# Correction Strategy of Online Midcourse Guidance for High-Speed Gliding Target Interceptor
## 3 Design of Online Dynamic Correction Strategy for Interceptor  
### The Description of THPEA  
In the actual interception process, the longer the defender tracks, the more trajectory information is obtained, and the accuracy of the trajectory prediction improves accordingly. This indicates that the PIP is constantly updated. In this paper, we refer to all areas where PIP may occur as targeting high probability existence areas (THPEA). As the warning detection system becomes more accurate, the THPEA will continue to reduce, which is consistent with an increase in target detection information. The calculation of the PIP position coordinates requires the estimation of target measurement information, target state continuous tracking, and prediction. If the instant of midcourse and terminal guidance trajectory transition is \(t_{e}\), the instant of the early warning system that starts to track the target is \(t_{0}\), then the total flight time satisfied \(t_{f}=t_{e}-t_{0}\). The target trajectory tracking refers to the extraction of the target measurement information with noise between the initial tracking instant \(t_{0}\) and the current instant \(t\) by the early warning detection system, and the duration is \(t-t_{0}\). According to the extracted target state information, different model sets are selected, and the model set and interactive multi-model algorithm are used to track the real trajectory of the target. Then, the future flight trajectory of the target is predicted based on the current state estimation and the model probability of each model set. The prediction stage starts from the current instant \(t\) and finishes at the transition instant \(t_{e}\), which indicates that the interceptor needs to predict the flight trajectory of the target in the future time \(t_{e}-t\), and the target prediction trajectory is extrapolated to determine the PIP and the THPEA. Since there is no measurement information of the target during the period \([t,t_{e}]\), the prediction of the target trajectory at the future time will show a divergent trend: the longer the prediction time is, the larger the error is. The work in each stage and the work timing relationship are shown in Figure 4.  
The mathematical expectation of the target position coordinates under the \(x,y,z\) axes is \(\left[u_{x}u_{y}u_{z}\right]\), and the variance is \(\left[\sigma_{x}\sigma_{y}\sigma_{z}\right]\). The three-position coordinates of the target are independent from each other. In reference [32], the coordinates obey Gaussian distribution, and the probability density function of the target position at a certain time is  
\[f_{k}(x,y,z)=f_{k}(x)f_{k}(y)f_{k}(z) \tag{18}\]  
among them  
\[f_{k}(x)=\frac{1}{\sqrt{2\pi\sigma_{x}}}\text{exp}(\,-\frac{(x-\mu_{x})^{2}}{ 2\sigma_{x}}) \tag{19}\]  
\[f_{k}(y)=\frac{1}{\sqrt{2\pi\sigma_{y}}}\text{exp}(\,-\frac{(y-\mu_{y})^{2}}{ 2\sigma_{y}}) \tag{20}\]  
Figure 4: Time-series relationships for target trajectory prediction. In the tracking stage, the measurement information of the target can be obtained, and the trajectory prediction is to predict the trajectory of the target in the prediction stage by the measurement information in the tracking stage. \[f_{k}(z)=\frac{1}{\sqrt{2\pi\sigma_{z}}}\text{exp}(-\frac{(z-\mu_{z})^{2}}{2\sigma_ {z}}) \tag{21}\]  
therefore, when the target tracking state converges, according to the \(3\sigma\) rule, the probability of the target position distributed in \((u-\sigma,u+\sigma)\) is 0.6827, the probability distributed in \((u-2\sigma,u+2\sigma)\) is 0.9545, and the probability distributed in \((u-3\sigma,u+3\sigma)\) is 0.9973. It can be considered that the target position is almost entirely concentrated in the three ellipsoid regions with the mathematical expectation coordinate as the center and the axial direction of \(3\sigma\). Therefore, the target THPEA (region) is defined as follows:  
**Definition 1**.