# A Comparative Study of Signal Processing Methods for Contactless Geodetic Monitoring
## 2 Materials and Methods
\begin{table}
\begin{tabular}{c c c} \hline \hline \multicolumn{3}{c}{**Geodetic Measurement Equipment**} \\ \hline
**Sensor** & **Measuring Equipment** & \
\begin{tabular}{c} **Frequency of Signal** \\ **Acquisition (Hz)** \\ \end{tabular} \\ \hline RTS50 &
\begin{tabular}{c} RTS Leica TS50 + \\ GeoCOM/ZG \\ RTS30 \\ GNSS Topcom Hiper Pro \\ \end{tabular} & 26–30 \\ \hline \hline \multicolumn{3}{c}{**Physical Measuring Equipment**} \\ \hline
**Sensor** & **Measuring Equipment** & \
\begin{tabular}{c} **Frequency of Signal** \\ **Acquisition (Hz)** \\ \end{tabular} \\ \hline ACC1 &
\begin{tabular}{c} Instantel Minimate Plus \\ \end{tabular} & 250 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Basic characteristics of measuring equipment. Figure 2: Geodetic instruments Leica TS30/50 for monitoring. four distances to four different satellites, as only in this case is a uniform determination of the three-dimensional position possible. To determine the exact position, modern GNSS receivers combine different signals and, at the same time, address observations using a geodetic code and phase. GNSS measurement methods are, by their nature, divided into relative and absolute methods. Absolute methods represent much more generalized approaches and are more valid than personal navigation methods, as their accuracy does not exceed a few meters. Relative methods are measurement methods with GNSS systems whereby high accuracy can be achieved. In such methods, one receiver, named a reference or base, is positioned in a place with known or unknown coordinates, and the other, a movable receiver (rover), is positioned in a place where we determine the position of new points [32]. In our experiment, we used the RTK (base-rover) method with a reading speed of 0.1 s (Figure 4). The static GNSS method would be quite useless in our case, due to the presence of too many metal parts near the antenna that would interfere with the satellite signal receiver and due to the confinement of the terrain. The dynamic response of the constriction was induced by two persons running with a total mass of 160 kg. Measurements in most scientific and engineering fields are characterized by the periodic signal of the measured objects, with periodicity determined by spectral analysis. Figure 4: Base station Topcon Hyper Pro. Figure 3: The GeoCOM/ZG program (**left**: all measurements, **right**: only measuring angles). In the field of spectral analysis, the most widely used technique is the Fourier transform calculation method. The Fourier transform has the disadvantage of requiring a constant (equivalent) measurement interval [32]. The Fourier transform is used in many mathematical fields. The main reason for using this method is to convert the complex operations of interpretation and convolution into a simple multiplicative operation. Thus, the Fourier transform is an important tool in solving differential equations. Uniform sampling can only be recorded with advanced automated measurement systems, such as accelerometers or strain gauges, which allow us to capture measurements up to 2000 Hz. In contrast to these, non-contact methods have the problem of non-uniform sampling, where data are acquired at regular or irregular time intervals. This is due to the inherent technical shortcomings of the instruments. These errors are considered to be gross errors due to insufficient frequencies, noise, and mechanical interruptions of the measurements. The Fourier transform becomes practically useless if the analysis considers results at unequal intervals. To solve this problem, [PERSON] and [PERSON] introduced the Lomb periodogram method, which allows spectral analysis of irregularly (and also correctly) sampled measurement data.