## 4 Impact of the Constellation Mesh Area on Localization Accuracy
### Experimental Results  
The constellation of the 4 anchors network was implemented in the real case scenario depicted in Figure 9c. The three mesh configurations represented in Figure 9b define three different case studies. In the experiments described herein after, the mobile tag was installed on a tripod at a fixed height of 1.1 m and moved across the reference points indicated on the map of Figure 9a, while a convenient number of 5 RSSI traces were acquired and averaged for each point. These traces were exploited to estimate the mobile tag position by the estimator of Equation (3). Finally, some mechanical positioning techniques (i.e., laser position measurements, and mobile tag antenna alignment) provide a better consistency of the measured data across the experiments. These experiments have a two-fold objective: the main consists in drawing conclusions about the trade-off between mesh size, the localization accuracy and room area; the second is the assessment about the reliability of the simulation presented in the previous section. Figure 12 depicts the CDF of the position estimation by the measured RSSI data for the three cases of study, respectively. Additionally, in this case the results are differentiated into two sets, namely the position errors inside the meshes and those across the entire room area, with each case of study differently colored. This approach is motivated by the fact that for large areas a system architect could be interested in covering the domain by implementing a constellation of smaller meshes instead of adopting a larger one. This solution leads to better accuracy at the expense of increased system complexity. The localization results for the three experiments is summarized in Table 3. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Configuration**} & \multicolumn{2}{c}{**A**} & \multicolumn{2}{c}{**B**} & \multicolumn{1}{c}{**C**} \\  & **Large** & **Medium** & **Tiny** \\ \hline \multirow{2}{*}{**Full Room**} & **Mean Error** & 0.71 m & 0.99 m & 3.11 m \\  & **Coverage * & 78.26\% & 66.52\% & 26.30\% \\ \hline \multirow{2}{*}{**Within the Mesh Area**} & **Mean Error** & 0.73 m & 0.51 m & 0.13 m \\  & **Coverage * & 73.21\% & 93.81\% & 100\% \\ \hline \hline \end{tabular}  
* Percentage of the full room area with sub-metrical localization error (\(\leq\)1 m).  
\end{table} 
Table 2: Simulated positioning error results. Figure 12: Measured localization error CDFs, for the three cases of study. Data acquired at the 299 points in the room of Figure 9a, assuming the mobile tag pointing upward, 5 averaged RSSI data for point and each antenna element, mobile tag height = 1.1 m.  
From the data we can observe what follows: Within the mesh boundary the localization accuracy increases when reducing the mesh area. Nevertheless, outside the same mesh the system is still able to provide effective localization with a meaningful accuracy. The wider mesh configuration, 'A', shows a good average localization error across the entire area, balancing its distribution all over the room. On the contrary, adopting the smallest mesh, i.e., 'C', the accuracy degrades significantly when evaluated in average across the entire room area. The 'B' mesh represents effectively a transition between the two cases, thus confirming the coherence between the experimental data. It is noteworthy that CRB simulation results as shown in Figure 8 show a qualitative identical trend when compared with experiments. In comparison with the curves in Figure 8 the minimum achievable localization error within the mesh area shows a monotonous growth as the corresponding mesh size increases, exactly as depicted in Table 3. On the contrary, considering the entire room area, the average error decreases by increasing the mesh size until realizing an \"optimum\" mesh-size for which it is minimized.