# 2D Phase-Based RFID Localization for On-Site Landslide Monitoring
## 4 Hamaliere Landslide Monitoring
### Real Phase Data  
Among the 32 tags installed in the field, 10 were read almost continuously by more than two antennas for 12 months (January 2021-February 2022). The rest of the tags yielded partial results that could not be used for 2D localization via the present scheme. Two main factors can explain the lack of readability of some tags, namely, the narrow horizontal directivity of the antennas (\(+\) / \(-\)30\({}^{\circ}\) aperture) and signal attenuation--the furthest tags  
Figure 4: Schematic description of the matrix transformations in phase space towards real 2D space for a 2-antenna system. (**a**) Representation of the simulated multipath-induced phase measurement distribution (orange) compared to the previously assumed centered distribution (blue), highlighting the scaling \(S\) and translation \(T\). The translation is illustrated by the shift between the center of the blue distribution and the center of the red distribution. (**b**) True space localization spot obtained by further transformation via the \(K^{-1}\) matrix. The antennas are not represented. The systematic bias is again illustrated by the shift between the real position (black point) and the center of the measured distribution (red point).  
showed the lowest signal quality. Generally speaking, the tags placed 50 cm above ground showed worse results than those placed 1 m above ground, both in terms of data quality and localization accuracy. This observation corresponds to the above theoretical results (see Section 4.2 and Figure 5c), which tend to show that displacements close to the ground are subject to stronger multipath interference. This study will only show the tags read by at least two antennas during the whole period. The unwrapped phase measured during the January 2021-February 2022 time period is presented in Figure 6 for tag A. The data (70 measurements per day) were averaged over 24 h periods before applying the localization algorithm to mitigate the daily phase variations due to humidity and temperature. The missing values correspond to strong weather events that most likely depleted the battery of the acquisition system, or to hardware failures.  
Figure 5: Mapping of the 2D localization error extracted from Equations (14) and (15), simulating the geometry of the Harmalière setup. The red dots represent the reader antennas, and the arrows show the principal antenna directions. The orange cross indicates the position of tag A. The vectors \((\vec{u}_{r},\vec{u}_{\theta},\vec{u}_{z})\) define the cylindrical coordinate system used later on. (**a**) The colormap shows the random localization error (maximum dimension of the localization spot) up to 2 cm, related to the phase random deviation \(\sigma_{nlm}\). The localization bias is not shown. (**b**) Color-mapping of the systematic localization bias (related to \(\phi_{b}\)) in the xOy plane shows oscillations with meter-order spatial frequency and increasing amplitude with distance from the measurement system. The random localization error is not shown. (**c**) Color-mapping of the systematic localization bias in the xOz plane, with higher oscillation amplitude and frequency. The ground is located at z\(=-3\) m.