# Analysis of Bluetooth RSSI for Proximity Detection of Ship Passengers
## 4 Impact of Quantization of Bluetooth RSSI Values
### Visualize RSSI Patterns in Different Poses  
Figure 8 shows two-dimensional plots of RSSI patterns from different poses at the same distance. The \(x\)-axis represents the RSSI of the sitting posture. The \(y\)-axis represents the RSSI of the standing posture. Note that the pattern of RSSIs of different poses cannot be grouped into clusters. The degree of separation does not increase as distance changes from 3 ft to 15 ft at different poses. This observation suggests that signals with more significant standard deviations (or variance) will make it more challenging to perform proximity detection. The 3-feet distance, as shown in Figure 9, has a substantially more distinct patterns than the other lengths. As a result, RSSI data from sitting and standing poses may be combined to obtain a 3-feet distance marker. On the other hand, the different distances produce no discernible pattern change. The RSSs of the sitting and standing poses for the 3-feet distance is closer simultaneously, but the RSSs of the two poses for the other ranges are further away. The overlap between the patterns becomes a bigger problem for proximity detection as the number of distances increases. This can be depicted in Figure 9 when plotting the three  
Figure 8: RSSI of different poses and distances. Figure 9: Three-dimensional density plots of RSSI with 3 ft, 8 ft, and 15 ft.  
dimensions for RSSI patterns. The density of the \(y\)-axis is the kernel density estimation (KDE) [33]. KDE is a non-parametric method used for estimating a random variable probability density function. The RSSI value can be considered as a point. The density of issues can be calculated to reveal the degree of clustering points. This degree of aggregation can form a pattern. Under different conditions, different degrees of the collection show different designs. KDE can visualize RSSI patterns. The formula is as follows:  
\[f_{h}(x)=\frac{1}{nh}\sum_{i=1}^{n}K\bigg{(}\frac{x-x_{i}}{h}\bigg{)} \tag{2}\]  
where \(K\) is the kernel (a non-negative function), and \(h\) is the bandwidth's smoothing parameter (\(h>0\)). \(x\) is any given RSSI. \(n\) is the number of RSSI. Figure 9 shows that the two RSSI patterns are easier to classify at 3 ft. However, the overlap between the patterns occurs at 8 ft and 15 ft. In general, the increasing number of RSSI data is one method of separating different distances. The effect of peoples' poses on the RSSI signal gradually decreases with distance [34]. Note that it is difficult to illustrate the frequency of each pattern at 3 ft, but we may deduce that the highest frequency of occurrence will be at the center of each cluster. In the case of long distances, the effect of the different poses of people producing different patterns of RSSI becomes smaller. In real situations, this intermittence of received signals can result in incomplete or censored RSSI patterns during the proximity detection phase [35]. This affects proximity detection performance when matching a preliminary RSSI pattern to proximity detection. In general, RSSI distance calculation is performed with a log-distance path loss model. However, only one RSSI value can be entered into this model. A single RSSI value is usually a representative RSSI value over time. This can be mean, median, mode, minimum, and maximum, and it can be different for the same distance due to the effects of the pose on RSSI distribution. This can cause a mistake in distance calculation. This mistake can reduce the accuracy of trilateral localization. Fingerprint profiles are also produced by using representative RSSI values, resulting in errors when comparing fingerprint profiles. While the pose impacts the RSSI distribution, this impact is constant over time. While the RSSI distribution for each position is different for the same distance, this difference can be used as a feature. In other words, RSSI can be marked in advance by pose and distance. For each posture and distance, the RSSI distribution is calculated.