# Design and Implementation of an Indoor Localization System Based on RSSI in IEEE 802.11 ax
## 3 Results
### Localization Data and Maximum Likelihood Method Analysis  
The localization data for the anchor nodes used in the Maximum Likelihood algorithm are presented in Table 16, which include their geographical latitude and longitude, as well as their Cartesian coordinates (X, Y) in meters. The table lists the six anchor nodes, along with their respective positions:  
* **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;
* **Node 4:** Located at the latitude 22.107678 and the longitude \(-100.845103\), with Cartesian coordinates of 309,667.282 m for X and 2,445,899.141 m for Y;
* **Node 5:** Positioned at the latitude 22.107777 and the longitude \(-100.845093\), with Cartesian coordinates of 309,668.417 m for X and 2,445,910.083 m for Y;
* **Node 6:** Found at the latitude 22.107830 and the longitude \(-100.845103\), with Cartesian coordinates of 309,667.488 m for X and 2,445,916.07 m for Y.  
RSSI measurements from the anchor nodes were used to estimate the distances between the unknown node and the reference nodes using signal propagation models. These distances were crucial to the application of the Maximum Likelihood algorithm, as shown in Table 17. Figure 12 shows the area where the measurements were taken, as well as the nodes, indicating the locations of the anchor nodes relative to that of the transmitter for the Maximum Likelihood 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 Maximum Likelihood localization algorithm, as detailed in Table 18, which presents the localization data for the unknown node, including its geographical latitude and longitude, as well as its Cartesian coordinates (X, Y) in meters:  
* **Latitude:** 22.10778663;
* **Longitude:** \(-100.8450936\);
* **X (m):** 309,668.4;
* **Y (m):** 2,445,911.15.  
Finally, the actual coordinates of the unknown node were compared with those calculated using the Maximum Likelihood localization algorithm, and the resulting error in meters was computed and is presented in Table 19.  
\begin{table}
\begin{tabular}{c c c c c} \hline \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 \\ Node 4 & 22.107678 & \(-100.845103\) & 309,667.282 & 2,445,899.141 \\  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Latitude** & **Longitude** & **X (m)** & **Y (m)** \\ \hline
22.10778663 & \(-100.8450936\) & 309,668.4 & 2,445,911.15 \\ \hline \hline \end{tabular}
\end{table}
Table 19: Errors in coordinates and position according to the localization algorithm.  
Figure 12: Map of the measurement area with anchor nodes and transmitter locations for the Maximum Likelihood 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 & \(-61\) & \(9.91\) \\ Node 4 & \(-64\) & \(11.97\) \\ Node 5 & \(-31\) & \(1.08\) \\ Node 6 & \(-55\) & \(6.2\) \\ \hline \hline \end{tabular}
\end{table}
Table 17: RSSI of anchor nodes and estimated distance for Maximum Likelihood algorithm.