## 4 Results and Discussion
### Estimation Accuracy--Vertical Gusts
Figure 50: Comparison of the gust value with the estimation results—microburst during a level flight; single vertical gust (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). ranges were selected for graphical presentation: the entire simulation (0-170 s) and the narrowed range of vertical gust occurrence (simulation time 60-110 s). Figures 51 and 52 demonstrate that a time constant of 1.0 s yields the most accurate estimation results relative to the reference measurement. Significant differences are observed in the return to zero values following the vertical gust, with the most favorable outcome occurring at a time constant of 1.0 s.  
In contrast to the two previously analyzed flight conditions, the peak values of the vertical gust are overestimated during the climb phase. Increasing the time constant reduces the discrepancy between the estimated and reference values, although, as indicated in Table 4, these differences remain relatively minor. For the weakening phase of the gust--specifically at the \(-0.5\) m/s velocity point--raising the time constant from 0.5 s to 1.0 s significantly reduced the estimation delay from 1.48 s to just 0.07 s. For this criterion, further increasing the time constants causes the estimation to be too far ahead of the reference  
Figure 51: Comparison of the gust value with the estimation results—climb crossing a microburst; entire simulation (complementary filter, (**A**) T\({}_{\text{cw}}\) = 0.5 s, (**B**) T\({}_{\text{cw}}\) = 1.0 s, (**C**) T\({}_{\text{cw}}\) = 1.2 s, (**D**) T\({}_{\text{cw}}\) = 1.5 s). measurement. However, further increases in the time constant lead to the estimation anticipating the reference measurement, while at the same time causing problems with stabilizing the zero values after the vertical gust has subsided. The vertical gust estimation results were evaluated by comparing them to the low-frequency signal and the recorded ideal gusts measurements. Analysis of the graphs from Section 4.3, indicates that the applied estimation method provides a more accurate representation of the gusts' shape, and therefore their velocity, than the low-frequency signal alone. The estimation more accurately captured the decrease in gust velocity, whereas the low-frequency signal exceeded the reference signal during this phase. The whole simulation graphs showed that, in the case of estimation, there was a quicker return to zero after the gust subsided, compared to the low-frequency signal, especially for a time constant equal to 1.0 s. The vertical gust estimation algorithm is less predictable compared to the developed head-on and side gusts estimation algorithms. Interestingly, the low-frequency signal slightly preceded the reference gust during its initial phase. The estimation is delayed by an average of 1.0 s for the level flight and climb phases and by an average of 1.5 s for the descent phase, relative to the recorded reference gust for the most accurate results in terms of value. Furthermore, a higher value of the complementary filter time constant leads to difficulties in maintaining stable zero values after the vertical gust has diminished. In the analyzed vertical gust scenario, the potential impact of a simultaneously occurring strong headwind gust and a minor crosswind component on the estimation results was considered. In the contrast, for the previously analyzed separated head-on and side gusts scenarios (Sections 4.1 and 4.2), the influence of other wind components was eliminated by carefully selecting the simulation conditions. Table 4 summarizes the computational comparisons of the selected cases discussed above (the most favorable results are in bold). Negative values in the difference columns mean underestimation, and positive values mean overestimation. When interpreting the average deceleration values from Table 4, the negative values of the last two time constants for the climb case must be taken into account, which lower these average results.