## 6 Results and Discussion
### Comparison  
We now compare our RFR-based models with our predecessors: the ANN(F) and the ANN(S) models. From Table 2, we can observe that the estimation MSE and RMSE of ANN(F) model is 5.15 dBm, which is higher than the RFR(F) estimation with a MSE of 3.20 dBm and RMSE of 1.79 dBm, which indicates the more accurate estimation of the RFR model over the ANN-based model. Similarly, we can also visualise the RFR(F) model's superiority over the state-of-the-art studies in [17] based on a global method (utilising the entire dataset), and in [24],which evaluates the effectiveness of Random Forest to estimate RSSI in LoRaWAN for agricultural settings. Next, the ANN(S) model was compared with the RFR(S) model. From this Table 3, we can visualise that the RFR(S) model has significantly lower MSE and RMSE than the ANN(S) model for most of the selected sequences. We also performed the averaged comparison by averaging the testing MSE of all the selected sequences for the RFR(S) and ANN(S)  
Figure 14: The results of selected sequence using the features [0.5, 1, 2]. Figure 12: The results of selected sequence using the features [1, 1, 2]. Figure 13: The results of selected sequence using the features [0.5, 0, 2]. models. The averaged testing MSE of the RFR(S) model shows the 1.62 dBm, while the ANN(S) model shows the average MSE of 2.17 dBm, which is less than the RFR(S) model. In comparison with the state-of-the-art (TinyDraGon) model in [17], the higher testing MSE and RMSE of 10.24 dBm and 10.24 dBm also indicates the superiority of RFR(S) model over the TinyDraGon. The significant outperformance of the RFR(F) and RFR(S) approaches compared to the conventional ANN(F) and ANN(S) methods can be attributed to differences in their underlying algorithms and their handling of dataset characteristics. The RFR(F) and RFR(S) methods benefit from an ensemble-based structure that aggregates predictions from multiple decision trees. This property makes them particularly effective in scenarios with  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Selected Sequence**} & \multicolumn{2}{c}{**Training**} & \multicolumn{2}{c}{**Testing**} & \multirow{2}{*}{**Training Time (s)**} & \multirow{2}{*}{**Testing Time (s)**} \\ \cline{2-2} \cline{5-6}  & **MSE** & **RMSE** & **MSE** & **RMSE** & \\ \hline \multicolumn{6}{c}{Sequence-based RFR Estimation Model} \\ \hline
[3, 0, 1] & 1.66 & 1.28 & 5.65 & 2.37 & 0.0010 & 0.0007 \\ \hline
[3, 1, 1] & 0.92 & 0.96 & 1.41 & 1.19 & 0.0008 & 0.0006 \\ \hline
[2, 0, 2] & 0.40 & 0.63 & 3.83 & 1.95 & 0.0007 & 0.0006 \\ \hline
[2, 1, 2] & 1.36 & 1.16 & 0.26 & 0.50 & 0.0008 & 0.0007 \\ \hline
[1, 0, 2] & 0.45 & 0.67 & 0.74 & 0.86 & 0.0008 & 0.0006 \\ \hline
[1, 1, 2] & 3.11 & 1.76 & 2.90 & 1.70 & 0.0014 & 0.0008 \\ \hline
[0.5, 0, 2] & 0.43 & 0.66 & 0.79 & 0.89 & 0.0006 & 0.005 \\ \hline
[0.5, 1, 2] & 0.55 & 0.74 & 0.34 & 0.58 & 0.0010 & 0.0011 \\ \hline \multicolumn{6}{c}{Sequence-based ANN Estimation Model [30]} \\ \hline
[3, 0, 1] & 2.94 & 1.71 & 9.40 & 3.06 & 0.7091 & 0.0006 \\ \hline
[3, 1, 1] & 1.23 & 1.11 & 1.51 & 1.23 & 0.4962 & 0.0005 \\ \hline
[2, 0, 2] & 0.91 & 0.95 & 4.36 & 2.08 & 0.369 & 0.0009 \\ \hline
[2, 1, 2] & 2.86 &complex, nonlinear relationships or variations that might lead to overfitting in other models. In our case, the specific features of the data that favour the RFR(F) and RFR(S) approaches include instances with noisy measurements and fluctuations in received signal strength. The RFR method is better equipped to handle these situations by averaging predictions across diverse trees, thereby reducing variance and improving generalisation. Moreover, the RFR method is less sensitive to small-scale variations in the dataset compared to ANN, which relies heavily on well-tuned hyperparameters and larger datasets for effective learning. This robustness gives RFR an advantage, especially when operating with limited or noisy data.