# Collaborative Indoor Positioning by Localization Comparison at an Encounter Position
## 4 Experiments
### Evaluation on Localization  
The proposed method was evaluated in 100 trials using each walking dataset. The evaluation metric for the localization is described in Section 3.3.3. There are two comparison methods for indoor localization using map images. The first comparison method is the  
Figure 8: Test dataset. Red is a walking path. Cyan is an encounter position. The non-English terms in the maps are the room and store names.  
baseline method using PDR and particle filter described in Section 3.1. The second comparison method, [PERSON]'s method [9], improves the baseline method by modifying the weights of particles using encounter communication. When the standard deviation of the collaborator's particles, \(\sigma_{C}\), is within 10 m, the weight of the particle \(W_{i}\) with index \(i\) is updated by Equation (6). \(p_{i}\) is the position of the particle and \(l_{C}\) represents the estimated location of the collaborator at the encounter. The hyperparameters \(\mu_{\text{BLE}}\) and \(\sigma_{\text{BLE}}\) represent the average and standard deviation of distances between two devices measured by BLE. Values of \(d=1.91\) and \(\sigma_{E}=1.26\) were determined experimentally.  
\[W_{i}=\exp\biggl{(}-\frac{(\|p_{i}-l_{C}\|-\mu_{\text{BLE}})^{2}}{2(\sigma_{C} +\sigma_{\text{BLE}})^{2}}\biggr{)} \tag{6}\]  
Table 2 shows the localization results. The proposed method improved the baseline of the average metric by about 18 pixels. On the other hand, the improvement by [PERSON]'s method was about 2 pixels, which was much smaller than the proposed method. [PERSON]'s method did not sufficiently utilize the collaborator's position when modifying the localization. The proposed method exhibited some slight degradations in accuracy, such as route 2 in Fujisaki and Mitsukoshi. Since the collaborator's position was far from the encounter point, the particles were updated to the wrong positions.  
Figure 9 shows an example of the correction for route 1 in Agriculture. The cyan dots are the start positions. The red and blue dots are the estimated position and the turning point, respectively. The red and blue cross marks are the detected encounter positions of the user and its counterpart, respectively. The proposed method correctly estimated the position after collaborative localization correction at the detected encounter. In contrast, the baseline method accumulated errors. [PERSON]'s method slightly modified the localization using the collaborator's position. However, the effect of the modification was insufficient.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Facility** & **Walk** & **Baseline** & **Qiu [9]** & **Ours** \\ \hline \multirow{2}{*}{Bldg. No. 1} & 1 & 21.4 & **21.0** & 22.3 \\  & 2 & 28.3 & **28.1** & 28.3 \\ \hline \multirow{2}{*}{AER1F} & 1 & 93.5 & 90.9 & **66.2** \\  & 2 & 62.5 & 61.2 & **57.2** \\ \hline \multirow{2}{*}{AER2F} & 1 & 100.4 & 97.5 & **88.5** \\  & 2 & 135.2 & 134.6 & **112.1** \\ \hline \multirow{2}{*}{Fujisaki} & 1 & 184.8 & 178.0 & **90.0** \\  & 2 & **25.0** & **25.0** & 31.1 \\ \hline \multirow{2}{*}{Mitsukoshi} & 1 & 58.7 & 54.4 & **43.9** \\  & 2 & 39.7 & **38.1** & 51.8 \\ \hline \multirow{2}{*}{Agriculture} & 1 & 69.1 & 57.0 & **34.4** \\  & 2 & 30.2 & 28.9 & **28.6** \\ \hline \multirow{2}{*}{Complex} & 1 & 44.6 & 44.5 & **41.3** \\  & 2 & **44.7** & **44.7** & 46.7 \\ \hline \multirow{2}{*}{SPAL} & 1 & 95.0 & 118.7 & **50.2** \\  & 2 & 214.2 & 193.6 & **173.6** \\ \hline \multirow{2}{*}{Average} & & 78.0 & 76.0 & **60.4** \\ \hline \hline \end{tabular}
\end{table}
Table 2: Average metric (error distance in pixels) in map images for indoor localization. Bold is the best result. Lower is better.