# Experimental Study of Accuracy of High-Rate GNSS in Context of Structural Health Monitoring
## 3 Results and Discussion
### Evaluation of Accuracy of the 100-Hz Displacement Time Series
#### 3.2.2 Quasi-Static Motion Test  
Figure 5 shows the 100-Hz displacement time series corresponding to the quasi-static motion test computed with the PPP, PPP-AR, and RTK techniques. Significant discrepancies can be seen among the different solutions. The GPS-only solutions have the lowest accuracy, with the RMSE value being 21.56 mm, 7.07 mm, and 6.51 mm for the PPP, PPP-AR, and RTK techniques, respectively. The BDS-only solutions show an improvement of up to 70% compared to the GPS-only solutions due mainly to the much smaller number of GPS satellites observed than that of BDS satellites (about 15 C and 5 G, Figure A2). The combined use of the GPS and BDS observations improved the accuracy by about 10% over the BDS-only solutions as judged by the RMSE value. When data from all four systems were used, the accuracy of the displacements was enhanced significantly for all three positioning techniques where the RTK technique achieved a sub-millimeter level of accuracy (RMSE = 0.75 mm), followed by the PPP-AR which allowed millimeter-level measurements of the quasi-static and abrupt motions.  
The histograms of the displacement errors of the different processing techniques are shown in Figure 6 where the rows and columns represent the different processing techniques and the different combinations of GNSS observations, respectively. The range of the G and C solution errors from the PPP (first row in Figure 6) was from -4.62 to 2.27 cm, which was reduced significantly after the GC (\(-\)1.40-1.75 cm) and GCER (\(-\)0.83-1.48 cm) observations were used. The majority of the errors from the GCER observations were greater than 1 cm. When the PPP-AR technique was applied, the errors were reduced markedly to the range of \(-\)1.58-2.78 cm. The distribution pattern of the PPP-AR errors was similar to that of the PPP error: although, more errors were centered around 0 even for the GPS-only solutions. The GCER solutions achieved the best results with most of the errors within 1 cm. All the errors of the RTK results were within \(\pm\)5 mm except for the GPS-only results that ranged between \(-\)0.40 and 1.40 cm.  
Figure 4: Amplitude–frequency spectra of 3D displacement results from G, C, GC, and GCER observations and PPP, PPP-AR, and RTK techniques in the stationary test. 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 amplitude-frequency spectra of the displacement errors from each positioning technique computed with Fast Fourier Transform (FFT) are shown in Figure 7 where the smaller amplitude indicates higher accuracy. The results indicate that the RTK results are more accurate than the other two positioning techniques, especially for those in the low-frequency band (less than 1 Hz). The displacement error spectra of PPP-AR are similar to that of PPP. The main discrepancies among different satellite system results are in the low-frequency band, where the GPS-only results have the worst performance for all positioning techniques due to limited  
Figure 5: Displacement time series from the quasi-static motion test computed with observations from the different satellite systems and (a) PPP, (b) PPP-AR, (c) and RTK techniques (starting from 08:26.00 GPST).  
Figure 6: Histograms of displacement errors. From top to bottom, results from PPP, PPP-AR, and RTK; from left to right, results calculated by G, C, GC, and GCER, respectively. Statistics (maximum, minimum, and median) of each time series are given in each plot (in cm).  
satellites. The results suggest that using the combination of the multi-GNSS observations could improve the displacement estimation performance effectively.