## 4 Results and Discussion
### Estimation Accuracy--Vertical Gusts
Two data ranges were selected for graphical analysis: the entire simulation (0-100 s) and the narrowed range during vertical gust occurrence (simulation time 45-75 s). The CF results reflect the influence of varying the time constant \(\mathrm{T_{cw}}\) on the estimation performance. For analysis, the same time constants were selected for comparison. Data analysis based on Figures 49 and 50 indicates that time constants of 0.5 s and 1.0 s provided the closest match between the estimated results and the reference measurement. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**F. Phase**} & \multirow{2}{*}{**Rising Gust Speed**} & \multicolumn{2}{c}{**Weakening Gust Speed**} & \multicolumn{2}{c}{**Average Values**} \\ \hline \(\mathbf{T_{cu}}\) & **Difference** & **Delay** & **Difference** & **Delay** & **Difference** & **Delay** \\ \hline D/\(\mathrm{T_{cu}}\) = 0.5 s & \(-\)0.90 m/s & \(\mathbf{-0.50}\) s & 0 & 3.07 s & \(-\)0.45 m/s & **1.285 s** \\ D/\(\mathrm{T_{cu}}\) = 1.0 s & \(-\)0.35 m/s & 1.09 s & 0 & 1.91 s & \(-\)0.175 m/s & 1.5 s \\ D/\(\mathrm{T_{cu}}\) = 1.2 s & \(\mathbf{-0.11}\) ms/s & 1.52 s & 0 & 1.67 s & \(\mathbf{-0.055}\)**m/s** & 1.595 s \\ D/\(\mathrm{T_{cu}}\) = 1.5 s & 0.19 m/s & 1.59 s & 0 & **1.56 s** & 0.095 m/s & 1.575 s \\ \hline L/\(\mathrm{T_{cu}}\) = 0.5 s & \(\mathbf{-0.05}\) ms/s & \(\mathbf{0.56}\) s & 0 & 1.74 s & \(\mathbf{-0.025}\)**m/s** & 1.15 s \\ L/\(\mathrm{T_{cu}}\) = 1.0 s & 0.13 m/s & 0.90 s & 0 & 1.05 s & 0.065 m/s & 0.975 s \\ L/\(\mathrm{T_{cu}}\) = 1.2 s & 0.17 m/s & 0.91 s & 0 & **0.91 s** & 0.085 m/s & **0.91 s** \\ L/\(\mathrm{T_{cu}}\) = 1.5 s & 0.12 m/s & 0.90 s & 0 & 1.05 s & 0.06 m/s & 0.975 s \\ \hline C/\(\mathrm{T_{cu}}\) = 0.5 s & 0.43 m/s & \(\mathbf{0.92}\) s & 0 & 1,48 s & 0.215 m/s & 1.2 s \\ C/\(\mathrm{T_{cu}}\) = 1.0 s & 0.31 m/s & 0.95 s & 0 & **0.07 s** & 0.155 m/s & 0.51 s \\ C/\(\mathrm{T_{cu}}\) = 1.2 s & 0.28 m/s & 0.95 s & 0 & \(-\)0.18 s & 0.14 m/s & 0.385 s \\ C/\(\mathrm{T_{cu}}\) = 1.5 s & \(\mathbf{0.25}\) m/s & 0.97 s & 0 & \(-\)0.39 s & \(\mathbf{0.125}\)**m/s** & **0.29 s** \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Computational comparison of the selected peak gusts values for complete vertical wind estimation with reference measurements for different time constants and flight phases (D—descent, L—level flight, C—climb). Figure 48: Comparison of the gust value with the estimation results—descent crossing a microburst; single vertical gust (complementary filter, (**A**) \(\mathrm{T_{cw}}\) = 0.5 s, (**B**) \(\mathrm{T_{cw}}\) = 1.0 s, (**C**) \(\mathrm{T_{cw}}\) = 1.2 s, (**D**) \(\mathrm{T_{cw}}\) = 1.5 s). A detailed look at the arrows annotated with numerical data for the selected increasing gust in Figure 50 enables a computational comparison. With a time constant of 0.5 s, the estimated peak vertical gust differs from the reference by only 0.05 m/s, with a delay of 0.56 s. However, this time constant also results in a delay of 1.74 s for reaching a velocity of 0.5 m/s during the gust's decline. Figure 50 indicates a notably accurate return to zero after the vertical gust ends when using a time constant of 1.0 s, with an average overall delay of 0.975 s. In comparison, the other time constants analyzed perform less favorably in this aspect. According to Table 4, increasing the time constant further to 1.2 s and 1.5 s does not significantly affect the total delay, which remains approximately 0.5 s shorter than in the previously examined descent flight phase. The third scenario analyzed to evaluate the vertical gust estimation algorithm using complementary filtering involved flying through a microburst during climb. Two data  
Figure 49: Comparison of the gust value with the estimation results—microburst during a level flight; entire simulation (complementary filter, (**A**) T\({}_{\rm cw}\) = 0.5 s, (**B**) T\({}_{\rm cw}\) = 1.0 s, (**C**) T\({}_{\rm cw}\) = 1.2 s, (**D**) T\({}_{\rm cw}\) = 1.5 s).