# Design and Implementation of an Indoor Localization System Based on RSSI in IEEE 802.11 ax
## 3 Results
### Localization Data and Min-Max Method Analysis  
The localization data for the anchor nodes used in the Min-Max algorithm are presented in Table 12, which include their geographical latitude and longitude, as well as their Cartesian coordinates (X, Y) in meters. The table also lists the positions of the three anchor nodes, along with their respective locations:  
* **Node 1:** Located at the latitude 22.107776 and the longitude \(-100.84508\), with Cartesian coordinates of 309,669.41 m for X and 2,445,910.071 m for Y;
* **Node 2:** Positioned at the latitude 22.107777 and the longitude \(-100.845054\), with Cartesian coordinates of 309,672.42 m for X and 2,445,910.03 m for Y;
* **Node 3:** Found at the latitude 22.107705 and the longitude \(-100.84510\), with Cartesian coordinates of 309,667.31 m for X and 2,445,902.12 m for Y.  
RSSI measurements from the anchor nodes were used to estimate the distances between the unknown node and the reference nodes through signal propagation models. These distances were critical to the application of the Min-Max algorithm, as shown in Table 13. Figure 11 shows the area where the measurements were taken, as well as the nodes, indicating the locations of the anchor nodes relative to the transmitter for the Min-Max method. Once the coordinates of the anchor nodes and the distances between these nodes and the unknown node were obtained, the coordinates of the unknown node were determined using the Min-Max localization algorithm, as detailed in Table 14, which displays the localization data for the unknown node, including the geographical latitude and longitude, as well as the Cartesian coordinates (X, Y) in meters, for the unknown node:  
* Latitude: 22.10778349;
* Longitude: \(-100.8450892\);
* X (m): 309,668.849;
* Y (m): 2,445,910.797.  
Finally, the actual coordinates of the unknown node were compared with those calculated using the Min-Max localization algorithm, and the resulting error in meters was computed and is presented in Table 15.  
\begin{table}
\begin{tabular}{c c c c} \hline
**Latitude** & **Longitude** & **X (m)** & **Y (m)** \\ \hline
22.10779443 & \(-100.8451071\) & 309,667.0153 & 2,445,912.03 \\ \hline \end{tabular}
\end{table}
Table 10: Unknown node localization data via the trilateration algorithm.  
\begin{table}
\begin{tabular}{c c c c} \hline
**Algorithm** & **Error in X (m)** & **Error in Y (m)** & **Position Error (m)** \\ \hline Trilateration & 0.3997 & 1.9350 & 1.9758 \\ \hline \end{tabular}
\end{table}
Table 11: Errors in the coordinates and position obtained through the trilateration localization algorithm.  
\begin{table}
\begin{tabular}{c c c c c} \hline
**Anchor Nodes** & **Latitude** & **Longitude** & **X (m)** & **Y (m)** \\ \hline Node 1 & 22.107776 & \(-100.84508\) & 309,669.41 & 2,445,910.071 \\ Node 2 & 22.107777 & \(-100.845054\) & 309,672.42 & 2,445,910.03 \\ Node 3 & 22.107705 & \(-100.84510\) & 309,667.31 & 2,445,902.12 \\ \hline \end{tabular}
\end{table}
Table 12: Localization data for anchor nodes for the Min–Max algorithm (latitude, longitude, X, Y coordinates).  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Latitude** & **Longitude** & **X (m)** & **Y (m)** \\ \hline
22.10778349 & \(-\)100.8450892 & 309,668.849 & 2,445,910.797 \\ \hline \hline \end{tabular}
\end{table}
Table 14: Unknown node localization data via Min–Max algorithm.  
Figure 11: Map of the measurement area with anchor nodes and transmitter locations for the min–max method.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Anchor Nodes** & **RSSI (dBm)** & **Estimated Distance (m)** \\ \hline Node 1 & \(-\)39 & 1.93 \\ Node 2 & \(-\)54 & 5.77 \\ Node 3 & \(-\)61 & 9.91 \\ \hline \hline \end{tabular}
\end{table}
Table 13: RSSI of anchor nodes and estimated distance for Min–Max algorithm.