# In-flight Wind Field Identification and Prediction of Parafoil Systems
## 5 Simulation and Analysis
### Simulation of Wind Field Identification  
Under conditions of different deflections and wind fields, wind field identifications are conducted, and the results are shown in Table 2.  
From Table 2, we observe that the identification results are substantially equal to the applied wind field vectors, which indicates that the proposed method is feasible to identify the ambient wind velocity of parafoil systems. As for practical in-flight identification of the wind field, by calculating the lateral position data collected by GPS, the average wind field information at different altitudes are obtained. According to the relative errors \(e_{r}\), especially from 4 to 6, we can see that with the increase of deflection, the relative errors increase. The best results appear when the deflection is 20%. Thus, to get better wind field identification results, it is best to keep the deflection at 10% to 30%.  
Furthermore, we investigate the identification accuracy corresponding to different unilateral deflections. A crosswind with an average speed of 4.472 m/s and a direction of 1.1071 rad is added into the simulation environment, different unilateral deflections of 5%, 10%, 20%, 30%, 40%, 50%, 60%, 70%, 80% are applied to the parafoil system. The results are shown in Figure 7. We see that when the unilateral deflection is too small or large, the wind field identification error is large. As the unilateral deflection is 20%, the speed and direction identification errors are the smallest, i.e., the identification accuracy reaches the highest.  
\begin{table}
\begin{tabular}{l l l l l} \hline \hline
**No.** & **Deflection (Left, Right)** & **Wind Velocity Vector \(v_{user}\) (m/s)** & **Identification** & **Result** & \(v_{wild}\) & **Relative Error \(e_{r}\)** \\  & & & **(m/s)** & & \\ \hline
1 & (10\%, 0\%) & (2.0, 4.0) & (2.1510, 3.8600) & (7.55\%, 3.5\%) \\
2 & (30\%, 0\%) & (\(-\)2.0, \(-\)5.0) & (\(-\)2.0735, \(-\)4.9470) & (3.68\%, 1.06\%) \\
3 & (60\%, 0\%) & (2.0, \(-\)4.0) & (1.7385, \(-\)4.8084) & (13.07\%, 20.21\%) \\
4 & (0\%, 20\%) & (2.0, 4.0) & (2.0150, 3.9757) & (0.75\%, 0.61\%) \\
5 & (0\%, 30\%) & (2.0, 4.0) & (2.1546, 3.7059) & (7.73\%, 7.35\%) \\
6 & (0\%, 60\%) & (2.0, 4.0) & (1.7385, 4.8084) & (13.08\%, 20.21\%) \\ \hline \hline \end{tabular}
\end{table}
Table 2: Simulation settings and wind field identification results.  
Figure 7: Error distribution under unilateral deflection. (**a**) Speed error distribution. (**b**) Direction error distribution.  
Furthermore, the same cross wind with the speed of 4.472 m/s and the direction of 1.1071 rad is added in the simulation environment, and 20% unilateral deflection is applied to the parafoil system. The wind field identification results are shown in Figure 8. The results show that after adding of deflection control, the wind field caused significant disturbances to the airspeed of the parafoil system in the early stage when the error of the wind field identification is large. As the flight state of the parafoil system gradually stabilizes, the identification result converges rapidly and enters a stable state after 90 s. The average wind speed identification error is 0.1 m/s, and the wind direction error is close to 0 rad, which indicates high identification accuracy.