## 5 Simulation and Results
### Positioning Accuracy Assessment  
We performed simulations to evaluate the effectiveness of each algorithm. As shown in Figure 22, all four methods exhibited a significant decrease in positioning error after noise reduction and area division, although improvement levels varied. As seen in Table 5, DT demonstrated the most positive change, with 59.21% improvement for the center area, and 45.89% improvement for the edge area. The least improved method was kNN, which showed 32.54% improvement and 10.06% improvement for the center area and edge area, respectively. The RF and SVM algorithms also showed a very positive improvement when the average RMSE percentage was approximately the same and around 37%. To acquire a more accurate assessment of the degree of influence of each process (i.e., noise reduction and area division) on the final positioning accuracy, the RMSEs of each algorithm (i.e., DT, kNN, RF, and SVM) are surveyed under four cases (Figure 23):  
* (I): Without noise reduction and without area division
* (II): Without noise reduction and with area division
* (III): With noise reduction and without area division
* (IV): With noise reduction and with area division \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Position of Data** & **DT** & **kNN** & **RF** & **SVM** \\ \hline
**Center** & 59.21 & 32.54 & 46.18 & 42.75 \\
**Edge** & 45.89 & 10.06 & 28.90 & 30.43 \\
**Average** & 52.55 & 21.30 & 37.54 & 36.59 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Root mean square error (RMSE) comparison (%). Figure 22: RMSE comparison. Case II (incorporating area division) showed a relatively small improvement in the RMSE, with the kNN and SVM algorithms showing 2.13% and 6.54% improvement, respectively. This means that area division has a negligible effect on these two algorithms in term of accuracy. In contrast, the DT and RF algorithms were strongly influenced by the area division process, showing an improvement of 33.73% and 26.54%, respectively. Case III, with noise reduction and no area division, showed a very promising decline in positioning errors compared to Case I. SVM achieved the best improvement, followed by RF. The DT algorithm continued to show the lowest level of accuracy. It is clear that the mean positioning errors tended to gradually improve progressing from Case I to Case IV. The highest accuracy (8.6 cm) occurs with SVM in Case IV. The worst accuracy (16.8 cm) occurs with DT. It is interesting to note, however, that the DT algorithm had the highest improvement, showing an RSME reduction of nearly 60% (from 48.1 cm in Case I to 16.8 cm in Case IV). Also, RF showed the same improvement level as DT but RF has a much better positioning accuracy of 10.2 cm. This result is only slightly worse than SVM. Of the four algorithms, kNN shows the least improvement at 30.85%. In summary, all four methods achieve better positioning accuracy after noise reduction and area division, in the following ascending order of accuracy: DT, kNN, RF, and SVM. The area division technique had a relatively small impact on the accuracy of kNN and SVM, although it did provide significant savings in execution time, as was discussed in the previous Section. Next, we analyzed the positioning errors, based on the hypothetical roadmap of a mobile robot. On this route, the robot started from the left upper corner, as shown in Figure 24, then went to the opposite position with LED 1 (see Figure 1), then proceeded through the center of the floor and the area near the wall. Finally, the robot went to the corner opposite the start point. Since the effects of multipath reflections and noises varied greatly from location to location in the room, this route helped us to evaluate the efficiency of the proposed solution under varying conditions. Figure 23: Detailed mean of positioning error comparison. Before applying our proposed solution, the positioning errors in the two corners were very bad (Figure 24). A contrasting image, however, is shown in Figure 25, which shows the results after our solution is deployed.