# Experimental Study of Accuracy of High-Rate GNSS in Context of Structural Health Monitoring
## 3 Results and Discussion
### Comparison of Displacement Results from Data of Different Sampling Rates  
There has been a general understanding that high-sampling rate GNSS measurements may be noisier (e.g., [26]). We first tested data acquired when the antenna was stationary to study the accuracies of the displacement time series computed from data of different sampling rates. The 3D displacement time series are given in Figure 12 together with the standard deviations of the results. In general, the higher-rate results are slightly noisier; although, the differences are not very significant, and there are also some exceptions. The results indicate that PPP and PPP-AR are more sensitive to the increase in the sampling rate. There is also a bias that can be observed in the eastern and vertical PPP-AR results, in addition to noisier data for higher-rate observations. The possible reason is that high-rate observations not only contain white noise but also have relatively high levels of color noise [28], which may degrade the accuracy of the PPP-AR solutions [40]. There are not any noticeable differences in the RTK results.  
\begin{table}
\begin{tabular}{c c c c c c} \hline
**GNSS** & \multicolumn{3}{c}{**1 st Peak (Ref: 0.11/1.04)**} & \multicolumn{3}{c}{**2 nd Peak (Ref: 0.34/2.68)**} \\
**System** & **PPP** & **PPP-AR** & **RTK** & **PPP** & **PPP-AR** & **RTK** \\ \hline G & 0.11/0.97 & 0.11/0.98 & 0.11/1.07 & 0.34/2.63 & 0.34/2.64 & 0.34/2.65 \\ C & 0.11/1.02 & 0.11/1.03 & 0.11/1.03 & 0.34/2.64 & 0.34/2.66 & 0.34  
The measured displacement time series when the antenna was in quasi-static and  
Figure 12: Three-dimensional displacement time series from multi-GNSS data of 100-, 10-, and 1-Hz, respectively, and PPP, PPP-AR, and RTK techniques. The upper, middle, and lower panels represent displacements in the East, North, and Up directions, respectively, while the left, middle, and right columns represent results from PPP, PPP-AR, and RTK, respectively. The standard deviation (in mm) of each time series is given in the corresponding color (Starting from 07:25:00 GPST).  
The RMSE of each of the time series in Figure 13 is given in Table 3. It is clear from the results that the higher the sampling rate is, the lower the accuracy. On average, the 10 Hz and 100 Hz results are 5.5% and 10.3% noisier than the 1 Hz results, respectively. Among the three positioning techniques, the accuracy of RTK is the highest and that of PPP is the lowest. The 1-Hz displacement results are significantly different in some parts of the time series, especially during the first two sinusoidal motion sections. This is considered due to the aliasing problem. The amplitude-frequency spectra of the first two sinusoidal motion sections calculated by the LDT solutions are shown in Figure A4. The peak frequencies of the two displacement signals were 0.50 Hz and 0.68 Hz, respectively, which could not be fully detected by the 1 Hz displacement series. Parts of the displacement time series were enlarged and shown in Figure 9b,c. The 10-Hz solutions were nearly the same as the 100-Hz solutions, although the 100-Hz solutions provided more detailed deformation. The advantage of 100 Hz solutions (i.e., the redundancy of data) is important in case of data filtering and data analysis, such as estimating the high-frequency parameters in certain loads (e.g., pre-dominant frequency of earthquakes loading [41] and accurate peak ground velocity in the near field [42]).