## 5 Simulation and Analysis
### Algorithm Simulation and Analysis  
(1) Algorithm simulation verification  
The strong tracking algorithm is verified against the state mutation of maneuvering target (Figure 6):  
As can be seen from Figure 7, the target has a state mutation at time 40 and 135. The RMSE of the traditional IMM-CKF is obvious when the state mutation occurs, and the tracking accuracy is reduced. The strong tracking algorithm based on multiple fading factors proposed in this paper can improve the tracking accuracy by adjusting the gain  
Figure 5: HTV-2 trajectory. The blue track part shows the entire movement process of the hype-sonic target in a step jump process, and the red track part shows the radar observation period. Figure 6: Tradition target maneuver trajectory. The traditional target has two state changes during maneuver, and IMM-CKF and IMM-STCKF track it. matrix in real time, so that it can reduce the impact of state mutation residual. Therefore, the following simulation results can be obtained by applying the algorithm in this paper to the strong maneuver phase of the hypersonic target trajectory. As shown in the Figure 8, three algorithms are used to simulate and verify the strong maneuvering segment of the hypersonic target. It can be seen from the trajectory tracking graph of X, Y, Z axes that the three algorithms have achieved effective tracking. The algorithm proposed in this paper has the highest tracking accuracy in the three axes. It is obvious from the z-axis tracking process that the hypersonic target has a strong maneuver in about 150 s. The algorithm proposed in this paper can reduce the impact of state mutation and improve the tracking accuracy. According to the strong maneuvering phase of the hypersonic target, the algorithm in this paper is compared with the recent literature:  
Figure 8: Trajectory tracking of hypersonic target. (**a**) Hypersonic target strong maneuver phase; (**b**) X-axis trajectory tracking; (**c**) Y-axis trajectory tracking; (**d**) Z-axis trajectory tracking. Figure 7: RMSE of position (**a**) and velocity (**b**). The red line is RMSE of IMM-CKF, the blue line is RMSE of IMM-STCKF. Compared with the reference [13], this paper proposed adaptive IMM. The comparative simulation results are as follows (Figure 9):  
From the experimental simulation results, it can be seen that the tracking accuracy of the algorithm in reference [13] is lower than AIMM in this paper, and the mean square error variance is large. Take the Jerk model as an example, it can be seen from the change trend of the trace value of the position gain matrix in the figure that at time t = 158-164 s, the trace value of the position gain matrix has a sudden change, and the model state has changed; The gain matrix \(K_{k}\) trace value of the algorithm in this paper changes less than that of the algorithm in reference [13], so the adaptability of the model matching degree is enhanced. (2) Hypersonic target tracking simulation  
Take the weak maneuver phase as an example, the hypersonic target tracking algorithm is simulated. The initial value of the hypersonic target was set as \(x_{0}\) = [\(-\)719,000, 4270, 1, 0.2, 233,000, \(-\)1530, \(-\)0.6, 0.3, 199,000, 1030, \(-\)5.9, 0.5], and the target maneuvering frequency was set as \(\alpha=1/20\). In the CS model, the maximum and minimum accelerations of the \(x\) axis, \(y\), axis and \(z\) axis were, respectively, \(\pm\)700 m/s\({}^{2}\), \(\pm\)500 m/s\({}^{2}\), and \(\pm\)200 m/s\({}^{2}\), and the observation noise covariance matrix was set as \(\mathbf{R}=\text{diag}[0.5^{2}\quad 0.5^{2}\quad 500^{2}]\). In the IMM algorithm, the initial probability matrix of the model was \(\mathbf{u}_{1}= \begin{bmatrix}1/3&1/3&1/3\end{bmatrix} \), and the initial Markov transition probability matrix was  
\[\mathbf{P}_{1}= \begin{bmatrix}0.9&0.05&0.05\\ 0.05&0.9&0.05\\ 0.05&0.05&0.9\end{bmatrix}  \tag{49}\]  
After conducting 100 Monte Carlo simulations, the performance of the algorithm was measured by the root mean square error (RMSE) and the mean value of the RMSE.