## 4 Simulation Results  
In this section, two representative scenarios will be generated as HGV maneuvering trajectories and tracked using the above three algorithms. In order to make the simulation results objective and practical, we choose the average values of the variation ranges of the two control variables as the initial states. We generate the HGV trajectory using the following initial augmented state: \(V=6000\) m/s; \(\theta=-5.73^{\circ}\); \(\sigma=0^{\circ}\); \(r=6.378\times 10^{6}+50\times 10^{3}\) m; \(\lambda=0^{\circ}\); \(\phi=0^{\circ}\). Furthermore, the HGV makes skipping longitudinally flight at the fixed AOA \(10^{\circ}\). To validate the effectiveness of the HGV maneuvering trajectory tracking algorithms proposed in this paper, two lateral maneuvering methods are given from  
\[\left\{ \begin{array}{c}\
u=20^{\circ},V>V_{1}\\ \
u=0^{\circ},V_{2}<V<V_{1}\\ \
u=-20^{\circ},V<V_{2}\end{array} \right. \tag{12}\]  
\[\
u=20\sin(t\pi/40) \tag{13}\]  
where \(V_{1}=5000\) m/s and \(V_{2}=4500\) m/s; \(t\) denotes the flight time. Equation (12) shows the HGV maneuvers laterally at the biggest degree. Equation (13) shows the HGV maneuvers laterally with the bank angle changing in the sine law with a period of 80 s and an amplitude of \(20^{\circ}\). Then two HGV trajectory scenarios can be generated as shown in Figure 2.  
Figure 2: Hypersonic glide vehicle (HGV) maneuvering trajectory. In Figure 2, scenario 1 is generated based on Equation (12) and scenario 2 is generated based on Equation (13). From Figure 2 we can know that the HGV maneuvers laterally more strongly when the bank angle changes according to Equation (12). We set that the radar is located at the position: \(r=6.378\times 10^{6}+200\) m; \(\lambda=-5.625^{\circ}\); \(\phi=11.25^{\circ}\). The standard deviation of the radar measurement errors is set as  
\[\left[ \begin{array}{cc}\sigma_{R}&\sigma_{A}&\sigma_{E}\\ \end{array} \right]=\left[ \begin{array}{cc}10\;\mbox{m}&0.0286^{\circ}&0.0286^ {\circ}\\ \end{array} \right] \tag{14}\]  
Every process noise covariance matrix in all tracking models is set as  
\[Q=diag\Big{(}\Big{[}5^{2},0.0573^{2},0.0573^{2},50^{2},0.000573^{2},0.000573^{ 2},0.01^{2},0.01^{2}\Big{]}\Big{)} \tag{15}\]  
In the algorithm simulation, the time interval \(T\) is 0.1 s. In addition, the initial state for all HGV tracking algorithms is set as  
\[X_{0}=\left[ \begin{array}{cc}6000&-5.73&0&(6.378\times 10^{6}+50\times 10^{3}) &0&0&9&0\\ \end{array} \right] \tag{16}\]  
Based on the set about the radar and the initial state, the turning point from the multiple model algorithm to the single model algorithm is approximately \(t_{s}=17.9\)s. So we use approximately \(t_{s}=20\)s in the hybrid model algorithm for HGV tracking. The model switching probability \(\rho_{ij}\) for the multiple model algorithm is a constant matrix with a large value on the diagonal elements. The nine-model switching probability for the nine-model IMM algorithm can be set as  
\[\rho_{ij}=\left\{ \begin{array}{c}0.6,i=j\\ 0.05,i\
eq j\\ \end{array} \right. \tag{17}\]  
The initial model probability for the nine-model tracking algorithm is taken assuming the first model is near to the real model of the HGV, that is:  
\[\omega_{0}^{j}=\left\{ \begin{array}{c}0.2,j=1\\ 0.1,\mbox{otherwise}\\ \end{array} \right. \tag{18}\]  
Then we can conduct HGV tracking using the three algorithms mentioned above and run 100 Monte-Carlo simulations for every algorithm on each trajectory. We use the root mean square error (RMSE) of the position and velocity to contrast the performances of the different tracking algorithms.