## 5 Experiments
### Analysis of Results
\begin{table}
\begin{tabular}{|c|c|c|c|c|c|c|c|c|c|} \hline \multicolumn{2}{|c|}{**Node**} & \multicolumn{4}{c|}{**Multilateration—Error**} & \multicolumn{4}{c|}{**Proposed method—Error**} \\
**TX** & **RX** & **RSSI** & **distance** & **RSSI** & **distance** & **RSSI** \\  & & **[dB]** & **a.v.[m]** & **[\%]** & **a.v.[dB]** & **[\%]** & **a.v.[m]** & **[\%]** & **a.v.[dB]** & **[\%]** \\ \hline \multicolumn{2}{|c|}{**Office**} \\ \hline
00-00 & 28-1F & 12 \(\div\) 20 & 2.52 & 44.5\% & 7 & 35 \% & 0.01 & 0.3\% & 0 & 0\% \\
00-00 & 95-4C & 19 \(\div\) 27 & 2.32 & 52.7\% & 10 & 37 \% & 0.25 & 13.7\% & 0 & 0\% \\
00-00 & 1E-57 & 14 \(\div\) 22 & 0.98 & 25.6\% & 1 & 4.5 \% & 0.57 & 25\% & 0 & 0\% \\
95-4C & 28-1F & 22 \(\div\) 30 & 2.51 & 58.5\% & 12 & 40 \% & 1.3 & 42.2\% & 6 & 20\% \\
28-1F & 1E-57 & 31 \(\div\) 39 & 1.10 & 49.8\% & 9 & 23 \% & 0.02 & 1.8\% & 0 & 0\% \\
95-4C & 1E-57 & 18 \(\div\) 26 & 0.10 & 4.1\% & 0 & 0 \% & 0.02 & 0.9\% & 0 & 0\% \\ \hline \multicolumn{2}{|c|}{**mean**} & 1.58 & 39.2\% & 6.5 & 68.2\% & 0.36 & 14.0\% & 1 & 3.3\% \\  & **variance** & 1.01 & 20.5\% & 24.3 & 59.7\% & 0.51 & 16.9\% & 6 & 0.5\% \\ \hline \multicolumn{2}{|c|}{**Flat**} \\ \hline
00-00 & 28-1F** & \(-\)18 \(\div\) -10 & 0.63 & 8.1\% & 2 & 20\% & 0.7 & 8.9\% & 0 & 0\% \\
00-00 & 95-4C** & \(-\)12 \(\div\) -4 & 0.51 & 8.7\% & 1 & 25\% & 1.31 & 19.7\% & 0 & 0\% \\
00-00 & 1E-57** & \(-\)6 \(\div\) 2 & 1.76 & 31.3\% & 8 & 400\% & 0.7 & 15.3\% & 0 & 0\% \\
95-4C & 28-1F* & 2 \(\div\) 10 & 1.68 & 33.2\% & 7 & 70\% & 0.23 & 6.4\% & 0 & 0\% \\
28-1F & 1E-57* & 1 \(\div\) 9 & 1.39 & 27.7\% & 9 & 100\% & 0.41 & 10.2\% & 0 & 0\% \\
95-4C & 1E-57** & \(-\)6 \(\div\) 2 & 1.56 & 29.2\% & 10 & 50\% & 1.39 & 26.9\% & 2 & 100\% \\ \hline \multicolumn{2}{|c|}{**mean**} & 1.25 & 23.0\% & 6.17 & 170.5\% & 0.79 & 14.6\% & 0.33 & 16.7\% \\
**variance** & 0.55 & 11.5\% & 14.16 & 418\% & 0.47 & 7.7\% & 0.67 & 13.2\% \\ \hline \end{tabular}  
* _Path with one wall_; **_Path with two walls_.  
\end{table} 
Table 4: _Cont._  
Figure 8: Distance estimation error in percentage using 10 anchors. Table 4. Other than the absolute values (referred to as \"a.v.\"), the table presents the error in percentage. It can be noted that the errors in the conference room are smaller than in other scenarios. This result is due to the presence of more obstacles in both the office and the flat. This is a cause of stronger multipath fading that affects the measurements. It is also possible to note another problem when looking at the path loss logarithmic progress in Figure 10. For short distances, a small variation in the distance value corresponds to small variations in the path loss, whereas the same variation at greater distances corresponds to larger variations in terms of path loss. Accordingly, the absolute value of the error has to be considered together with the distance it is related to. This problem is more evident in large environments than in smaller ones, as can be clearly seen in Table 4.  
The estimation of physical layer performance is clearly improved with the application of the indirect observations (\"proposed method\"columns in Table 4). This method achieves significant improvements also in the scenarios characterized by the problem of large environments discussed before, allowing for compensating multipath fading effects due to the presence of more consecutive obstacles. As show in Table 4, it allows for reducing the RSSI estimation error from the results obtained with the application of the multilateration algorithm of 1.33 dB for the conference room scenario, 5.5 dB for the office room scenario and 5.85 dB for the flat scenario. The more complex is the scenario, the higher are the benefits of applying the proposed algorithm. With respect to the distance estimation, the RSSI evaluation presents lower errors. This is due to the fact that the RSSI and the node distance are linked by  
Figure 10: Path Loss progress. Figure 9: RSSI estimation error in percentage using 10 anchors. a logarithmic relationship, as discussed in Section 5.2.