# Analysis of Bluetooth RSSI for Proximity Detection of Ship Passengers
## 4 Impact of Quantization of Bluetooth RSSI Values
### Autocorrelation Analysis  
Figure 6 shows the variation of RSSI for two different poses of 3 ft and 15 ft. The measurement is performed over a continuous period of 3 min on different distances and poses. The RSSI range difference of sitting and standing poses is evident at 3 ft. However, it is not distinct at 15 ft--the RSSI of sitting and standing at 15 ft stabilized in a similar range. The RSSI of sitting and standing postures is clearly distinguished at 3 ft. RSSI content is almost identical with different poses at 15 ft. The RSSI of stand poses fluctuates mainly between \(-50\) dBm and \(-55\) dBm in the range of 0 to 1000 in the horizontal coordinate of 3 ft. In that range, the RSSI fluctuation interval of the sitting poses is two: One is in the horizontal coordinate of 0 to 500 range where the RSSI fluctuation interval is \(-55\) dBm to \(-70\) dBm. The other is in the horizontal coordinate of the 500 to 1000 range; the RSSI fluctuation interval is \(-50\) dBm to \(-55\) dBm. That is to say that in a specific time range of a close distance case, there is a significant difference in RSSI for various poses, and in the long-distance case, this difference gradually decreases. From the above analysis, we conclude that as distance increases, the difference in RSSI at various poses gradually decreases. Mean and skewness features for distinguishing different poses gradually disappear. In the case of close distance, the RSSI of different poses have various fluctuation intervals in different periods.  
This study performs autocorrelation analysis in order to determine how correlated RSSI values are over time. The equation for autocorrelation is as follows.  
\[R(k)=\frac{1}{(n-k)\sigma^{2}}\sum\
olimits_{t=1}^{n-k}(x_{t}-\mu)(x_{t+k}-\mu) \tag{1}\]  
Exploring the autocorrelation of RSSI focuses on measuring the relationship between RSSI at the current moment and the next moment. However, the relationship between the individual and RSSI also needs to be considered. Therefore, variance and mean are also  
Figure 5: Samples of RSSI distribution over three minutes (3 ft, Stand).  
included in the calculation. \(\sigma\) is variance, and \(\mu\) is mean. \(x_{t}\) is the RSSI at time \(t\), and \(x_{t+k}\) is the RSSI at time \(t+k\).  
This study assumes that RSSI is time-dependent. The correlograms are plotted in Figure 7. Figure 7 depicts similar shapes for 3 ft and 15 ft in sitting and standing pose. Note that the 15 ft (Sit and Stand) plot in Figure 7 has much smaller correlation coefficients at more considerable time lags, which indicated that dependences of RSSI sample reduced faster in 15 ft. This implies a faster signal change resulting from rapid change in the distance.  
Meanwhile, the RSSI of the standing pose correlation coefficients at the same distance had smaller values than the sitting pose. The visual tests for this sample suggest the possibility of a stationary process. The higher the distance, the larger the autocorrelation coefficient, and the smaller the distance, the smaller the autocorrelation coefficient, according  
Figure 6: RSSI over 3 min at 3 ft and 15 ft (Sit, Stand).  
Figure 7: Correlograms of RSSI (3 ft and 15 ft, Sit and Stand).  
to the correlogram. The influence of different postures on the autocorrelation coefficient is relatively minimal from the standpoint of the posture. The autocorrelation coefficient of the standing posture is slightly lower than that of the sitting posture. In other words, regardless of whether you sit or stand, the RSSI autocorrelation coefficient does not change appreciably. Note that since autocorrelations in the plots are significantly non-zero, the RSSI does have a strong correlation between consecutive samples as an assumption.