# Intelligent Trajectory Prediction Algorithm for Reentry Glide Target Based on Intention Inference
## 3 Parameter Value Prediction Network
### Association Models between Strategic Places and Trajectory
#### 4.2.2 Realization Method  
(1) Calculation of reach region. In order to calculate the reach region, the modified last state in Section 3 is taken as the initial state of integration of trajectories. According to the prediction control parameter \(K_{Dp},K_{Lp}\) based on the parameter value prediction network, the constant bank angle is combined, which selects a value uniformly within \([-\pi/2,\pi/2]\) at a fixed step size. Let the setting height as the terminal condition, then a bunch of trajectories is obtained when the lateral position and reaching time of terminal state are recorded. The projection position of the reachable region is shown in Figure 5a. In order to determine whether the target is within the reachable region, the lateral position is fitted with ellipse function \(A\phi^{2}+B\phi\varphi+C\varphi^{2}+D\phi+E\varphi+F=0\) when \(A>0\). Assuming that the position of \(i-th\) key point is \([\phi_{i},\varphi_{i}]\), if \(A\phi_{i}^{2}+B\phi_{i}\varphi_{i}+C\varphi_{i}^{2}+D\phi_{i}+E\varphi_{i}+F<0\), it means that the key point is within reachable region, and the time-to-go needs to be estimated, while if \(A\phi_{i}^{2}+B\phi_{i}\varphi_{i}+C\varphi_{i}^{2}+D\phi_{i}+E\varphi_{i}+F<0\), the time-to-go is setting to infinity. Moreover, as can be seen from Figure 5b, by connecting the lateral position of different trajectories at the same time, the bank angle-time grid can be obtained, which is useful to calculate the bank angle for the key points \(\beta_{k}\) and mapping corridor of no-fly zones. (2) Calculation of the bank angle and time-to-go for key points. Obtain the nearest grid position to the key point within the reachable region \([\phi_{b,t}^{\prime},\varphi_{b,t}^{\prime}]\), and compare the distance between \([\phi_{b,t}^{\prime},\varphi_{b,t}^{\prime}]\) and key point position with \([\phi_{b-1,t}^{\prime},\varphi_{b-1,t}^{\prime}]\), \([\phi_{b+1,t}^{\prime},\varphi_{b+1,t}^{\prime}]\), \([\phi_{b,t+1}^{\prime},\varphi_{b,t+1}^{\prime}]\) and \([\phi_{b,t-1}^{\prime},\varphi_{b,t-1}^{\prime}]\), by which the grid position key point location can be determined. Then, through interpolation, the bank angle of key point can be obtained, and the time of nearest grid position \(t\) can be seen as the time-to-go of key point \(t_{\text{t}}\). (3) Calculation of mapping corridor of no-fly zones. The influence of no-fly zones should be considered when the centre of no-fly zones is within the reachable region. Calculate the minimum distance \(d_{\beta i}\) and the corresponding time \(t_{\beta i}\) between the trajectories of each bank angle \(X_{\beta i}\) and the centre of no-fly zones, where \(i=1:N\), and \(N\) is the number of setting bank angle. Then, assuming that the distance between trajectories and no-fly zones is \(\Delta d\), \(\Delta d_{i}=R_{b}-d_{\beta i}\). The \((p-1)-th\) and  
Figure 5: Reachable region and bank angle-time grid: (**a**) represents the reachable region; (**b**) represents the bank angle-time grid. \(p-th\) trajectories that satisfy \(\Delta d_{p-1}\Delta d_{p}<0\) are selected to estimate the bank angle of tangent trajectory for no-fly zones \(\beta_{b}\). \[\beta_{b}=\frac{\left|\Delta d_{p-1}\right|\beta_{p}+\left|\Delta d_{p}\right| \beta_{p-1}}{\left|\Delta d_{p}\right|+\left|\Delta d_{p-1}\right|} \tag{8}\]  
The estimated tangent time is \(t_{gb}\), which represents the time when the trajectory of \(\beta_{b}\) is closest to the no-fly zones. The relationship between the no-fly zone and the reachable region can be divided into full inclusion and partial inclusion. When one boundary of the no-fly zone is out of the reachable zone, as shown in Figure 6a,c, the tangent point on one side should be discussed. When the no-fly zone and the reachable zone are shown in Figure 6b, the positions of tangential points on both sides of the no-fly zone need to be determined. The corridor condition can be expressed as  
\[\left\{