# Improving GNSS Landslide Monitoring with the Use of Low-Cost MEMS Accelerometers
## 4 MEMS Sensor Features and Calibration Results
### Some Considerations on the Calibration of a Family of TE4030 Sensors  
The calibration values of the eight accelerometers and their RMS are reported in Table 4. They are very different from each other, for example, the scale factor of the three axes, i.e., the diagonal of the \(E\) matrix, varies from \(10^{-1}\) to \(10^{-3}\) but the value of their standard deviation has an order of magnitude of \(10^{-5}\). Let us look for example at the accelerometer number two, which has lower calibration values, and the accelerometer number three with high values--the RMS of the 12 parameters are, however, of the same order of magnitude. Even the least square residuals are comparable (Figures 5 and 6). Therefore, although the calibration parameters are very different from instrument to instrument, they can be correctly estimated.  
It is clear that these low-cost sensors must be individually calibrated. The calibration procedure can be performed in a very simply way, starting from a rectified plane and a box with orthogonal walls. The acquisition procedures on the six faces are simple and the homemade software that produces the calibration matrix is immediately applicable. This \"low-cost calibration\" is suitable for these cheap sensors and can be performed by technical personnel, even those who are not particularly specialized. A robotized procedure that rotates the sensor on the six faces can be useful, but requires specific and sophisticated devices.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Time**} & \multicolumn{3}{c}{**raw [g]**} & \multicolumn{3}{c}{**calibrated [g]**} & \multicolumn{3}{c}{**tilt [gon]**} \\ \cline{2-9}  & **ax** & **ay** & **az** & **ax** & **ay** & **az** & \(\mathbf{\Omega}\) & \(\mathbf{\Phi}\) & \(\mathbf{\Psi}\) \\ \hline
7060 & 0.05286 & 0.07283 & 1.09189 & 0.00439 & \(-\)0.00324 & 1.00806 & \(-\)0.2047 & 0.2774 & 100.3447 \\
7065 & 0.05286 & 0.07283 & 1.09189 & 0.00439 & \(-\)0.00324 & 1.00806 & \(-\)0.2047 & 0.2774 & 100.3447 \\
7070 & 0.05286 & 0.07283 & 1.09189 & 0.00439 & \(-\)0.00324 & 1.00806 & \(-\)0.2047 & 0.2774 & 100.3447 \\
7075 & 0.05286 & 0.07283 & 1.09189 & 0.00439 & \(-\)0.00324 & 1.00806 & \(-\)0.2047 & 0.2774 & 100.3447 \\
7080 & 0.05286 & 0.07283 & 1.09189 & 0.00439 & \(-\)0.00324 & 1.00806 & \(-\)0.2047 & 0.2774 & 100.3447 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Raw calibrated acceleration values and tilts.  
Figure 4: The accelerometer inside a calibration box during the six-faces test.  
The accuracy obtained is a few hundredths of a gon and can be useful not only to monitor the verticality of the antenna support but also as an inclinometer, if compatible with geologically defined threshold values. No specific inclinations were required on the analyzed Madonna del Sasso site. The values recorded are not significant with respect to the accelerometer experimental accuracy. The tested accelerometer is suitable for monitoring inclinations with an accuracy of a few hundredths of a gon--in Figure 6, it is between \(-0.04\) and \(+0.03\) gon. Other accelerometers can be cheaper, like those inside smartphones and drones, but they are not rugged and can be problematic for very high or very low temperatures. The TE4030 is designed for outdoor use even in critical conditions (\(-40+85\)\({}^{\circ}\)C) and also in winter or summer it continues to work properly.