## 4 Results and Discussion
### Estimation Accuracy--Head-on Gusts
Three data ranges were selected for graphical representation: the entire simulation (0-143 s), a series of selected gusts (65-115 s), and a single gust (80-105 s). As in the previous case, the complementary filter (CF) results reflect the influence of varying the time constant \(T_{s}\) on the estimation performance. The same four time constants--[0.5 s, 0.8 s, 1 s, and 1.5 s]--were used for comparative analysis. The evaluation of charts presented in Figures 32-34 leads to the conclusion that the best representation of the estimation results compared to the reference measurement was obtained for the time constant of 0.8 s. By examining the arrows annotated with numerical values for the selected rising gust speed in Figure 33, a computational comparison can be made. When using a time constant of 0.5 s, the peak gust value is 0.2 m/s lower than the reference measurement in the full estimation, with a more pronounced difference of 1.04 m/s in the low-frequency estimation. The full estimation shows a relatively small  
Figure 31: Comparison of the gust value with the estimation results—descent crossing a gust area; single selected gust (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). Figure 30: Comparison of the gust value with the estimation results—descent crossing a gust area; series of selected gusts (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). delay of 0.5 s compared to the reference, which is an improvement over the 0.7-s delay observed in the low-frequency estimation. Increasing the time constant to 0.8 s leads to a peak value that exceeds the reference by 0.46 m/s, while still maintaining the 0.5-s delay in the full estimation. However, further increases in the time constant to 1.0 and 1.5 s resulted in progressively worse numerical performance. Reviewing the numerical labels on the arrows in Figure 34 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 0.58 m/s in the full estimation and by 1.62 m/s in the low-frequency estimation. The corresponding delays relative to the reference measurement are 0.3 s and 0.31 s, respectively. Among the full estimation results, the closest match to the reference is observed at a time constant of 0.8 s, differing by just 0.03 m/s and keeping the delay at 0.3 s. Increasing the time constant to 1.0 s results in an underestimation of 0.39 m/s, while a time constant of 1.5 s leads to a larger underestimation of 1.2 m/s and a slight delay increase to 0.32 s.  
Figure 33: Comparison of the gust value with the estimation results—level flight through a gust area; series of selected gusts (complementary filter, (**A**) T\({}_{\rm cu}\) = 0.5 s, (**B**) T\({}_{\rm cu}\) = 0.8 s, (**C**) T\({}_{\rm cu}\) = 1.0 s, (**D**) T\({}_{\rm cu}\) = 1.5 s). Figure 32: Comparison of the gust value with the estimation results—level flight through a gust area; entire simulation (complementary filter, (**A**) T\({}_{\rm cu}\) = 0.5 s, (**B**) T\({}_{\rm cu}\) = 0.8 s, (**C**) T\({}_{\rm cu}\) = 1.0 s, (**D**) T\({}_{\rm cu}\) = 1.5 s). For both the increasing and decreasing gust scenarios, the most accurate results were achieved with a time constant of 0.8 s. Nonetheless, the overall match between the estimated and reference data should also be considered in drawing final conclusions. Conversely, raising the time constant to 1.5 s resulted in an overestimation of peak gust values, as seen in charts as well as in numerical analysis. The third case analyzed for evaluating the headwind estimation algorithm using complementary filtering was climbing through a layer of head-on gusts. Three data ranges were chosen for graphical presentation: the entire simulation (0-190 s), a series of selected gusts (55-120 s), and a single gust (55-80 s).