## 3 Prediction of Manned Aircraft Trajectory in Terminal Areas
### Trajectory Prediction Results of the Manned Aircraft  
To testify the performance of the GRU model, two commonly used trajectory prediction methods are selected as benchmark methods, including the LSTM and SVR models. Since the trajectory prediction results of manned aircraft are mainly used to evaluate the short-term collision risk between manned aircraft and drones, the prediction time length is initially set to be 20 s. Through the model prediction errors, the prediction performances of the three different models are compared for the take-off phase and the landing phase, respectively. A comparison of prediction errors in longitude, latitude, and height are shown in Table 4 and Figure 2.  
The prediction timestep is gradually increased in one second time intervals to obtain the prediction error. It can be seen from Figure 2 that, in the take-off stage, the prediction error of GRU is about 400 m for the 20 s time interval. The prediction error of LSTM is slightly larger than that of GRU. The prediction error of SVR has reached 500 m for the 10 s time interval. This prediction error is generally comparable with the results in previous studies, which ranges from several hundred meters to over 1000 m during the take-off and landing stages [6; 32].  
In the landing stage, for the prediction timestep of 20 s, the prediction error of GRU is about 600 m, the prediction error of LSTM is about 800 m, and the prediction error of SVR is as high as 1000 m. It can be seen that the prediction error of the SVR model is significantly larger than that of the GRU and LSTM models. As the prediction timestep increases, the error shows an overall upward trend. By comparing Figure 2a,b, it can be seen that the error in the landing stage is generally higher than that in the take-off stage, indicating that the manned aircraft trajectory prediction model has better performance in the take-off stage.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Prediction** & **Method** & \
\begin{tabular}{c} _EDE for the Take-Off_ \\ **Stage (m)** \\ \end{tabular} &
\begin{tabular}{c} _EDE for the Landing_ \\ **Stage (m)** \\ \end{tabular} \\ \hline \multirow{3}{*}{5 s s} & GRU & 151.95 & 193.10 \\  & LSTM & 270.44 & 311.81 \\  & SVR & 350.05 & 484.55 \\ \hline \multirow{3}{*}{10 s} & GRU & 292.69 & 411.35 \\  & LSTM & 389.81 & 540.66 \\  & SVR & 524.62 & 740.65 \\ \hline \multirow{3}{*}{15 s} & GRU & 363.65 & 541.06 \\  & LSTM & 425.01 & 728.62 \\  & SVR & 762.20 & 899.54 \\  & GRU & 416.33 & 620.61 \\
20 s & LSTM & 454.67 & 846.69 \\  & SVR & 926.82 & 1085.70 \\ \hline \multirow{3}{*}{25 s} & GRU & 443.99 & 641.25 \\  & LSTM & 501.54 & 870.42 \\  & SVR & 1458.09 & 1831.64 \\ \hline \multirow{3}{*}{30 s} & GRU & 515.81 & 760.49 \\  & LSTM & 602.21 & 896.20 \\  & SVR & 1630.39 & 2060.62 \\ \hline \multirow{3}{*}{35 s} & GRU & 536.05 & 872.92 \\  & LSTM & 660.77 & 935.91 \\  & SVR & 1847.63 & 2486.47 \\ \hline \multirow{3}{*}{40 s} & GRU & 583.63 & 960.82 \\  & LSTM & 725.68 & 955.61 \\ \cline{1-1}  & SVR & 1989.57 & 2603.30 \\ \hline \hline \end{tabular}
\end{table}
Table 4: The prediction error for manned aircraft in the take-off and landing stages.  
Figure 2: Performance comparison for three models.