# 2D Phase-Based RFID Localization for On-Site Landslide Monitoring
## 4 Hamaliere Landslide Monitoring
### Application of the Model to a Real Geometry
#### 4.2.2 Systematic Localization Bias of the Experimental Field  
The systematic localization bias (related to \(\phi_{b}\), Equation (13)) presented in Figure 5b,c is not to be understood as a raw localization error, but as a varying bias when moving in space; the interference between LOS and the reflected signal changes with tag position.  
To better understand the effect of the multipath-induced phase bias on 3D displacement measurements, we propose to consider the typical case of a 1 m displacement along a given spatial direction, starting from the position of tag A. The symmetry of our experiment being mainly cylindrical, we consider a cylindrical coordinate system with its central axis in (\(x=0\), \(y=0\)). For this displacement, we compute the localization bias fluctuation, and project it on every space direction (along \(\vec{u_{\theta}}\), \(\vec{u_{r}}\), \(\vec{u_{z}}\)) to obtain an amplitude value. The displacement length of 1 m was chosen both because it encompasses about one phase bias cycle, and because it corresponds to the actual displacement we measured in the real landslide scenario (see next section).  
Table 2 reports the simulated localization bias amplitude in the three space directions, together with real error measurements that were performed on field.  
* The direction that produces the least bias variation is a \(\vec{u_{\theta}}\) displacement, which corresponds to the quasi rotational symmetry of the system.
* A horizontal displacement along \(\vec{u_{r}}\) yields a small localization error. This confirms previous studies and demonstrates a centimeter precision for the RFID technique in the horizontal plane [18].
* A vertical displacement along \(\vec{u_{z}}\) undergoes several strong bias oscillations (Figure 5c). The subsequent localization error is a cumulative effect of both the strong multipath interference and the small vertical aperture of the measurement system.  
These results tend to show that vertical localization in the current localization scheme cannot be performed with precision. The multipath effect, along with the high system sensitivity in this direction, yield a very high localization bias. This is why we will not present \(Oz\) localization results in the following section. This model highlights the importance of the geometrical features of the system, such as antenna position and spacing, tag height and direction of displacement.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Bias** & **Dir.** & \(\vec{u_{\theta}}\) & \(\vec{u_{t}}\) & \(\vec{u_{z}}\) \\ \hline max. \(\vec{u_{\theta}}\) bias & \(<\)1 cm & \(<\)1 cm & 10 cm \\  & & (1 \(cm\) ) & (20 \(cm\)) \\ \hline max. \(\vec{u_{r}}\) bias & 1 cm & 1 cm & 2 cm \\  & & (1 \(cm\)) & (15 \(cm\)) \\ \hline max. \(\vec{u_{z}}\) bias & 1 cm & \(<\)1 cm & 70 cm \\  & & (5 \(cm\)) & (10 \(cm\)) \\ \hline \hline \end{tabular}
\end{table}
Table 2: Direction-dependent localization bias in the 3 directions (cylindrical coordinates), for a typical 1 m displacement. Each column corresponds to a different direction of displacement. Each line represents the localization bias amplitude along a certain direction, during the 1 m displacement. The _values in italic_ correspond to field experiment localization bias measurements.