## 5 Discussion  
From Tables 1 and 2 we can see that the hybrid model algorithm has the best \(V\) ARMSE and \(V\) PRMSE in these algorithms, because the fixed coarse grid (multiple model) is good for reducing the \(V\) RMSE caused by the uncertain initial control variables and the fine grid (single model) is good for reducing the \(V\) RMSE caused by excessive \"competition\" from the \"unnecessary\" models in the stable tracking stage. However, the \(r\) ARMSE using the hybrid model algorithm is a bit higher than that using the single model algorithm and the \(r\) PRMSE using the hybrid model algorithm is about the same as that using the multiple model algorithm. In the initial tracking stage, using the multiple model results in a bigger \(r\) RMSE because it is slow that the changes of the speed propagate to that of the position in a nonlinear system with excessive models, and the fixed coarse grid does not come into effect in the initial tracking stage. The higher \(r\) PRMSE using the hybrid model algorithm is caused by the multiple model algorithm in the initial tracking stage. The \(r\) ARMSE using the hybrid model algorithm is about 1.6% greater than that using the single model algorithm. However, the \(V\) RMSE using the single model algorithm is about 30% greater than that using the hybrid model algorithm. The numbers of the model filters mainly determine the computational cost of the HGV tracking algorithm. There is only one model filter in the single model algorithm and there are nine model filters in the multiple model algorithm. Obviously, the computational cost of the hybrid model algorithm is slightly higher than that of the single model algorithm but much lower than that of the multiple model algorithm. It is acceptable that the \(V\) accuracy is improved significantly with the slightly higher computational cost. In a system for defending HGVs we take more consideration of the speed accuracy in the whole tracking stage and the position accuracy in the stable tracking stage, because we need to launch the interceptor missile in the stable tracking stage and the speed accuracy has more effect on the trajectory prediction as time goes on. From Figures 3 and 4, we can know that the \(V\) RMSE and \(r\) RMSE using the hybrid algorithm are quick to converge. The hybrid model algorithm has the lowest \(V\) RMSE in these algorithms and about the same \(r\) RMSE as the single model algorithm. Thus, the hybrid model algorithm is the best choice for HGV tracking of the three algorithms. The hybrid model algorithm may be promising for some general-maneuvering target tracking, which will be studied in future research. **Acknowledgments:** The authors would like to thank all the reviewers for helping improve the clarity of the presentation of this paper. This work is supported by the National Key Technology Support Program of China (2015 BAK34B02). \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Algorithm** & \(V\) **ARMSE (m/s)** & \(V\) **PRMSE (m/s)** & \(r\) **ARMSE (m)** & \(r\) **PRMSE (m)** \\ \hline Multiple model & 5.30 & 17.96 & 74.18 & 214.09 \\ Single model & 3.89 & 15.33 & 61.36 & 164.95 \\ Hybrid model & 2.95 & 9.49 & 62.34 & 217.18 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The performances for tracking scenario 1, ARMSE: average root mean square error; PRMSE: peak root mean square error. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Algorithm** & \(V\) **ARMSE (m/s)** & \(V\) **PRMSE (m/s)** & \(r\) **ARMSE (m)** & \(r\) **PRMSE (m)** \\ \hline Multiple model & 5.29 & 16.26 & 70.87 & 219.16 \\ Single model & 4.04 & 15.69 & 59.70 & 161.32 \\ Hybrid model & 2.91 & 9.88 & 60.63 & 214.73 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The performances for tracking scenario 2. **Author Contributions:** [PERSON] designed and performed the experiments, analyzed the data and wrote the paper. [PERSON] and [PERSON] are supervisors of [PERSON], and revised the paper. [PERSON], [PERSON] revised the paper. **Conflicts of Interest:** The authors declare no conflict of interest.