## 1 Introduction  
Traditionally, the guidance and autopilot design of the flight vehicle are treated as two independent processes, in which the guidance loop is the outer loop to generate the acceleration commands. The autopilot is the inner loop to track the acceleration commands. This method ignores the coupling characteristics of the guidance and autopilot, and requires that the guidance loop has a much slower response speed than autopilot, i.e., the spectral separation rule [1]. However, with the flight envelope becoming larger or the vehicle-target distance becoming smaller, the response speed of the guidance loop may increase, which may further break the spectral separation rule between guidance and autopilot loops and eventually lead to a large miss distance. In recent years, integrated guidance and control (IGC) has attracted growing research interest for flight vehicles [2] and has been successfully applied in some flight vehicles [3]. IGC treats the guidance and control loops as a whole system and generates the fin deflection command directly [4]. From the perspective of control theory, the relative motion of the flight vehicle and the target, and the attitude model of the flight vehicle are combined, in the framework of IGC. The motion model of the flight vehicle can be regarded as a high-order uncertain nonlinear dynamical system containing matched and unmatched disturbances [5]. Furthermore, due to the harsh flight environment, some parameters, such as aerodynamical parameters, are not easy to obtain accurately, which may introduce parameter perturbation. Apart from the disturbance and parameter perturbation, gain-loss actuator faults are another significant factor, which may influence the stability of the system. To some extent, actuator faults can be seen as a special disturbance for the flight vehicle system, which, however, is input-related. The upper bound of the parameter perturbation or disturbance item can usually be parameterized by a known or unknown constant and a known function. In contrast, if taking the actuator fault into consideration, the uncertain item can no longer be parameterized before the control law is determined. Therefore, fault-tolerant IGC (FTIGC) requires further research. As mentioned earlier, the flight vehicle model can be treated as a high-order nonlinear system with the states describing the relative motion of the flight vehicle and target and the attitude motion of the flight vehicle. According to the parallel approaching method, it is expected that the line-of-sight (LOS) angular rate should converge to zero. To achieve the control target, all the state information should be measured or calculated. The seekers, including the gimbaled seeker and strapdown seeker, are devices used to provide the relative motion information. Compared with the gimbaled seeker, the strapdown seeker removes the mechanical servo system, which decreases the cost and the complexity of the structure, and increases the reliability [6]. Instead, the strapdown seeker is body-aligned. Hence, the optical axis of the seeker will not point to the target and only the body-line-of-sight (BLOS) angles can be provided [7; 8]. The absence of the LOS angular rate will indeed pose a significant challenge in the design of guidance laws. According to the discussion above, this paper focuses on the problem of IGC considering the potential gain-loss actuator fault, without the LOS angular rate measurement information. To achieve this, the LOS angular rate is reconstructed by an Extend State Observer (ESO) with the measured BLOS angle information. Furthermore, backstepping-based FTIGC is then investigated with the estimated LOS angular rate. The main contributions of this work are as follows:  
1. A linear ESO is established based on the measured body-LOS angle information, and the uniformly ultimately bounded stability of the estimation error of the LOS angular rate is guaranteed. 2.