# Correction Strategy of Online Midcourse Guidance for High-Speed Gliding Target Interceptor
## 1 Introduction
The above methods avoid repeatedly reoptimizing the trajectory, so they achieved a high solving efficiency. However, due to the optimization near the nominal trajectory, it cannot cope with the situation that the terminal constraint update range is large and the updated law is uncertain. Some references attempted to introduce the rolling time domain control method [24], the model predictive static programming method [25], and the iterative guidance method [26; 27] to continuously and iteratively correct the trajectory, but they could not effectively solve the problem of the PIP random update in a wide range. Combining the above two types of correction algorithms, we can see that reoptimizing the trajectory method requires a large amount of computation, because the target's PIP will be updated multiple times during the interceptor's guidance process, and the exact coordinates of the next update are unknown; as such, using this method will significantly increase the computation of the computer, and while the second method of correction based on the nominal trajectory is less computationally intensive, it is only applicable to the PIPs updated in a small range. Neither correction method can be applied to the actual situation where the target PIPs are updated in a wide range. In addition, fuel savings in the midcourse guidance need to be considered to ensure that the interceptor has sufficient maneuvering capability in the terminal guidance. To solve the fuel-saving problem of spacecraft in orbit correction and realize energy management, the study in [28] introduced piecewise linear and exponential damping, changing the sensitivity of target maneuvering with the distance between the missile and the target; however, it was mainly aimed at the terminal guidance stage with clear target information, which could not be suitable for the midcourse guidance with uncertain target position information. For the space rendez-vous problem of spacecraft and non-cooperative targets, the differential game was used to describe the pursuit-evasion game problem under continuous thrust in reference [29]. The optimal control and game theory were combined to achieve the optimization of fuel consumption in the process of intercepting non-cooperative targets. However, as the basis for solving this problem, the motion model of non-cooperative targets was clear. In reference [30], an analytical calculation method based on vector form was proposed for the Lambert dual-pulse rendez-vous problem with optimal energy and optimal fuel, and the vector form analytical solution of the Lambert dual-pulse rendez-vous problem with optimal energy and optimal fuel was given, which effectively improved the fuel consumption. The motion models of the targets in the above studies are clear, but in this paper, the target's maneuvering model is unknown, the update law of the PIP is random, the target is active in a discrete and dynamic spatial environment, the prior knowledge is incomplete, and the subsequent information is not clear. Furthermore, to achieve online real-time trajectory correction, then not only must the computer efficiency and correction accuracy be balanced, but the fuel-saving ability of the interceptor must be ensured. In this paper, we propose a midcourse guidance method for guiding the interceptor to the final PIP while reducing fuel consumption. The method takes the HGV as the interceptor target and utilizes the target high probability existence area (THPEA) model to describe the gradual convergence process of the PIP error range, which provides terminal position constraints for midcourse guidance. We adopted the [PERSON] orbit correction method based on the two-body theory for midcourse guidance and designed an engine start-up threshold changing strategy to avoid unnecessary start-ups while meeting the terminal position constraint with low fuel consumption. The main contributions of this study are as follows:  
1.