## 1 Introduction  
Quadrotors have been widely used in many fields, such as agriculture, cargo delivery, surveillance, aerial photography, military fields and environmental monitoring [1]. This evidently reveals that the flying area of quadrotors gradually covers most of the areas where people live. Therefore, the safety of people under the flying area is now a concerned and an important issue. To ensure the safety of flight of the quad-rotor and the safety of people under or nearby the flying area, it is necessary to adopt an appropriate field safety strategy, such as fault-tolerant control, when a quad-rotor is malfunctioning. Actually, FTC strategies have been investigated for decades and applied to many different fields. Among various methods for FTC published in the literature, observer-based approaches are effective and reliable. In [2], a speed sensor FTC for electric-vehicle (EV) powertrains was proposed. The approach considers two observers and a voting algorithm for the sensor fault decision making. Based on a higher order sliding mode (HOSM) observer, a reconfiguration scheme is proposed to maintain a good speed tracking control performance of a permanent-magnet synchronous motor in the event of sensor faults/failures [3]. To achieve on-line speed sensor fault detection, a simple adaptive observer-based scheme for induction motors is developed in [4] for the FTC of EVs under cruise operation mode. However, external vehicular disturbances, which may perturb the fault estimation accuracy, were not considered. In the literature, many other FTC methods have also been proposed for quadrotor systems, such as model-reference adaptive control [5; 6; 7], multiple model switching and tuning [8; 9; 10; 11; 12; 13], feedback linearization [14] and sliding mode control [15; 16; 17]. Generally, FTC can be classified into passive and active FTC [18; 19], which relies on the fault detection and isolation (FDI) result. The techniques of FDI [20] could be classified as model-based [21; 22] and data driven [23; 24; 25] approaches. Model-based methods are more economical and efficient as they do not require one to process massive datasets. An example is demonstrated in [26], which shows that with accurate fault information, the corresponding FTC could be implemented precisely and immediately when faults occur. In some papers, nonlinear adaptive thresholds are designed to enhance the robustness and fault sensitivity of the properties FDI algorithm [27; 28]. Moreover, a Thau observer is applied in [29] to generate a diagnostic residue whose value would be almost zero without faults happening inside the fault detection system, but in practical cases, it is hard for the residual to be zero owing to noise, disturbance and the system uncertainties. Hence, an adaptive threshold is adopted to ensure the system robustness and to judge if the real fault exists or not. Another adaptive Thau observer (ATO) was proposed in [30]. Based on the residuals monitoring, the FDI aims to identify the faults as well as estimate the fault offset parameters. Different from the former study, an innovative fault diagnosis strategy was developed to not only detect the actuators fault, but also to quantify the magnitude of faults. Nevertheless, it would take much time to process the fault estimation since it used some techniques to improve and optimize the original observer, like compensating for the uncertainties based on system identification and filtering the noise by a specified low-pass filter. Some examples of applications of FTC and FDI on aircraft are revealed. For instance, developing a flight control algorithm based on a linear parameter varying (LPV) controller to fulfill tracking during normal and fault conditions [16; 31; 32]. The study [33] designs adaptive sliding mode Thau observer (ASTMO) to derive the estimation of fault magnitude and the system parameters are solved in terms of the linear matrix inequalities (LMIs). Recently, actuator fault estimation and FTC was demonstrated using model-based observer as well [34].