## 4 Experimental Results  
The efficiency of the proposed technique for wind speed estimation based on the reflected signal is evaluated in this section. The observation dataset was collected during the typhoon Utor, which was a powerful tropical cyclone that formed in the Eastern part of the Philippines and dissipated in Southern China. The in situ wind speed measurement was collected from two periods, the first period was from 3 to 8 August 2013, in which the minimum and maximum wind speeds were 0.1 and 8.9 m/s, respectively. The second period was from 12 to 14 August 2013, in which the minimum and maximum wind speeds were 2.5 and 37.9 m/s, respectively. Figure 5 shows the wind speed changes over the two periods. Figure 4: A schematic of the particle filter process. The reflected signal from the BeiDou G4 satellite was collected over the ocean surface at the same time as the in situ wind speed. The signal consisted of phase \(I\) and \(Q\) components, examples of which are presented in Figure 6a,b, respectively. Subsequently, the \(I\) and \(Q\) components were integrated by \(I^{2}+Q^{2}\) in order to compute the power waveform, as shown in Figure 6c. The scatter plot in Figure 6d shows the normalized density of each lag, and the black line shows the connection of the mean values between lags. Accordingly, the final power waveform is shown in Figure 7.  
Figure 5: The in situ wind speed measurement from the buoy station from 3 to 8 August 2013 and 12 to 14 August 2013. The average wind speed of each time period are approximately 3.5 and 16 m/s, respectively. Figure 6: An example of a real reflected signal from the BeiDou G4 satellite captured on 3 January 2014: (**a**) phase \(I\); (**b**) phase \(Q_{i}\) (**c**) integration of phases \(I\) and \(Q\) (\(I^{2}+Q^{2}\)) and (**d**) normalized density of the sample. The sensitivity of the power waveform to wind speed is a key parameter for wind speed estimation. This research used the delay-related and spectral-related observables, computed from the power waveform, as input information for the ANN approach. The delay-related observable is expressed by:  
\[\alpha(\tau)=\frac{Z_{r}(\tau)-N_{floor}}{Z_{r}^{max}(\tau)-N_{floor}}, \tag{20}\]  
where \(Z_{r}(\tau)\) is a delay, and \(N_{floor}\) is the noise floor of the power waveform. \(Z_{r}^{max}\) is the peak amplitude, which is computed by a third-degree polynomial on the power waveform. The spectral-related observable is expressed by:  
\[f(\tau)=\frac{\int_{f_{1}}^{f_{2}}f\cdot S_{r}(f,\tau)\mathrm{d}f}{\int_{f_{1} }^{f_{2}}S_{r}(f,\tau)\mathrm{d}f}, \tag{21}\]  
where \(S_{r}(f,\tau)\) is the Doppler spectrum, and \(f_{1}\) to \(f_{2}\) is the frequency range of the Doppler spectrum. The cross-validation function of MATLAB 2016a based on HoldOut was used to select the training samples at 30% and 70% of all datasets, respectively. Figures 8 and 9 present the training sample for the learning process of ANN, which consists of the in situ wind speed, the delay-related and spectral-related observables of BeiDou G4. In addition, the correlation of the reflected signal and the training sample are presented. Figure 8: An example of the reflected signal at lag 26: (**a**) 30% training sample; (**b**) relationship between the training sample and the wind speed. Figure 7: The final power waveform of an example of a real reflected signal from the BeiDou G4 satellite captured on 3 January 2014. Based on the training sample, it is evident that the derived results show good agreement with in situ wind speed measurement. Figures 10 and 11 show the wind speed estimation results, which are presented in three different types of graphs: a line graph, a box plot, and a scatter plot. On the line graph, the proposed technique (cyan line) shows high efficiency and good correlation compared to a regression (red line), an ANN based back-propagation (BP, green line), and an ANN based PSO (magenta line) technique. The box plot presents the statistical error comparison of each technique.