# Localization in Low Power Wide Area Networks Using Wi-Fi Fingerprints
## 2 Methods and Materials
### Wi-Fi Databases
Figure 1:0 Cumulative distribution of the location error at the eighth measurement location, using the WiGLE database. A detail of Figure (**a**) is shown in Figure (**b**). The mean location error is 101 km, the median location error is 45 m.

When sending the combination of BSSIDs with the highest RSSI values to the WiGLE database, the mean error of all measurement locations decreases from 6.24 km to only 103 m. The median error decreases from 77 m to 66 m. The probability that neither of those BSSIDs could be found, however, is 11.1%; no location can be estimated at those locations. Figure 7 shows the distribution of the error. ### LocationAPI Results

The location estimates when localizing using the LocationAPI database are much less prone to large errors than with the WiGLE database, see Figure 1:1 The overall mean location error is 21.06 km, while the overall median location error is 37 m. The 75 th percentile location error is never larger than 0.5 km. Seven locations have an error greater than 2 km, which is clipped in Figure 1:2 One of those is location 1. The mean location error is 546 km and the median location error is 23 m. The cumulative distribution of the errors at this location is shown in Figure 1:3 There is one combination of BSSIDs with a significant location error: 8543 km. However, more than 93.6% of the BSSID combinations have an error smaller than 43 m, see Figure 9b. Figure 1:4 Probability of finding no match for either of two BSSIDs in the WiGLE and LocationAPI database. The mean chance of finding no match over all locations is 13.2% for WiGLE, 12.5% for LocationAPI, and 1.9% for the combination. Figure 1:5 Cumulative distribution of the location error when two BSSIDs with the highest Received Signal Strength Indicator (RSSI) are transmitted. One outlier of LocationAPI and the combination is at 2.01 km. The average probability of finding neither BSSIDs in the LocationAPI database of a combination of WAPs seen at one of the 36 location is 12.5%. This is calculated as in Equation (2). Since it is not possible to request a single BSSID to the LocationAPI database, the chance of match of a single BSSID cannot be calculated. A graph of the probability of finding neither BSSIDs in the LocationAPI database is shown in Figure 1:6

When only sending the combination of BSSIDs with the highest RSSI values to the LocationAPI database, the mean error of all measurement locations decreases from 16 km to only 114 m. The median error decreases slightly, from 37 m to 33 m. The probability that neither of those BSSIDs can be found, however, is again 19.4%; no location can be estimated at those locations. Figure 7 shows the distribution of the error. ### Combination of WiGLE and LocationAPI

A straightforward solution to improve the results is to combine the WiGLE and LocationAPI databases. As a first approach, we propose to combine the location estimates from both database by taking their average; this result can be seen in Figure 1:7 The overall mean location error is 31.79 km, while the overall median location error is 53 m. The 75 th percentile location error is only once larger than 1 km. Fifteen locations have an error greater than 2 km, which is clipped in Figure 1:8

Figure 1:9 Overview of the location error on all 36 locations using the LocationAPI database. Errors larger than 2 km are clipped. Figure 2:0 Cumulative distribution of the location error at the first measurement location, using the LocationAPI database. A detail of Figure (**a**) is shown in Figure (**b**). The mean location error is 546 km, the median location error is 23 m.

The location error overview of the second approach, which favors the LocationAPI database since it generally has a lower location error, is shown in Figure 2:1 The overall mean location error is 24.17 km, while the overall median location error is 40 m. The 75 th percentile location error is never larger than 0.5 km.