# RSSI and Device Pose Fusion for Fingerprinting-Based Indoor Smartphone Localization Systems
## 4 Results and Analysis
### RSSI Data Distribution  
The distributions of the RSSI measurements of the anchors for the different use cases at each location are given in Figure 8 for the static files (i.e., user stationary in the particular device pose use case). In order to quantitatively explore the effect of device pose on the RSSI, the two-sample two-sided Kolmogorov-Smirnov (KS) statistic was calculated for all  
Figure 7: Experimental setup for data collection. locations, device pose use cases, and static/dynamic files. The two-sample KS statistic is a nonparametric statistic defined by:  
\[D_{AB}=\underset{x}{\text{max}}(|F_{A}-F_{B}|) \tag{1}\]  
where \(F_{A}\) and \(F_{B}\) are the empirical cumulative distribution functions (ECDFs) of two different sample sets. The KS test was used because it is a nonparametric test used to identify whether two sample sets come from the same distribution [23]. The KS test statistic's p-values for the RSSI of Anchor1 for all locations and all device-pose use cases for the static file are shown in Figure 9 (because \(D_{AB}=D_{BA}\) in Equation (1), only the lower triangular entries of the symmetric matrix are relevant). The KS test null hypothesis (\(H_{0}\)) is that the samples come from the same distribution. The instances (cells) where the KS test's \(H_{0}\) would fail to be rejected (using the typical \(p\)-value \(\geq 0.05\)) are indicated with red font and outlined with a border, and represent KS test type II errors. The KS test type II errors represent a failure of true negative (TN) classification (i.e., true negative is the rejection of \(H_{0}\) when \(H_{0}\) is false). The KS test statistic p-values were calculated in this manner for all anchors for all locations and device poses and for both the static and dynamic files. In Table 3, these instances of the KS test type II errors are grouped by location, and the total number of type II errors between the locations for the anchors are given. Several trends can be seen in these RSSI distributions as well as from the KS statistics:  
1. Anchors closest to a location tended to have the highest RSSI: As mentioned in Section 3.3, each zone had a nearby anchor. The trend of an elevated median RSSI value at that zone for its nearest anchor is clearly depicted in Figure 8, where Anchor 2, Anchor 3, Anchor 4, and Anchor 5 have high median values for nearly every use case for their corresponding closest positions. 2. RSSI variation due to device pose that resulted in distributions from different locations seemed alike: This trend encapsulates the premise of the proposed framework. For example, referring to column ZA_AE and row ZB_IH in Figure 9, the RSSI distribution for Anchor 1 in the static dataset while standing in the ZA zone and holding device AtEar leads to the null hypothesis acceptance of the KS test, implying that it is from the same RSSI distribution as the ZB zone while the device is held InHand (i.e., a KS test type II error for the distribution conditioned on location). Thus, based on the RSSI of Anchor 1 alone, it would be difficult to distinguish the ZA location from the ZB location while the phone is in those device poses. This would reduce the localization accuracy of any pattern recognition approach wherever Anchor 1's distribution emerges as an important feature for classifying the ZA and ZB locations. Importantly, as Table 3 shows, the KS test has type II errors more often for RSSI distributions grouped by different locations (which would affect localization accuracy) than for distributions grouped in the same location (which would not affect localization accuracy). 3. Most KS test Type II errors involving ZB: From Table 3, looking at the zones with the three highest numbers of KS test type II errors (bold and underlined in the right-most column of the table), these are for ZB and ZD, and ZA and ZB. Therefore, given the hypothesis of this study, it could be predicted that adding device pose information likely results in the highest improved TN rates for zone ZB.