-controller.