# Intelligent Trajectory Prediction Algorithm for Reentry Glide Target Based on Intention Inference
## 5 Intelligent Trajectory Prediction Algorithm Based on Intention Inference
### Factors Influencing the Target Threat Value  
Since the target may adopt different lateral guidance logic and avoid methods, the lateral guidance law of the target does not change completely as the threat value increases. The trajectory of the target may not meet the Markov process, such as the predictor-corrector guidance algorithm. Aimed at this problem, several influencing factors related to the threat value should be analyzed according to the observation data, and it should be determined which key point is the attack position of the target. What is more, the attack process is a guidance process of reentry glide targets. Referring to the common guidance methods of reentry targets [23], the prediction of target attack intention is realized from the guidance theory. In this paper, the cross-range, longitudinal range, time-to-go and relative importance of different strategic places are selected as influencing factors to evaluate the threat value of targets. 1. Analysis of the influence of cross-range. According to the analysis of lateral guidance logic, the cross-range between the target and key points [28] can effectively reflect the lateral guidance effect of the target. The formula of cross-range is as follows: \[\chi_{i}=\arcsin\Bigl{(}\sin\Bigl{(}S_{fi}\Bigr{)}\sin(\Delta\psi_{i})\Bigr{)}\] (11) where \(\chi_{i},S_{fi},\Delta\psi_{i}\) respectively represent the cross-range, range-to-go and flight heading deviation angle of \(i-th\) key point. Furthermore, \(S_{fi}=\arccos(\cos\varphi_{f}\cos\varphi\cos(\phi_{f}-\phi)+\sin\varphi_{f} \sin\varphi)\), \(\psi_{f}=\arcsin\Bigl{(}\sin(\phi_{f}-\phi)\cos\varphi/\sin\Bigl{(}S_{logo_{ f}}\Bigr{)}\Bigr{)}\), \(\Delta\psi_{f}=\psi-\psi_{f}\). In general, the cross-range is smaller, the threat value of the target for the key point is higher, and the threat value is inversely proportional to the cross-range. 2. Analysis of the influence of longitudinal range In order to analyze the longitudinal guidance of the target, the flight height should decrease as the range-to-go decreases. To reflect the longitudinal effect, the longitudinal range of \(i-th\) key point at time \(t\) is defined as \[Z_{i,t}=\left\{ \begin{array}{l}H_{t}/\sin\Bigl{(}S_{fi,t}\Bigr{)},if\ 0< Z_{i,1,\ldots t-1}<1\\ 0,if\ Z_{i,1\ldots t-1}\geq 1\ \text{or}\ Z_{i,1\ldots t-1}=0\end{array} \right.\] (12)  
Generally, if the target intends to attack the key point, the longitudinal range should increase gradually to close to 1. When the range-to-go is less than the flight height in the observation flight trajectory, it means that the target has crossed the center of strategic places, and the threat value of this key point decreases to 0 immediately. Therefore, when \(Z<1\), the longitudinal range is higher, the threat value is higher, and it is proportional to the longitudinal range. 3. Analysis of time-to-go. For the convenience of analysis, the time-to-go calculated through the trajectories association model in Section 4 is nondimensionalized; \(\tau_{fi}=t_{f_{i}}\sqrt{g_{0}/R_{e}}\). The time-to-go is smaller, the threat value is higher and it is inversely proportional to the time-to-go. 4. Analysis of relative importance. According to the analysis of the importance map of the target in Section 4.1, when the reachable region of the target changes, the relative importance of each strategic place is calculated as follows:  
\[I_{i}^{\prime}=\left\{ \begin{array}{l}\int\limits_{i}\pi_{i}f_{i}(\phi,\varphi )d_{\varphi}d_{\varphi}/\sum\limits_{i=1}^{n}\int\limits_{\Omega}\pi_{i}f_{i}( \phi,\varphi)d_{\varphi}d_{\varphi},if\text{ key point is the center of strategic place}\\ \sum\limits_{i=1}^{n}\int\limits_{\Omega}\pi_{i}f_{i}(\phi,\varphi)d_{\varphi }d_{\varphi}/q\sum\limits_{i=1}^{n}\int\limits_{\Omega}\pi_{i}f_{i}(\phi, \varphi)d_{\theta}d_{\varphi},if\text{ key point is generated newly}\\ \end{array} \right. \tag{13}\]  
\[I_{i}=I_{i}^{\prime}/\sum\limits_{i}^{n}I_{i}^{\prime} \tag{14}\]  
where \(\Omega\) represents the predicted reachable region.