## 4 Results and Discussion  
### Estimation Accuracy--Head-on Gusts  
The graphs in this section compare the ideal measurement scenario with the obtained low-frequency signal (\(U_{g\text{-}lo}\)) and the complete estimation (\(U_{g\text{-}est}\)). The latter combines low-frequency and high-frequency signals using a complementary filter (CF) across three analyzed flight phases. The first flight phase examined was descent. Three data ranges were selected for graphical analysis: the entire simulation (0-330 s), a series of selected gusts (200-255 s), and a single gust event (220-238 s). The CF results illustrate the effect of varying the time constant \(T_{cu}\) on the estimation outcome. For comparison with the recorded gusts, four selected values of time constant--[0.5 s, 0.8 s, 1 s, 1.5 s]--were taken into account. Based on Figures 29-31, it can be concluded that the most accurate estimation results compared to the reference measurement, were obtained with time constants of 0.8 s and  
Figure 28: Registered ideal gusts measurements from the simulation weather section—climb phase; (**A**)—wind speed as a function of time, (**B**)—wind speed as a function of altitude. Figure 27: (**A**) Altitude, (**B**) IAS, and (**C**) VVI recorded during simulated flight—climb phase. 1.0 s. Increasing the time constant from 0.5 s to 0.8 s improved the alignment between the estimation and the ideal headwind gust measurements. Taking a closer look on the arrows annotated with numerical data for the selected increasing gust in Figure 30, a computational comparison could be made. For the time constant of 0.5 s, the peak gust value is 0.64 m/s lower than the reference measurement for complete estimation (for low-frequency estimation this diffrence is more significant and amounts to 2.03 m/s). The delay of the full estimation in relation to the reference measurement is relatively small and is equal to 0.39 s, which is a better value in relation to the delay of the low-frequency estimation, which equaled 0.5 s. Increasing the time constant to 0.8 s allowed for an almost perfect match (0.02 m/s difference between the reference measurement) of the peak gust value considered while maintaining the full estimation delay of 0.39 s. Analysis of the numerical annotations of the arrows in Figure 31 allows for an accurate comparison of the minimum numerical values for the selected weakening gust case. Starting from a time constant of 0.5 s, the differences in the minimum value are 0.37 m/s for the full estimation and 0.84 m/s for the low-frequency estimation. The delays with respect to the reference measurement are 0.95 s for the full estimation and 1.39 s for the low-frequency estimation. When comparing the changes in the full estimated values for this selected case, the closest value to the reference measurement was achieved for a time constant of 0.8 s (only 0.04 m/s difference), while maintaining the delay at the level of 0.95 s. A time constant of 1.0 s already underestimates the minimum value by 0.2 m/s, while a time constant of 1.5 s underestimates it by 0.34 m/s, also increasing the estimation delay to 1.05 s.  
For the considered cases of a gust with increasing velocity and a gust with decreasing velocity, the best results were obtained for a time constant of 0.8 s. However, the overall fit should also be taken into account for the final evaluation and conclusions. In this respect, the results for a time constant of 1.0 s are also satisfactory. On the other hand, an increase in the time constant to 1.5 s led to an overestimation of the peak gust values both in assessment and computational comparison of charts. Figure 29: Comparison of the gust value with the estimation results—descent crossing a gust area; entire simulation (complementary filter, (**A**) T\({}_{\text{cu}}\) = 0.5 s, (**B**) T\({}_{\text{cu}}\) = 0.8 s, (**C**) T\({}_{\text{cu}}\) = 1.0 s, (**D**) T\({}_{\text{cu}}\) = 1.5 s). Subsequently, the estimation results for the simulation performed during level flight were analyzed.