# Correction Strategy of Online Midcourse Guidance for High-Speed Gliding Target Interceptor
## 1 Introduction  
With their high speed, high maneuverability, and a large airspace, high-speed gliding vehicles (HGVs) pose significant challenges for defense systems. Multi-stage guidance for the interceptor is an effective method, and the entire flight of the interceptor can be divided into three stages: the boost stage, the midcourse guidance stage, and the terminal guidance stage. The main role of the boost stage is to make the interceptor lift off quickly. The midcourse guidance stage guides the interceptor to the vicinity of the HGV based on limited target information. Once the target seeker turns on and discovers the HGV after meeting the position constraint, the interceptor enters the handover of midcourse and terminal guidance, and the terminal guidance stage uses the information obtained by the target seeker to achieve the final intercept. The midcourse guidance plays an important role in determining whether the interceptor can successfully enter the terminal guidance stage to capture the target. The method based on the predicted intercept point (PIP) is a common approach in midcourse guidance for guiding the interceptor to the vicinity of PIP [1, 2]. However, factors such as the detection accuracy, prediction accuracy of the target trajectory, and target avoidance maneuver may prevent the defense system from determining the final PIP at one time. There will be more than one continuously updated PIP during the interceptor's flight, and the interceptor has to make trajectory corrections according to the updated PIPs. As shown in Figure 1, the interceptor corrects the trajectory twice in the midcourse guidance stage due to two PIP updates. When the PIP is updated for the third time, the interceptor flies near the target and enters the terminal guidance stage. This figure is only a schematic diagram, and the actual process will have more than three PIP updates. When the trajectory prediction is more accurate, the defense system can obtain more precise PIP location information. Although some researchers have studied the problem of predicting target trajectories [3; 4; 5], no study has been able to accurately predict a target's trajectory. With the arrival of HGVs, the amount of target information and trajectory prediction accuracy increases, leading to discrete updates of PIP during the flight of the interceptor in midcourse guidance. The PIP at one moment may differ significantly from the next, making continual corrections necessary until the terminal seeker captures the target. Based on this analysis, the two main difficulties of the problem are:  
1. Uncertainty in PIP updates during midcourse guidance. To overcome the uncertainty and reach, the true PIP vicinity at the end of the midcourse, the interceptor must continually modify its trajectory with online correction strategies. 2. The need to conserve energy during midcourse guidance by avoiding unnecessary maneuvers. Direct force maneuvering would still require fuel in the terminal guidance stage. Therefore, the key is to formulate an online correction strategy for the interceptor when PIP is randomly updated, ensuring that the interceptor reaches the terminal guidance with a certain level of accuracy while saving fuel and leaving a sufficient maneuvering margin in the terminal guidance stage. When the trajectory tracking error is large or the target maneuvers, the interceptor needs to correct the existing flight trajectory. There are two types of correction algorithms applied to the trajectory correction problem. The first type is to re-optimize a trajectory for the interceptor, and some researchers propose the method of the online re-optimization trajectory according to the changes of state and constraint. In [6], an improved zero effort miss and zero effort velocity (ZEM/ZEV) guidance law was proposed for the guidance of anti-ballistic missiles outside the atmosphere. According to the updated terminal conditions, a flight trajectory was re-optimized.