## 1 Introduction  
The quadrotor has been widely used in economic, commercial, entertainment [1], and military industries--for example, prospecting, documentary filming, spraying medicine, reconnaissance, attack, and other tasks. As a result, quadrotors play an essential role in the livelihoods, businesses, and the military for people. Position trajectory control is the key to realizing these applications when flying in turbulent environments [2; 3], flight path planning [4], and avoiding dynamic obstacles [5]. Due to the maneuverability and applicability of the quadrotors, it has attracted extensive research interest in recent years. The study [6] presented an adaptive controller that introduced the artificial neural network to adjust the control gain adaptively. The study [7] proposed a combination of backstepping and sliding model approaches based on a PID-type sliding surface to address the position control problem of the quadrotors. In [8], an optimal bounded robust control algorithm for secure autonomous navigation of a quadrotor is proposed. Other related research includes: the backstepping controllers [9; 10; 11; 12; 13; 14], sliding mode controllers [15; 16], and adaptive controllers [6; 17; 18]. Several research studies considered fuselage drag in the model [16; 18]. The viscous drag force depends on the fluid viscosity, air speed, humidity, and the fuselage design prototype. It is hard to make a deterministic analysis of the effects of drag. In general, the quantitative results are estimated by conducting the experimental studies [19; 20]. Nevertheless, some researchers did not consider the drag force in the external disturbances [8; 9; 11; 15]. To fulfill the practical scenarios, the time-varying, and state-dependent external disturbances are considered in these studies [21; 22; 23]. Some of the studies do not include measurement noise [6; 7; 8; 10; 15; 18; 24] and actuator saturation limitations [25] in the numerical simulations. These imperfections lead to mismatches between numerical simulation and practical implementations. In fact, the saturation of actuators may lead to system instability. The measurement noise may be amplified when conducting the numerical differentiation. This skill causes serious control chattering of the control signals. With regard to the position flight controller, some of the articles [7; 9; 10; 11; 13; 18; 26; 27] separate the dynamics into the position loop and attitude loop, and then design the controller individually. In these works, the attitude transients are ignored based on the assumption that the attitude response is fast enough. However, transient behavior in the attitude loop does exist due to the nature of the quadrotor flight properties and finite inner-loop control bandwidth. Therefore, the tracking performance of the position loop is limited due to the transient response of the attitude loop. To address this cascade transition issue, the integral backstepping control algorithm is introduced inspired by the work [28], where the integral term is applied to suppress the effects of disturbances [29]. However, the construction of the virtual control law needs information from unmeasurable states. The studies [9; 14] conducted the numerical differentiation and applied a low-pass filter. It should be mentioned that the drawback of a low-pass filter gives rise to the phase delay. To avoid the control delay problem, the analytic form of virtual controls is derived. The analytic form is obtained by dividing the virtual control into a disturbance-independent term and a disturbance-dependent term and then applying the compensation for the former. Simulation results reveal that the relatively smooth control signals are available from the proposed analytic form of virtual controls. The objective of this study aims to develop a position tracking control algorithm for a quadrotor in the presence of both the disturbance and the measurement noise.