# Real-Time Water Level Monitoring Based on GNSS Dual-Antenna Attitude Measurement
## 4 Results  
### Variation of Water Surface Height  
Through our experiments, we obtained water level data at 1 s intervals from 12 May to 8 June 2022 and from 4 July to 8 August 2022. Unfortunately, data for certain time periods is unavailable due to equipment and network issues. Figure 8 displays a scatter plot of water level changes, obtained using the double difference method with a time interval of  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Types of Antennas** & **RHCP Antenna** & **LHCP Antenna** \\ \hline Operating temperature & \(-40\)\({}^{\circ}\)C\(\rightarrow\)70 \({}^{\circ}\)C & \(-40\)\({}^{\circ}\)C\(\rightarrow\)70 \({}^{\circ}\)C \\ \hline Antenna gain & \(40\pm 2\) dB & \(40\pm 2\) dB \\ \hline \multirow{8}{*}{Working frequency} & BDS B1/B2/B3 & BDS B1/B2/B3 \\ \cline{2-3}  & GPS L1/L2/L5 & GPS L1/L2/L5 \\ \cline{2-3}  & GLONAS L1/L2 & GLONAS L1/L2 \\ \cline{2-3}  & GALILEO E1/E5a/E5b & GALILEO E1/E5a/E5b \\ \cline{2-3}  & L-Band & L-Band \\ \cline{2-3}  & SBAS & SBAS \\ \hline Phase center error & \(\pm 2\) mm & \(\pm 2\) mm \\ \hline Weight & \(\leq\)500 g & \(\leq\)500 g \\ \hline Size & \(\Phi 147\times 67.7\) & \(\Phi 147\times 67.7\) \\ \hline \hline \end{tabular}
\end{table}
Table 1: Parameters of RHCP and R-RHCP antennas.  
Figure 7: Dual antennas in the experiment. (**a**) Vertical upward RHCP antenna, vertical downward LHCP antenna and signal clapboard; (**b**) The signal clapboard prevents the RHCP antenna from receiving reflected signals from the water surface and the LHCP antenna from receiving direct signals from satellites.  
\(1\) s, during the period from 4 July to 8 August. To validate the accuracy of our experimental results, we compared them with water level data recorded by on-site staff using a water gauge. On-site staff were required to record water level data daily at 7:30, 15:30, and 18:30. While the staff cannot guarantee the precise recording of the water level at the specified moment, its margin of error will not exceed ten minutes. To reduce errors caused by time asynchrony, we selected water level data from 07:25 to 07:35, 15:25 to 15:35 and 18:25 to 18:35 each day for sliding average filtering. The average value was then taken as the water level data for the corresponding moment.  
Figures 9 and 10 present the combined results of the experiments conducted from 12 May to 8 June 2022 and from 4 July to 8 August 2022, respectively. The results include the 1 s experimental data, the experimental data smoothed over a 10 min interval, and the readings obtained using a water gauge. As shown in Figures 9 and 10, the trends of GNSS-R altimetry data and water gauge data are generally consistent. The root mean square errors (RMSE) between the 1 s water level data, 10 min averaged water level data, and the readings obtained using a water gauge for the period from 12 May to 8 June 2022, are 2.77 cm and 2.69 cm, respectively. The RMSE between the 1 s water level data, 10 min averaged water level data, and the readings obtained using a water gauge for the period from 4 July to 8 August 2022, are 2.54 cm and 2.49 cm, respectively. The results demonstrate that real-time water level monitoring with centimeter-level accuracy can be achieved through the water level monitoring method based on GNSS dual-antenna attitude measurement. The RMSE results indicate that averaging the water level data over a 10 min period can reduce the error caused by time asynchrony.  
Figure 8: Water level changes, obtained using the double difference method at 1 s intervals, were observed during the period from 4 July to 8 August.  
Figure 9: Water level changes for the period from 12 May to 8 June 2022.