## 3 Results
### Using GNSS with Tilt Sensors  
Today, manufacturers offer GNSS systems equipped with an IMU unit, sometimes supplemented by an electronic compass to compensate for the tilt of the rod. The purpose of this solution is to be able to measure inaccessible points where the vertical position of the rod is not possible. In addition to the uncertainty of the GNSS position, there is also the uncertainty of the tilt compensation. From the point of view of accurate measurements, it is necessary to distinguish the state of the instrument when the compensation is switched on or off. For accurate measurements, the tilt compensation should not be used as the accuracy deteriorates. Testing of two types of tilt sensors using a magnetometer and a micro-electro-mechanical system (MEMS) and an inertial measurement unit (IMU) has been published, e.g., in [21]. Table 3 describes the result of the test of the measurements on the calibration base. Coordinates of the points were measured using the GNSS RTK method for 5 min with the tilt compensation switched on. The sensor was then rotated 180\({}^{\circ}\) in the horizontal plane, and the same procedure was repeated with the tilt compensation off and on. Six repetitions were taken using this procedure. This series of measurements was then repeated twice, each time at least 3 h apart. The total series was 18 measurements with tilt compensation off and 18 measurements with tilt compensation on. Table 3 shows the RMS accuracy values shown on the instrument display and the RMS calculated from the variance of a series of measurements and the systematic deviation from the reference position. Turning on the tilt compensation resulted in a deterioration of approximately 25% in the accuracy characteristics of the data displayed on the sensor display and calculated from the variance of a series of measurements, as compared to the condition in which the tilt compensation was turned off. At the same time, the accuracy data displayed on the sensor display differed from the accuracy results calculated from the variance of the measurement series (by approximately 50%). \begin{table}
\begin{tabular}{c c c} \hline
**GNSS Instrument** & **\(\mathbf{\mathbf{\mathbf{\mathbf{\mathbf{\mathbf{\mathbf{\mathbf{\mathbf{\mathbf{ \mathbf{\mathbf{\mathbf{\mathbf{\mathbf{\mathbf{\mathbf{\mathbf{\mathbf{  }}}}}}}}}}}}}}\) & **\(\mathbf{\mathbf{\mathbf{\mathbf{\mathbf{\mathbf{\mathbf{\mathbf{\mathbf{\mathbf{ \mathbf{\mathbf{\mathbf{\mathbf{\mathbf{\mathbf{\mathbf{\mathbf{\mathbf{\mathbf{ }}}}}}}}}}}}}}}}\)** \\ \hline Trimble R2 (2023) & \(3.2\) & \(2.2\) \\ Trimble R780 (2024) & \(1.8\) & \(4.0\) \\ \hline \end{tabular}
\end{table} 
Table 2: Achieved accuracy of used GNSS instruments at the calibration base Brno-South. \begin{table}
\begin{tabular}{c c c c c c c} \hline
**GNSS Instrument** & **When Tilt Correction Is** & **When Tilt Correction Is** & **When Tilt Correction Is** & **When Tilt Correction Is** & **Mean** & **Mean** \\
**Instrument** & **OFF–Sensor RMS [mm]** & **ONF–Sensor RMS [mm]** & **ONF–Sensor Computed RMS [mm]** & **ONF–Sensor RMS [mm]** & **ONF–Sensor Error \(c_{\mathbf{Y}}\)[mm]** & **ONF–Sensor Error \(c_{\mathbf{X}}\)[mm]** \\ \hline Trimble R780 & 6.4 & 8.0 & 4.4 & 5.4 & –0.5 & –0.2 \\ \hline \end{tabular}
\end{table} 
Table 3: Comparison of achieved GNSS accuracy when tilt correction is switched off and on. Furthermore, possible systematic deviations in the two perpendicular directions of the coordinate axes in the horizontal plane were investigated. The systematic deviations were calculated from the reference coordinates determined from the measurements when the tilt compensation was switched off (average of the two positions). The systematic deviations when the compensation is switched on in the vertical GNSS position, with respect to the measurement uncertainties, are shown to be small and inconclusive. In the diploma thesis [22], the GNSS equipment Topcon Hiper HR was tested, which is equipped with an IMU in combination with an electronic compass.