## 5 Discussion  
In order to assess the efficiency of the proposed technique, the root mean square error (RMSE) was used as a standard statistical metric to measure the model's performance. The RMSE used for evaluation in this section is expressed by:  
\[RMSE=\sqrt{\frac{1}{n}\sum_{i=1}^{n}(y_{i}-\hat{y_{i}})^{2}}, \tag{22}\]  
where \(y_{i}\) is the in situ wind speed measurement from the buoy, \(\hat{y_{i}}\) is the wind speed estimation, and \(n\) is number of observations. Table 1 shows the statistical results of each technique. The overall RMSE of the proposed technique is better than the regression, the ANN based BP, and the ANN based PSO techniques by approximately 4, 1.5, and 0.5 m/s, according to the PF based autoregressive model that used information from the previous time step. For wind speeds higher than 20 m/s, the results showed greater errors compared to lower wind speeds due to the lack of high wind speed samples. The in situ data used in this research only provided 18 samples for wind speeds higher than 20 m/s. In order to improve the efficiency of the high wind speed results, an appropriate number of training samples is required. For this research, when the cross-validation function was applied for selecting 30% of the training sample, the total random sample is 174 samples, which consist of 156 samples of wind speed higher than 20 m/s and 18 samples of wind speed lower than 20 m/s. Likewise, when \begin{table}
\begin{tabular}{l c c c c c c} \hline \hline  & \multicolumn{6}{c}{RMSE (m/s)} \\ \cline{2-7}
**Algorithm** & \multicolumn{3}{c}{**30\%**} & \multicolumn{3}{c}{**70\%**} \\ \cline{2-7}  & **WS \textless{} 20** & **WS \textless{} 20** & **Overall** & **WS \textless{} 20** & **WS \textgreater{} 20** & **Overall** \\ \hline Regression & 4.7839 & 13.4543 & 5.9009 & 4.7261 & 13.6445 & 5.8908 \\ ANN based BP & 4.4942 & 6.5375 & 4.6796 & 2.5595 & 4.4798 & 2.7516 \\ ANN based PSO & 2.8843 & 3.4397 & 2.9299 & 2.3081 & 3.1553 & 2.3826 \\ ANN based PSO & 2.3982 & 3.5124 & 2.4997 & 1.8524 & 3.1126 & 1.9758 \\ combined with PF & & & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Comparison of the statistical results of wind speed estimation. Figure 11: Comparison of wind speed estimation results using different techniques with 70% of the training sample. 70 % of the training sample was selected, the total random sample is 385 samples, which consist of 350 samples of wind speed higher than 20 m/s and 35 samples of wind speed lower than 20 m/s. The number of artificial neurons in the hidden layers is an important factor when deciding to select an ANN architecture. This research compared different numbers of neurons (6, 8, 10, 12, and 14 neurons) in order to find the optimal number of artificial neurons for wind speed estimation. Figure 12 shows the scatter plots of the relationship of in situ wind speed measurements and wind speed estimation for the different hidden layer architectures. These combine the results of the assessments using 30% and 70% of the training dataset and include \(R^{2}\) values. The statistical comparison of each hidden layer is represented in the box plot. The overall RMSE of the ANN based PSO with 10 artificial neurons was approximately 2.9 m/s when 30% of the training sample was used and 2.3 m/s when 70% of the training sample was used, as shown in Table 2. According to these results, the optimal number of neurons for wind speed estimation from the information of the BeiDou reflected signal is 10 neurons, since this produced the lowest RMSE. One important factor for achieving a higher efficiency of particle filters is the number of particles. The filter approximates the posterior distribution with high efficiency when the number of particles tends to infinity. On the other hand, the computational cost grows with the number of particles.