# Development of a Multi-Sensor GNSS-IoT System for Precise Water Surface Elevation Measurement
## 4 Results
### Averaged Solutions  
To assess the system's accuracy and stability at various temporal resolutions, this section presents and analyses WSE solutions (10 min/1 h/6 h) averaged over different time intervals: 10 min, 1 h and 6 h. These averaged solutions are computed from the original epoch data and provide insights into the trade-offs between temporal resolution and measurement stability. To compare the 10 min solution, the reference data are directly drawn from IWL raw data, whereas to compare the 1 h and 6 h solutions, the reference data are derived from IWL averaging over 1 h and 6 h. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & \multicolumn{3}{c}{**Observed over 2 Weeks**} & \multicolumn{3}{c}{**Observed over 4 Weeks**} \\
**Data Type** & **Mean** & **Std** & **Range** & **Mean** & **Std** & **Range** \\ \hline Epoch & \(-19.217\) & 0.028 & 0.266 & \(-19.219\) & 0.027 & 0.266 \\
6 h & \(-19.218\) & 0.004 & 0.013 & \(-19.219\) & 0.006 & 0.025 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Datum offset/correction estimation (unit: m). Figure 13 illustrates the 10 min averaged solutions. Figure 13a shows the WSE time series of the reference, \"orig\", and \"high\" solutions. Both solution types closely follow the reference trend with reduced scatter compared to the epoch solution in Figure 12, demonstrating the effectiveness of averaging with multi-epoch resolution. Figure 13b presents the difference between the system and reference values, highlighting the much fewer deviations over \(\pm\)10 cm. Figure 13c shows the histogram of the differences, where the distribution for \"high\" solutions is notably narrower, indicating improved consistency. Figure 14 displays the 1 h averaged solutions, providing a balance between temporal detail and stability. As shown in Figure 14a, the \"high\" solutions exhibit excellent agreement with the reference averaged values. Figure 14b reveals that the magnitude of differences has further reduced compared to the 10 min average, with most values staying within \(\pm\)5 cm. Figure 14c shows that the 1 h solution difference becomes increasingly Gaussian and centred around zero. The reduced variability at this interval suggests that 1 h averaging provides reliable performance suitable for centimetre-level hydrological or environmental monitoring. Figure 12: System epoch solutions. (**a**) Reference, “orig” and “high”. (**b**) The difference between the reference and “orig” and “high”. (**c**) A histogram of the difference distribution. Figure 13: System’s 10 min averaged solutions. (**a**) Reference, “orig”, and “high”. (**b**) Difference between reference and “orig” and “high”. (**c**) Histogram of difference distribution. The 6 h averaged solution offers a more comprehensive view of WSE trends over the GNSS session working periods, as shown in Figure 15. Figure 15a displays the time series of reference, \"orig\" and \"high\" solutions. The \"high\" solutions are very close to the reference results. Figure 15b depicts the differences between reference and \"orig\" and \"high\" 6 h averaged solutions. The overall difference between the reference and the system is less than 0.02 m, excluding the days with no solutions. Figure 15c illustrates the distribution of the two solutions differences. This long-interval averaging is ideal for detecting gradual water level changes and evaluating system performance over longer durations. Table 7 presents the statistical evaluation of the system's performance under different processing strategies and temporal resolutions. Comparisons are made between the \"orig\" and \"high\" GNSS solutions at the epoch level, as well as after applying moving averages over 10 min, 1 h, and 6 h intervals. Figure 14: System 1 h averaged solutions. (**a**) Reference, “orig” and “high”. (**b**) Difference between reference and “orig” and “high”. (**c**) Histogram of difference distribution. Figure 15: System 6 h average solution. (**a**) Reference, “orig” and “high”. (**b**) Difference between reference and “orig” and “high”.