## 4 Results
### Estimation Results  
In order to validate the accuracy and applicability of our proposed system, different sampling rates were used for training and testing the regression models. In this study, six sampling intervals were considered, 10 s, 20 s, 1 min, 2 min, 5 min and 10 min. The dataset is down sampled from 2 s intervals to the corresponding sampling interval by averaging the values. Each regression model is separately trained and tested for different sampling intervals. In Table 1, the error metrics for ANN, SVM and LR regression models are reported. The coefficient of determination (R\({}^{2}\)) [71,72] and root mean squared error (RMSE) and mean absolute error (MAE) [40] are reported in order to evaluate the wind speed and direction estimation performance. The wind speed estimation performance of the ANN model surpassed those of the SVM and LR models. Consistently, for each sampling interval the ANN model could estimate the wind speed with a high accuracy. Especially for sampling intervals above 1 min, the wind speed ANN model's R\({}^{2}\) score was higher than 0.95 and reached a maximum of 0.99 for the 10 min sampling interval. The RMSE and MAE errors of the ANN model were also below 1 m/s and the best performances were achieved for the 10-min sampling interval, at 0.279 and 0.207, respectively. The SVM and LR models for wind speed estimation showed similar performances throughout the different sampling rates. Therefore, in the case of a tradeoff between accuracy and computing resources, the LR model can be preferable for on-device estimation of wind speeds. For wind direction estimation, the ANN model showed an R\({}^{2}\) score above 0.83 for each sampling interval, reaching a maximum of 0.941 for the 10-min interval. However, the SVM regression model for wind direction performed poorly, but the LR model could provide reasonable estimations at 5-min and 10-min sampling intervals.  
Figure 5: The plots of 168 h of data collected for this study, including thermopile array, ambient temperature, wind speed and wind direction.  
The observed vs. estimated/predicted wind speeds at the 10-s sampling interval are presented for ANN in Figure 6a, SVM in Figure 6b and LR in Figure 6c. From the plot, it can be seen that the ANN model is able to model the stochastic trends of wind speed using the thermopile array and ambient temperature data. The SVM and LR models can also reach a reasonable accuracy for wind speed estimation. However, for highly stochastic changes, especially at higher wind speeds, the ANN model performance was superior to those of SVM and LR. For wind direction estimation, the ANN model could capture most of the stochastic changes in trends, as shown in Figure 7a. However, the wind direction estimation accuracy was relatively lower than the wind speed estimation. The SVM model for wind direction could only model the average changes in trends, therefore the overall accuracy was poor, as shown in Figure 7b. The LR model was able to predict/estimate the wind direction better than the SVM model, however, it fell behind the ANN model's performance, as  
Figure 6: Comparison of predicted/estimated and observed wind speed at 10-s sampling interval for (**a**) ANN, (**b**) SVM and (**c**) LR.  
Figure 7: _Cont._