# Improving GNSS Landslide Monitoring with the Use of Low-Cost MEMS Accelerometers
## 5 Control of Accuracy Achieved with Total Station Measurements  
To check the accuracy of the inclinometer in an independent way, the angular values calculated from the accelerations were compared with the reference values obtained with a total station with 0.2 mgon accuracy, to which the TE4030 sensor was fixed (Figure 5). By varying the elevation of the telescope, the zenith angle was compared with the value obtained from the inclinometer on each axis. The comparison was made for the angles computed with the accelerations before and after their calibration, to evaluate their impact on accuracy. In this procedure, the Y accelerometer axis is placed first, roughly in the direction of the collimation axis (a\({}_{3}\)), and then the X accelerometer axis is parallel on the secondary rotation axis (a\({}_{2}\)) (Figure 7).  
These tests were performed by varying the inclination \(\alpha\) of the telescope from \(-15\) gon to \(+15\) gon with constant intervals of 5 gon. Consequently, the \(\omega\) inclination measurable by the accelerometer should mainly be of very similar values.  
Figure 5: LS (Least Square) residuals accelerometer ID2.  
Figure 6: LS (Least Square) residuals accelerometer ID3  
In fact, due to a few unavoidable mechanical misalignments, the accelerometer axis system (X, Y, Z) was not parallel to that of the total station (a1, a2, and a3). We labeled these angular misalignments with lowercase Greek letters: \(\omega\), \(\varphi\), and, \(\kappa\). Before performing this test, these values must first be estimated.  
The values were therefore estimated at an elevation \(\alpha\) = 15 gon of the telescope, the maximum tilt value of the tests. After these estimates, to impose the parallelism of the X and a3 axes and of the Y and a2 axes, we applied these rotations to transform the accelerometer system measurements to match the total station system measurements. This was achieved with the following transformation:  
\[R(\alpha)=R(\omega,\varphi,\kappa)R(\Omega,\Phi) \tag{11}\]  
A \"robust\" procedure based on mobile median filtering with a window of 20 measurement epochs was used to remove gross errors during data acquisition.  
The residuals between the tilt measurements from the accelerometer and the total station show values of a few hundredths of a gon (Figure 8). Note the great improvement of the calibrated data over the \"raw\" data with uncalibrated accelerations. The accuracy is improved by more than one order of magnitude--mean and standard deviation of the residuals are shown in Table 5.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline  & \multicolumn{2}{c}{**Calibrated Values**} & \multicolumn{2}{c}{**Uncalibrated Values**} \\ \cline{2-5}  & \(\Omega\) **(gon)** & \(\Phi\) **(gon)** & \(\Omega\) **(gon)** & \(\Phi\) **(gon)** \\ \hline
**average** & 0.010 & \(-\)0.020 & 1.081 & 1.150 \\ St. **dev.** & 0.008 & 0.015 & 0.161 & 0.141 \\ \hline \hline \end{tabular}
\end{table}
Table 5: Average error and standard deviation of tilt residues with respect to the total station.  
Figure 7: Accuracy test: in red, the axis of the 4030; in blue, the axis of a total station.