## 4 Results and Discussion
### Estimation Accuracy--Vertical Gusts  
The graphs in this section compare the ideal vertical gust measurements to the obtained low-frequency signal (\(W_{\text{g-lo}}\)) and the complete estimation (\(W_{\text{g-est}}\)), which combines the low-frequency signal (\(W_{\text{g-lo}}\)) and the high-frequency (\(W_{\text{g-fi}}\)) signals using a CF across the three  
Figure 46: Comparison of the gust value with the estimation results—climb crossing a gust area; single selected gust (complementary filter, (**A**) \(T_{\text{cv}}\) = 0.5 s, (**B**) \(T_{\text{cv}}\) = 0.8 s, (**C**) \(T_{\text{cv}}\) = 1.0 s, (**D**) \(T_{\text{cv}}\) = 1.5 s). Figure 45: Comparison of the gust value with the estimation results—climb crossing a gust area; series of selected gusts (complementary filter, (**A**) \(T_{\text{cv}}\) = 0.5 s, (**B**) \(T_{\text{cv}}\) = 0.8 s, (**C**) \(T_{\text{cv}}\) = 1.0 s, (**D**) \(T_{\text{cv}}\) = 1.5 s). phases of flight. Based on the literature review, no direct method for determining vertical gusts using onboard systems in commercial aircraft has been identified. The developed low-frequency signals do not accurately represent the vertical gust value. Values comparable to the reference measurement can only be obtained after the fusion of the signals through additional filtering. For the first analyzed flight phase--descent, two data ranges were selected for graphical presentation: the entire simulation (0-230 s) and a narrowed range during vertical gust occurrence (simulation time 100-140 s). The CF results illustrate the influence of varying the time constant \(T_{\mathrm{cw}}\) on the estimation accuracy. Four time constant values (0.5 s, 1.0 s, 1.2 s, 1.5 s) were selected to account for the comparison of the estimation against the recorded gust. Based on Figures 47 and 48, it can be concluded that the estimation results most closely matched to the reference measurements for time constant of 1.2 s. In Figure 47, it is clearly shown that combining low- and high-frequency signals through complementary filtering greatly enhances the shape of the gust, specifically its velocity profile over time. A closer examination of the arrows annotated with numerical data for the selected increasing gust in Figure 48 allows for a computational comparison. With a time constant of 0.5 s, there is a noticeable underestimation of the peak vertical gust velocity. Interestingly, the low-frequency and complete estimation signals initially lead the response, accurately capturing both the initial rise in gust velocity and the peak value. However, the accuracy deteriorates as the gust velocity returns to zero. To quantify the delay in reverting to pre-gust conditions, a reference point at a velocity of \(-0.5\) m/s was chosen for each signal analyzed. Despite initially leading the reference measurement, the signals exhibit a substantial lag--exceeding 3 s--at this point. The increase in time constants to 1.0 s and 1.2 s brings the peak value of the estimated vertical gust closer to the reference value at the cost of increasing the delay. However, there is an improvement due to the decrease in delay for decreasing the gust speed. Detailed comparative data are presented in Table 4. Data analysis allows a less precise return of the full estimate to zero after the gust has subsided. This issue becomes more pronounced with a time constant of 1.5 s, where the peak is also overestimated. Overall, it is important to note that the average delay is greater compared to the other two algorithms, reaching around 1.5 s during the descent phase of flight. Figure 47: Comparison of the gust value with the estimation results—descent crossing a microburst; entire simulation (complementary filter, (**A**) T\({}_{\mathrm{cw}}\) = 0.5 s, (**B**) T\({}_{\mathrm{cw}}\) = 1.0 s, (**C**) T\({}_{\mathrm{cw}}\) = 1.2 s, (**D**) T\({}_{\mathrm{cw}}\) = 1.5 s). Subsequently, the estimation results for the simulation conducted in level flight were presented.