# Low-Power LoRa Signal-Based Outdoor Positioning Using Fingerprint Algorithm
## 4 Experimental Results  
We set up the 340 m \(\times\) 340 m experimental area as shown in Figure 14. We installed four gateways equipped with Semtech Corporations' SX1276 chipsets. The training and test datasets were collected separately in the same area. When the fingerprint maps were generated for each gateway, the test dataset was excluded. In total, 340 \(\times\) 340 = 115,600 grid cells with 1 m \(\times\) 1 m resolution were constructed for the test. We fixed the LoRa spreading factor as 7.  
When duplicate RSSI values existed in the same grid, their mean value was assigned in that grid. Interpolated values were used to fill grids that had no RSSI value. In the offline phase, a matrix with 340 \(\times\) 340 cells was created and used for fingerprint map generation for each gateway.  
Candidate regions were extracted from the interpolated fingerprint map in the online phase. Then, probability maps were generated using these regions as inputs, and the most probable region was derived as the estimated location.  
Three different algorithms were applied to the probability map generation process. Algorithm 1 calculates the extracted candidate regions with the same weight factor. Algorithm 2 normalizes the weighting factors with the area of each region. Algorithm 3 calculates the factor by applying Equation (6); in this case, a higher weight is assigned to a stronger signal.  
A total of 46 points were selected as the test dataset, and errors were calculated using each algorithm. Table 2 shows the obtained error results. The average error of Algorithms 1-3 was 32.5 m, 29.8 m, and 24.1 m, respectively. The standard deviation of error for each algorithm was 26.5 m, 24.1 m, and 17.8 m. Therefore, algorithm 3 showed the best result.  
Figure 15 shows the cumulative probability distribution of errors for each algorithm, where the \(X\)-axis represents the error in meters and the \(Y\)-axis, the cumulative distribution function. Algorithms 1-3 are represented by red, green, and blue lines, respectively. Dashed lines indicate the average error over all test points for each algorithm. The solid vertical lines near 100 m indicate the maximum estimation errors. As seen in Table 2, Algorithm 1 (red) and Algorithm 2 (green) both showed maximum  
\begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Point**} & \multicolumn{3}{c}{**Algorithm**} & \multicolumn{3}{c}{**Point**} & \multicolumn{3}{c}{**Algorithm**} & \multicolumn{3}{c}{**Point**} & \multicolumn{3}{c}{**Algorithm**} \\ \cline{2-13}  & **1** & **2** & **3** & **Number**  
estimation errors of 107.7 m for sample point 18, and Algorithm 3 showed maximum estimation error of 91.7 m for sample point 15.  
The example of positioning for point 1 is described as follows. Gateways 1-4 measure the RSSI values as \(-125\), \(-97\), \(-79\), and \(-94\) dBm, respectively, and these values are sent to the positioning server. The candidate regions with a constant buffer are displayed over the fingerprint maps, as shown in Figure 16. The probability maps and errors for the three algorithms are shown in Figure 17. The red circle represents the true location of the end device and the white circle, the estimated location.  
Figure 16: Candidate regions extracted with buffer.  
Figure 17: Probability maps and errors for three algorithms.  
Figure 15: Cumulative probability distribution of errors.