## 5 Simulation Result and Discussion
### Real-Time Frequency Domain Identification Simulation  
Applying an active excitation signal to the control surface can stimulate the dynamic characteristics of the aircraft, so that the flight data contain more information and improve the accuracy of identification. In this paper, only the longitudinal pitch force distance identification is concerned, so only the elevator is applied. The excitation expression is:  
\[\mathrm{u}=0.5\times(\sin(\frac{4\pi t}{T}+2.8274)+\sin(\frac{8\pi t}{T}+2.1991 )+\sin(\frac{12\pi t}{T})+\sin(\frac{16\pi t}{T}+1.8850)) \tag{35}\]  
The image of each sine signal and the effect of their superposition are shown in Figure 5.  
Figure 5: Actuator surface excitation component. The flight state of the identification phase selected in this paper is shown in the Figure 6.  
Flight altitude is about 5000 m, speed is about 150 m/s, in the horizontal flight state dynamics identification. A 4-order Butterworth high-pass filter is used, Table 1 shows the specific information of the filter. In order to realize real-time identification, the flight data have to be detrended. The comparison of data before and after processing is shown in the figure below. In Figure 7, the blue solid line represents the untreated original data. When the data has a constant component or a component that is linearly related to time, after being converted into the frequency domain, there will be a high-peak low-frequency component, which affects the identification accuracy. In the above figure, it can be clearly seen that the angle of attack and the elevator angle have obvious constant components, so these data must be processed. Relatively speaking, the other two have small deviations, but they also need to be processed. The red solid line in the diagram is the result of real-time recursive detrending. In order to observe the detrending effectiveness more intuitively, after the simulation is completed, a more accurate batch detrending method is used offline for data processing, and all the results are displayed in a picture. It must be pointed out that this batch method does not meet the needs of real-time operation, because it requires simultaneous processing of all flight data. If all the previous data are processed in batches after each data acquisition, the effect of the similar inference method can be achieved. However, this will cause a very large amount of calculation and put forward high requirements for the hardware computing power of the aircraft. The results of offline batch processing are represented by blue dashed \begin{table}
\begin{tabular}{c c} \hline \hline
**Description** & **Symbol** \\ \hline filter types & Butterworth \\ order & 4 \\ sampling frequency & 100 \\ cut-off frequency & 0.1 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Filter configuration. Figure 6: Flight state in real-time parameter identification phase. lines. It can be clearly seen from the figure that it takes about 20 s to converge the nevus with the same accuracy as the batch processing method. This is because at the initial time, for the lack of flight data, the constant components contained in the flight data cannot be accurately identified. Through this experiment, a conclusion can be drawn that when using the recursive real-time detrending method, it is necessary to wait for a period of time after starting the detrending process to carry out the recursive aerodynamic identification. The specific waiting time length should be determined by flight data analysis. Here, the waiting time is 20 s.  
After the detrending, the frequency domain recursive identification can be performed. Figure 8 shows the identification results. In the stage of waiting for the convergence of the real-time filter, the identification result is artificially set to 0. In order to ensure that the identification result fluctuates greatly at the beginning of the recursion, the first 90 samples are taken for one batch, and the result is used as the initial value for subsequent recursion.