## 1 Introduction
However, all the control strategies in [21; 22; 23; 24; 25; 26; 27; 28], especially with regard to the backstepping controllers, require full-state measurements that may not be possible due to insufficient sensor numbers and/or sensor faults. In response, quadrotor researchers have proposed many solutions that either maintain the control performance or reduce the mass and cost of the vehicle by utilizing only partial state measurements. In [29; 30], based on a reduced-order observer, the authors presented robust TTC algorithms without using linear velocity measurements.The authors of [31] introduced an active disturbance rejection and predictive control strategy to deal with the tracking problem in the presence of disturbances in six degrees of freedom. The controller can guarantee a smooth tracking performance while employing only position and attitude measurements. Tracking controllers based on the hierarchical control strategy without linear velocity and angular velocity measurements are presented in [32; 33]. Yet another robust backstepping tracking controller using an extended state observer (ESO) to estimate unmeasurable states and disturbances from only position measurements was proposed in [34]. In [35], an ESO was used to supply estimations of internal states and external disturbances that are used by a target tracking backstepping controller and an attitude stabilized controller. The ESO has also been used in the design of controllers for a helicopter [36], fixed-wing airplane [37], spacecraft [38], and missile [39]. From a practical point of view, control input saturation occurs frequently and has a significant effect on a system's control performance degradation. To address this problem, the authors of [40] presented a quadrotor backstepping-based controller under input saturation. However, this approach cannot achieve TTC as it considers only attitude stabilization. Two different approaches to solve the tracking problem used a hierarchical inner-outer loop controller [41] or a linear quadratic regulator (LQR) [42]. However, both approaches are not sufficiently robust against disturbances. Once it was realized that input saturation further exacerbates the control problem of perturbed systems, the robust adaptive control problem with input saturation has been investigated. For example, in [43], the authors proposed an adaptive and robust saturated control to achieve the TTC of quadrotors under the presence of disturbances. Robust saturated tracking controllers were also presented in [44; 45; 46], with [44; 45] using a backstepping-based controller, whereas the work in [46] is based on the SMC technique. However, these studies [43; 44; 45; 46] require the full-state information from the sensor systems, which is not always possible to achieve. From the above observations, it is seen that the backstepping control technique plays important roles in solving the TTC of quadrotors. In addition, the references indicate that most of the previous studies are only capable of solving the TTC partially under the comprehensive presence of parameterized uncertainties, external disturbances, and control input saturation. The TTC still needs to be addressed to meet the higher control performance requirements posed by real-world applications. In this paper, we propose a novel ESO-based robust backstepping trajectory tracking controller for quadrotor under control input saturation which advances the current state of the art in three ways:  
(i) Unlike previous saturated control studies in [43; 44; 46], our method does not require full-state information of the system: partial state knowledge is sufficient. In addition, our approach can account for the presence of lumped disturbances (consisting of parameterized uncertainties and external disturbances) in both the translational and rotational dynamics of the quadrotor. In several studies of quadrotor [47; 48], achieving the TTC mission is difficult, as only the vehicle's position and attitude are provided by sensors.