# Measurement and Analysis of RSS Using Bluetooth Mesh Network for Localization Applications
## 5 Analysis of RSS Measurements Using Bluetooth Mesh Network
### Path Loss Models  
We have conducted extensive measurements in the ESPS Lab (B216) and a few other labs in the surrounding areas at the EE Department, UNT, as shown in Figure 12. Transmitter (i.e., beacon node) device is installed on a tripod and receiver (i.e., scanner node) devices are installed on the panning measurement platform shown in Figure 6. During measurement, transmitter is placed at the positions A, B, and C in the lab B216. For each transmitter position, receiver units are moved around the area and the RSS measurements are collected at each of the receiver positions. Some actual receiver positions are marked with \"x\" in the diagram shown in Figure 12, although there are many more receiver positions in the corridor and Lab B207 and Lab B217 that are located beyond the area that is shown in the diagram. During measurement, all six receivers were turned on to receive signals from the transmitter and measure RSS of the received signals. At each of the receiver positions, 60 RSS measurement data are collected by each of the six receivers, including 20 measurements for each of the three advertising channels. All measurement data collected from one of the six receivers are shown in Figure 13. From the scatter plot shown in Figure 13, we can observe slightly different trends for the data measured at the distances below 10 m and above 10 m, which indicates that a two-segment partitioned path loss model defined in (3) might be more appropriate than the non-partitioned model in (1). In addition, we can also observe a few outliers in the measurement data, which may significantly affect the  
Figure 11: RSS measurements in dBm unit using six receiver antennas installed at the positions P1 to P6 on the measurement platform. Transmitter and receiver devices are 4 m apart in distance and all devices use the external 6 dBi omnidirectional antenna. Figure 12: Measurement positions in ESPS Lab (B216) and surrounding areas. path loss models derived using linear regression methods. Therefore, in the following, we used median, instead of average, when combining multiple measurements at each receiver position to reduce small-scale fading effects. It is well known that median is more robust to outliers statistically than average. As mentioned earlier, at each of the receiver positions, 60 RSS measurements are collected by each of the six receivers, including 20 measurements from each of the three advertising channels. Figure 14 presents the path loss models derived using one random data sample from only one receiver and the model parameter values are summarized in Table 1. From the results shown in Figure 14 and Table 1, we can observe that the RSS measurement data collected from different advertising channels conform to different path loss models. In generating the path loss model plots in Figure 14, we plotted RSS versus distance since the measured RSS value is the received signal power in dBm unit. The RSS \(\bar{P}_{r}(d)\) is defined in (1) with reference to the path loss \(L(d)\). Because the path loss \(L(d)=P_{t}[\text{dBm}]-\bar{P}_{r}(d)[\text{dBm}]\) when both \(P_{t}\) and \(\bar{P}_{r}(d)\) are in dBm unit, we can easily transform the path loss model formula in (1) to the following,  
\[\bar{P}_{r}(d)[\text{dBm}]=\bar{P}_{r}(d_{0})[\text{dBm}]-10\alpha\log_{10}( \frac{d}{d_{0}})-\chi. \tag{4}\]  
Figure 14: Two-segment path loss models derived using one random data sample from only one receiver. Figure 13: Scatter plot of all RSS measurement data that are collected from one of the six receivers. The two-segment path loss model defined in (3) can also be transformed similarly. The RSS at the reference distance \(d_{0}=1\) m, i.e., \(\bar{P}_{r}(1)\), is first determined through measurements. Then, measurement data are collected by moving receivers to different locations as described earlier. Each measurement data consists of the RSS measurement, receiver ID, and the message sequence ID, which are used in postprocessing to identify and group the measurements collected from multiple receivers simultaneously.