## 5 Simulation and Analysis
### Algorithm Simulation and Analysis
\[RMSE_{i}=\sqrt{\frac{1}{N}\sum_{k=1}^{N}\left(X^{i}-\hat{X}^{i}\right)^{2}+ \left(Y^{i}-\hat{Y}^{i}\right)^{2}+\left(Z^{i}-\hat{Z}^{i}\right)^{2}} \tag{50}\]  
where \(N\) refers to the number of Monte Carlo simulations, \(X^{i}\), \(Y^{i}\), \(Z^{i}\) refer to the real state of each axis in the \(i\) simulation, and \(\hat{X}^{i}\), \(\hat{Y}^{i}\), \(\hat{Z}^{i}\) refer to the filter estimation value of each axis. The simulation results are as follows. The tracking trajectory of the target is shown in Figure 6. It can be seen that the three algorithms could effectively track the hypersonic target. In order to compare the tracking accuracy of the three algorithms, the position and speed root mean square errors of each axis were simulated, as shown in Figures 10 and 11. Additionally, the comparison table of  
Figure 9: Comparison of algorithm with reference [13]. (**a**) RMSE of position; (**b**) Change of trace value \(K_{k}\) of position gain matrix of Jerk model. the root mean square error and mean value of the three algorithms was obtained through calculation, as shown in Table 1. The model transition probability of IMM-CKF is shown in Figure 12a, and the model transition probability of the algorithm in this paper is shown in Figure 12b. Figure 11: Velocity RMSE of three algorithms: (**a**) RMSE of velocity in the x-axis direction; the RMSE is about 400 m/s; (**b**) RMSE of velocity in the y-axis direction; (**c**) RMSE of velocity in the z-axis direction; (**d**) RMSE of velocity. Figure 10: Position RMSE of three algorithms: (**a**) RMSE of position in the x-axis direction; (**b**) RMSE of position in the y-axis direction; (**c**) RMSE of position in the z-axis direction; (**d**) RMSE of position. As defenders, the velocity tracking error and position tracking error are the main indicators for HTV-2 tracking performance [29; 30; 31]. According to Figures 10 and 11 and Table 1, the RMSE of the \(x\), \(y\), \(z\) positions and speed can be found:  
1. The IMM-CKF and IMM-STCKF algorithms converged faster because the setting error of the initial value of the axis position and speed was small. Due to the large error of the initial value, the convergence time of the two algorithms was about 40 s. In contrast, the AIMM-STCKF algorithm has model adaptability, so the convergence time was significantly faster. Overall, it was about 25 s, and the convergence speed was increased by about 37.5%. 2. The AIMM-STCKF algorithm proposed in this paper significantly improved the accuracy of the algorithm after adding the Markov adaptive matrix. Among the three algorithms, the root mean square error of the speed and position was the smallest, the tracking accuracy was the highest and the variance was small. Overall, the position tracking accuracy was about 16.51% higher than that of the IMM-STCKF algorithm, and the speed tracking accuracy was about 35.74%. 3. Since there was no obvious mutation in the state of the hypersonic target, the accuracy of the strong tracking algorithm was low. In contrast, the strong tracking algorithm based on adaptive model interaction could accelerate the model transformation and enhance the adaptive matching ability, so the convergence speed and tracking accuracy were better. By comparing the probability transfer diagram of the model, the following can be found: 1. As the maneuverability of the hypersonic target decreased, the probability of the Singer model with weak maneuverability gradually increased. As the maneuverability of the hypersonic target increased, the probability of the [PERSON] model with strong maneuverability gradually increased.