## 4 Analysis and Experimental Results
### Results
It can be observed that the improvements in the positioning error take place in stages, in agreement with the discrete exploration technique of the QPSO. No error improvement was achieved beyond QPSO iteration #56, which provided a positioning error m measured on test data alone. This value shows an improvement of \(\sim\)16% with respect to our previous best result, in which signal weighting was first introduced for the analysis of the same dataset. The final geometrical configuration that led to this positioning error provided a tile size (w, h) = (0.505, 0.587) m and an offset (u, v) = (0.059, 0.411) m. These values correspond to a tessellation of 11 tiles horizontally and 40 vertically. The tile size provides an intrinsic error of 0.209 m as per Equation (16), thus leading to a tile error of 0.402 m. In consideration of the tile size and the procedure of calculating the positioning error, it can be concluded that, on average, each test data carries a mismatch of a single tile. In our previously published work on the same dataset using fixed surface tessellation [27], it was observed that the positioning error was mainly caused by tile mismatches in the horizontal direction. For this reason, in this research, further attention was given to the separate contributions to the total positioning error by the horizontal and vertical tile \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Architecture Parameters** & \multicolumn{3}{c}{**Training Parameters**} \\ \hline Hidden layers & 3 & Learning rate & \(\eta\) = 0.001 \\ Hidden units & 18 per layer & Momenta Adam values & \(\beta_{1}\) = 0.9, \(\beta_{2}\) = 0.999 \\ Activation function & Logistic sigmoid & Runs per individual & 1000 \\ Training points & 96 & Training iterations & 5000 \\ Test points & 20 & Computing time & \(\sim\)28 h \\ \hline \hline \end{tabular}
\end{table} 
Table 2: MLP design and operational parameters. Figure 4: **(left)** The values of the horizontal and vertical contributions to the total positioning error, as calculated at each QPSO iteration. **(right)** The overall performance of the QPSO algorithm in terms of the positioning error reduction. A final value of 0.611 m was achieved. mismatches. At every QPSO iteration, the position error in each direction was recorded for the best individual out of the population of 20. Again, it can be observed that in the horizontal direction, the partial position error is larger and more widely distributed compared to the values recorded in the vertical direction. Figure 4 (left) shows that in the vertical direction, the error does not vary much around 40 cm, while in the horizontal direction, values are spread in the range of 0.6-1.2 m. Nevertheless, the particularly low value recorded at QPSO iteration #56 generated the final global best for this research. A comparison of the results obtained in this research with a selection of relevant previously published location average errors is presented in Table 3. Our previous work, based on the same raw data, is included together with other benchmark results available in the literature, showing a remarkable reduction in the positioning incertitude. The proposed method of data analysis does not present any particular challenges, apart from the extensive computing time. Nevertheless, the actual application of this technology would require some caveats about the stability and availability of the sources of the signals. Possible drifts and abrupt variations would render this method less accurate, thus requiring particular attention to the hardware of the whole installation. Further work beyond this method should possibly focus on the normalization of the input signals and the analysis of their spatial distributions.