## 4 Results and Discussion
### Estimation Accuracy--Side Gusts
The delay also increases, going from 0.38 s to 0.56 s. When the time constant is further increased to 1.0 s, the estimation aligns most closely with the baseline in terms of the gust peak value, though the delay grows to 0.64 s. A final increase to a time constant of 1.5 s results in poorer numerical accuracy, leading to an underestimation. Reviewing the numerical labels on the arrows in Figure 43 enables a precise comparison of the minimum values for the selected decaying gust scenario. With a time constant of 0.5 s, the minimum value deviates by 2.85 m/s in the full estimation and by 3.93 m/s in the low-frequency estimation. The corresponding delays relative to the reference measurement are 0.5 s and 0.16 s, respectively. In this scenario, increasing the time constant results in progressively more accurate adjustments to the minimum value. The closest match to the reference measurement is observed at a time constant of 1.5 s, with a deviation of only 0.34 m/s. However, when considering the remaining gusts, their values are underestimated, indicating a general trend of underestimation. Thus, for both rising and falling gust conditions, the time constant of 1.0 s offers the most accurate velocity values. Nonetheless, this comes with an expected increase in delay, reaching approximately 0.65 s compared to shorter time constants. The third case analyzed to evaluate the side gust estimation algorithm using complementary filtering involved climbing through a layer of head-on gusts. Three data ranges were selected for graphical presentation: the entire simulation (0-180 s), a series of selected gusts (55-95 s), and a single gust (65-80 s). \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**F. Phase**} & \multirow{2}{*}{**Rising Gust Speed**} & \multicolumn{3}{c}{**Weakening Gust Speed**} & \multicolumn{2}{c}{**Average Values**} \\  & & & \multicolumn{2}{c}{**Speed**} & & \\ \hline
**T\({}_{\text{cu}}\)** & **Difference** & **Delay** & **Difference** & **Delay** & **Difference** & **Delay** \\ \hline D/T\({}_{\text{cu}}\) = 0.5 s & 1.01 m/s & **0.79 s** & \(-\)0.68 m/s & **0.03 s** & 0.165 m/s & **0.41 s** \\ D/T\({}_{\text{cu}}\) = 0.8 s & **0.11 m/s** & 0.93 s & \(-\)0.37 m/s & 0.20 s & **-0.13 m/s** & 0.565 s \\ D/T\({}_{\text{cu}}\) = 1.0 s & \(-\)0.41 m/s & 0.99 s & \(-\)0.20 m/s & 0.33 s & \(-\)0.305 m/s & 0.66 s \\ D/T\({}_{\text{cu}}\) = 1.5 s & \(-\)1.42 m/s & 1.10 s & **0.12 m/s** & 0.43 s & \(-\)0.65 m/s & 0.765 s \\ \hline L/T\({}_{\text{cu}}\) = 0.5 s & 2.54 m/s & **0.38 s** & \(-\)2.85 m/s & **0.50 s** & **-0.155 m/s** & **0.44 s** \\ L/T\({}_{\text{cu}}\) = 0.8 s & 1.20 m/s & 0.56 s & \(-\)1.61 m/s & 0.60 s & \(-\)0.205 m/s & 0.58 s \\ L/T\({}_{\text{cu}}\) = 1.0 s & **0.45 m/s** & 0.64 s & \(-\)0.92 m/s & 0.66 s & 0.235 m/s & 0.65 s \\ L/T\({}_{\text{cu}}\) = 1.5 s & \(-\)0.91 m/s & 0.64 s & **0.34 m/s** & 0.76 s & \(-\)0.285 m/s & 0.70 s \\ \hline C/T\({}_{\text{cu}}\) = 0.5 s & \(-\)1.15 m/s & **0.43 s** & 0.92 m/s & **0.49 s** & \(-\)0.115 m/s & **0.46 s** \\ C/T\({}_{\text{cu}}\) = 0.8 s & \(-\)0.44 m/s & 0.58 s & **0.14 m/s** & 0.61 s & **-0.15 m/s** & 0.595 s \\ C/T\({}_{\text{cu}}\) = 1.0 s & **0.03 m/s** & 0.65 s & \(-\)0.33 m/s & 0.68 s & \(-\)0.15 m/s & 0.665 s \\ C/T\({}_{\text{cu}}\) = 1.5 s & 0.93 m/s & 0.77 s & \(-\)1.39 m/s & 0.78 s & \(-\)0.23 m/s & 0.775 s \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Computational comparison of the selected peak gusts values for complete sidewind estimation with reference measurements for different time constants and flight phases (D—descent, L—level flight, C—climb). Data analysis (Figures 44-46) shows that a time constant of 1.0 s provides the most accurate estimation results compared to the reference measurement. A numerical comparison, based on the arrows annotated with values for selected gusts in Figures 45 and 46, supports this observation. Similar to the two earlier flight conditions, the optimal estimation for lateral gusts is achieved with a time constant of 1.0 s during rising gusts and 0.8 s during falling gusts.