# Analysis of Bluetooth RSSI for Proximity Detection of Ship Passengers
## 4 Impact of Quantization of Bluetooth RSSI Values
### Statistical Analysis
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline
**Statistics** & **3 ft** & **4 ft** & **5 ft** & **6 ft** & **8 ft** & **10 ft** & **12 ft** & **15 ft** \\ \hline Mean (Sit) & \(-58.2\) & \(-62\) & \(-66.5\) & \(-69.5\) & \(-67.5\) & \(-68.0\) & \(-72.4\) & \(-71.2\) \\ \hline Median (Sit) & \(-56\) & \(-61\) & \(-66\) & \(-68\) & \(-67\) & \(-68\) & \(-72\) & \(-71\) \\ \hline Mode (Sit) & \(-51\) & \(-57\) & \(-62\) & \(-68\) & \(-61\) & \(-72\) & \(-72\) & \(-72\) \\ \hline Standard Deviation (Sit) & \(6.1\) & \(6.7\) & \(5.9\) & \(7.6\) & \(6.5\) & \(7.4\) & \(6.7\) & \(4.9\) \\ \hline Skewness (Sit) & \(-0.62\) & \(-0.62\) & \(-0.64\) & \(-1.03\) & \(-0.76\) & \(-0.14\) & \(-0.47\) & \(0.06\) \\ \hline Range (Sit) & \(26\) & \(36\) & \(40\) & \(40\) & \(35\) & \(40\) & \(41\) & \(33\) \\ \hline Minimum (Sit) & \(-76\) & \(-86\) & \(-93\) & \(-97\) & \(-91\) & \(-93\) & \(-98\) & \(-89\) \\ \hline Maximum (Sit) & \(-50\) & \(-50\) & \(-53\) & \(-57\) & \(-56\) & \(-53\) & \(-57\) & \(-56\) \\ \hline
**Statistics** & **3 ft** & **4 ft** & **5 ft** & **6 ft** & **8 ft** & **10 ft** & **12 ft** & **15 ft** \\ \hline Mean (Stand) & \(-54.0\) & \(-57.9\) & \(-58.0\) & \(-58.6\) & \(-60.7\) & \(-61.0\) & \(-67.4\) & \(-70.6\) \\ \hline Median (Stand) & \(-54\) & \(-57\) & \(-58\) & \(-58\) & \(-60\) & \(-60\) & \(-66\) & \(-69\) \\ \hline Mode (Stand) & \(-57\) & \(-54\) & \(-54\) & \(-55\) & \(-61\) & \(-56\) & \(-66\) & \(-65\) \\ \hline Standard Deviation (Stand) & \(5.2\) & \(6.2\) & \(5.5\) & \(5.2\) & \(4.9\) & \(5.4\) & \(5.8\) & \(6.2\) \\ \hline Skewness (Stand) & \(-0.18\) & \(-1.37\) & \(-1.36\) & \(-0.94\) & \(-0.67\) & \(-0.6\) & \(-0.8\) & \(-0.96\) \\ \hline Range (Stand) & \(35\) & \(45\) & \(43\) & \(33\) & \(35\) & \(36\) & \(44\) & \(36\) \\ \hline Minimum (Stand) & \(-77\) & \(-92\) & \(-92\) & \(-82\) & \(-85\) & \(-86\) & \(-97\) & \(-95\) \\ \hline Maximum (Stand) & \(-42\) & \(-47\) & \(-49\) & \(-49\) & \(-50\) & \(-50\) & \(-53\) & \(-59\) \\ \hline \end{tabular}
\end{table} 
Table 1: Statistics of RSSI measured from different distances (Sit and Stand cases) (source: PACT dataset). say that using the median value of RSSI for proximity detection will produce a significant error at these distances. In addition, it is not possible to reduce these errors from the standard deviation at these distances. Considering only the dispersion of Bluetooth RSSI values from the mean value, whether in sitting or standing poses, does not minimize errors. In skewness, all distributions are left-skewed, except for the 15 ft RSSI distribution in sitting pose, which is right-skewed. In addition, the minimum and maximum values of RSSI also do not conform to the rule that RSSI decays with increasing distance. From the above analysis, we conclude that the mean value of RSSI can be used to reduce error rather than relying on median, mode, minimum, and maximum when conducting proximity detection in two different poses: that of sitting and standing. If only RSSI dispersion is considered, reducing errors becomes challenging. Moreover, in most cases, RSSI values almost wholly belong to left-skewed distributions. Traditionally, RSSI is believed to be log-normally distributed according to the large-scale fading model impact on receiver design and coverage. There is still a lack of necessary understanding of RSSI properties from the perspective of proximity detection [27]. Due to propagating effects, such as reflection, diffraction, and dispersion caused by dense multipath and indoor environments, it is challenging to predict radio frequency (RF) signal variations [28]. The multi-path fading effect results from a constructive or destructive combination of multiple signal copies at the receiver, causing the signal received to fluctuate in a particular area around the mean value [29]. In the case of large-scale decreases and small-scale declines, the received signal is generally modeled [30]. Note that the measurements average small-scale fading results when RSSI is average [31].