## 4 Results
### Discussion  
Visual assessment of the charts allows for a general (qualitative) description of the accuracy of the estimation of the headwind gust value. In order to accurately (quantitatively) compare the estimation results with the reference signal, a performance index was defined. It enables analytical comparison of the estimation results considered in Section 4.2, obtained with the use of various filtration systems. The performance index assumes the calculation of the absolute value of the difference between the values of the ideal gust measurement (recorded directly in the flight simulator environment) and the results of numerical estimation. The averaged value of matching the results to the ideal measurement was obtained by dividing the sum of these differences by the amount of data in the considered measurement range. The formulas for quantifying the math of the low-frequency estimation and complete estimation signal to the reference signal are presented in Equations (23) and (24), respectively. Figure 21: Comparison of the gust value with the estimation results (cascaded complementary filter, estimation delay reduced by 1.5 s)—flight crossing a gust area; (**A**) whole simulation, (**B**) several selected gusts, and (**C**) single selected gust. Definition of performance index for low-frequency estimation of headwind gust:  
\[W_{g\text{-}lo} =\frac{\sum\left|U_{g\text{-}wind}-U_{g\text{-}lo}\right|}{Number\;of\; data}\] (23) Definition of performance index for complete estimation of headwind gust:  
\[W_{g\text{-}est} =\frac{\sum\left|U_{g\text{-}wind}-U_{g\text{-}est}\right|}{Number\;of\; data} \tag{24}\]  
The data ranges identical to those presented in the Figures 17-21 were considered in the analyses presented in this section. Detailed results are presented in the tables (Tables 2-4). The tables show the calculation results of the headwind gust performance indices for five time constants of the complementary filter (starting from \(T_{c}\) = 0.1 s to \(T_{c}\) = 2 s), non-linear complementary filter, and cascaded complementary filter. The following tables \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Simulation Scope** & \multicolumn{2}{c}{**10 \(\div\) 280 s**} & \multicolumn{2}{c}{**130 \(\div\) 185 s**} & \multicolumn{2}{c}{**136 \(\div\) 146 s**} \\ \hline  & \(W_{g\text{-}lo}\) & \(W_{g\text{-}est}\) & \(W_{g\text{-}lo}\) & \(W_{g\text{-}est}\) & \(W_{g\text{-}lo}\) & \(W_{g\text{-}est}\) \\ \hline CF \(T_{c}\) = 0.1 s & 0.487857 & 0.481736 & 0.982092 & 0.964243 & 1.208737 & 1.189704 \\ CF \(T_{c}\) = 0.5 s & 0.487857 & 0.470110 & 0.982092 & 0.901949 & 1.208737 & 1.191916 \\ CF \(T_{c}\) = 1.0 s & 0.487857 & 0.522065 & 0.982092 & 0.956012 & 1.208737 & 1.522830 \\ CF \(T_{c}\) = 1.5 s & 0.487857 & 0.614348 & 0.982092 & 1.111567 & 1.208737 & 1.861305 \\ CF \(T_{c}\) = 2.0 s & 0.487857 & 0.709409 & 0.982092 & 1.267276 & 1.208737 & 2.193865 \\ NCF & 0.487857 & 0.438372 & 0.982092 & 0.844902 & 1.208737 & **1.001125** \\ CCF & 0.487857 & 0.456016 & 0.982092 & 0.918667 & 1.208737 & **1.120209** \\ \hline \hline \end{tabular}
\end{table} 
Table 4: The results of computation of performance indices for delay = 1.75 s.