# Design and Implementation of an Indoor Localization System Based on RSSI in IEEE 802.11 ax
## 3 Results
Finally, to analyze the path loss, linear regression was performed using the RSSI data, resulting in the model shown in Figure 9. The equation obtained is  
\[PL(d)=PL(d_{0})+10(3.15379)\log\left(\frac{d}{d_{0}}\right)+54.11723 \tag{26}\]  
where 3.15379 represents the path loss coefficient, and 54.11723 is the fading factor \(X_{\sigma}\). Using this coefficient and the RSSI values, the distance to the unknown node is estimated using Equation (8). This distance is then applied in trilateration, Min-Max, and Maximum Likelihood algorithms to calculate the precise localization. Figure 4: Comparison of RSSI and distance between experimental data and data from Ding and Dong (2020) [1]. Figure 5: Relationship between RSSI and distance throughout the hours of the day. Table 3.0 Dispersion diagram of RSSI and distance. Table 3.1 Dispersion diagram of RSSI and measurement days. Table 3.2 Dispersion diagram for relationship between RSSI and measurement hours. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Distance (m)** & **Mean RSSI (dBm)** & **Standard Deviation** \\ \hline
2 & \(-36\) & \(1.6546\) \\
4 & \(-49\) & \(2.1884\) \\
5 & \(-50\) & \(2.2917\) \\
6 & \(-52\) & \(2.7710\) \\
7 & \(-54\) & \(2.9925\) \\
11 & \(-68\) & \(3.5216\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Mean RSSI and its standard deviation as a function of distance. Figure 9: Path loss model vs. distance. The RSSI values were measured over a distance range of 1 to 11 m, and the corresponding estimated distances were calculated using these values. The estimated distances were then compared to the actual distances, and the resulting percentage error was calculated. The results, as shown in Table 6, demonstrate that the distance estimates based on RSSI are generally accurate, with a maximum error margin of 10.50%. This indicates that the RSSI-based distance calculation provides a reasonable approximation of the real distance, falling within an acceptable error threshold. The data provided were based on using a \begin{table}
\begin{tabular}{c c c} \hline
**Day** & **RSSI Mean (dBm)** & **Standard Deviation (dBm)** \\ \hline  
\hline \end{tabular}
\end{table} 
Table 4: Daily RSSI means and standard deviations. \begin{table}
\begin{tabular}{c c c c c c c} \hline
**Hour/Distance** & **2 m** & **4 m** & **5 m** & **6 m** & **7 m** & **11 m** \\ \hline
10:00 a.m. & \(-\)33 & \(-\)48 & \(-\)52 & \(-\)55 & \(-\)61 & \(-\)63 \\
12:00 p.m. & \(-\)32 & \(-\)50 & \(-\)56 & \(-\)56 & \(-\)60 & \(-\)64 \\
02:00 p.m. & \(-\)31 & \(-\)50 & \(-\)55 & \(-\)57 & \(-\)63 & \(-\)66 \\
05:00 p.m. & \(-\)36 & \(-\)50 & \(-\)56 & \(-\)58 & \(-\)62 & \(-\)64 \\
08:00 p.m. & \(-\)35 & \(-\)50 & \(-\)55 & \(-\)57 & \(-\)60 & \(-\)62 \\
10:00 p.m. & \(-\)34 & \(-\)51 & \(-\)54 & \(-\)58 & \(-\)61 & \(-\)62 \\ \hline Mean & \(-\)33.50 & \(-\)49.83 & \(-\)54.67 & \(-\)56.83 & \(-\)61.17 & \(-\)63.50 \\ Std. Dev. & 1.64 & 0.98 & 1.63 & 1.17 & 1.17 & 1.52 \\ \hline \end{tabular}
\end{table} 
Table 5: RSSI measurements at different distances and times. Neo-6M GPS module to obtain geographic coordinates for both the unknown node and the anchor nodes. These coordinates were then transformed into Cartesian coordinates to optimize the localization process. Table 7 presents the localization data for the unknown node, detailing its geographic latitude and longitude, as well as its Cartesian coordinates (X, Y). The specific data row indicates a point with a latitude of 22.107777 and a longitude of \(-\)100.845103, which corresponds to Cartesian coordinates of 309,667.415 for X and 2,445,910.095 for Y.