# Development of a Multi-Sensor GNSS-IoT System for Precise Water Surface Elevation Measurement
## 3 Field Experiment
### Datum Offset Estimation  
AUSPOS is an online GPS positioning service offered by Geoscience Australia, allowing users to access advanced positioning analysis through an easy-to-use web interface. Typically, datasets comprising 6+ h of static GPS dual-frequency observations processed by AUSPOS can achieve an ellipsoid height uncertainty of approximately 3 to 5 cm. However, the derived AHD uncertainty is notably higher, ranging from 15 to 20 cm, primarily due to the uncertainty inherent in the AUSCeoid2020 model grid values [37; 39]  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Data Type** & **Max.** & **Min.** & **Mean** & **Median** & **Std.** & **Range** \\ \hline raw data & 1.649 & 1.419 & 1.543 & 1.541 & 0.024 & 0.230 \\ smoothed data & 1.639 & 1.439 & 1.543 & 1.541 & 0.019 & 0.200 \\ \hline \hline \end{tabular}
\end{table}
Table 5: Maximum, minimum, mean, median and std values of ultrasonic sensor readings (unit: m).  
Figure 9: Ultrasonic sensor readings from 1 February 2024 to 30 May 2024. (**a**) Raw and smoothed data time series. (**b**) Histogram of raw data and (**c**) histogram of smoothed data.  
To solve this issue, we introduce the concept of \(datum_{offset}\) in the WSE estimation mathematical model in Equation (3) to mitigate the errors or biases associated with the geoid model, utilizing several days of benchmark observations. According to Equations (6) and (11), \(datum_{offset}\) can be estimated using epoch observations that convert ellipsoidal height \(h_{mgsi}\) and the reference value \(wl_{ref}\), or averaged observations \(\overline{h}_{mgsi}\) and \(\overline{wl}_{ref}\).  
Figure 11 presents the parameter \(datum_{offset}\) estimated by both epoch and 6 h averaged data over the first two-week observation period. The epoch-based \(datum_{offset}\) solutions are clustered around the averaged one, though exhibiting some discrete variability. The averaged-based \(datum_{offset}\) solutions remain stable throughout the two-week period. It is noted that on 7 February 2024, the epoch solutions show a significant deviation from other days, which is attributed to increased pontoon movement, as indicated by the accelerometer readings.  
These results indicate that while the averaged data provide stable and consistent \(datum_{offset}\) estimations, the epoch data exhibit greater variability. To assess consistency over time, we also estimate \(datum_{offset}\) using a four-week dataset. The statistics for both the  
Figure 11: Datum offset estimation with epoch and 6 h averaged data over 2 weeks.  
Figure 10: The ultrasonic sensor’s daily average measurement in the experiment.  
two-week and four-week scenarios are summarised in Table 6, showing minimal difference between them. Specifically, the mean of \(datum_{offset}\) differs by only 1 mm between the two 6 h averaged solutions, with consistency observed in the STD. Based on the minimum STD, range and observation period, the \(datum_{offset}\) for this experiment is determined as \(-19.218\) m by incorporating the difference between ellipsoidal height and the derived AHD, as well as other constant biases.