# Development of a Multi-Sensor GNSS-IoT System for Precise Water Surface Elevation Measurement
## 2 Methodology
### WSE Estimation  
The system is designed to accurately measure absolute WSE relative to a given vertical datum. The typical GNSS-based tide gauge or buoy system generally requires the integration of a large solar panel, a battery management system, a GNSS antenna and receiver, connection cables, custom-shaped case, etc. By comparison, the device used in the system only requires one mounting bracket to secure it to a buoy or other floating platform. The vertical GNSS measurement is projected to an absolute WSE using the ultrasonic sensor measurement.  
For the WSE, we convert from the antenna phase centre (APC) ellipsoidal height to the given vertical height datum as follows:  
\[WSE=h_{apc}+bdg_{offset}+atx_{offset}-\left(uls+uls_{offset}\right)+ datum_{offset} \tag{3}\]  
where \(h_{apc}\) is the ellipsoidal height of the APC, \(bdg_{offset}\) is the offset between the BDG and the antenna reference point, \(atx_{offset}\) is the APC offset correction calibrated by Geoscience Australia on sample units, \(uls\) is the ultrasonic sensor measurement, \(uls_{offset}\) is ultrasonic sensor measurement correction (determined as 0.011 m, as described previously), \( datum_{offset}\) is the estimated datum correction from the local height of the system to the Australian Height Datum (AHD). Those correction or offset items in Equation (3) are constant values and can be combined into a single parameter \(tot_{offset}\) and categorised into device corrections \(dev_{offset}\) and coordinate system corrections \( datum_{offset}\), where  
\[tot_{offset}=dev_{offset}+ datum_{offset} \tag{4}\]  
\[dev_{offset}{=bdg_{offset}+atx_{offset}-uls_{offset}} \tag{5}\]  
If the water surface height reference value \(wl_{ref}\) is given, then \( datum_{offset}\) can be calculated as follows:  
\[ datum_{offset}=wl_{ref}-h_{sys} \tag{6}\]  
where \(h_{sys}\) is the system's converted ellipsoidal height, calculated as follows:  
\[h_{sys}=h_{apc}+dev_{offset}-uls \tag{7}\]  
So, Equation (3) can be simplified as follows:  
\[wl_{sys}=h_{sys}+ datum_{offset} \tag{8}\]  
\begin{table}
\begin{tabular}{c c} \hline
**RTKLIB Parameters** & **Settings** \\ \hline Positioning mode & Kinematic \\ Interval & 15 s \\ Filter type & Combined \\ Elevation mask & 20 degrees \\ Satellite ephemeris & Broadcast \\ Ionospheric correction & Broadcast \\ Tropospheric correction & Saastamoinen \\ Ambiguity resolution & GPS Fix and Hold \\ Ambiguity ratio & 4 \\ Constellations & GPS, Galileo, BDS and QZSS \\ \hline \end{tabular}
\end{table}
Table 2: The main configuration parameters of RTKLIB applied in the system.  
The averaged solution of \(\overline{w}l_{sys}\) is then calculated as follows:  
\[\overline{w}l_{sys}=\frac{1}{n}\sum_{i=1}^{n}h_{i}^{apc}-\frac{1}{m}\sum_{i=1}^{ m}uls_{i}+tot_{offset} \tag{9}\]  
where \(h_{i}^{apc}\) and \(uls_{i}\) represent the epoch solution APC ellipsoidal height and epoch measurement of the ultrasonic sensor, respectively, \(n\) is the number of \(h_{apc}\) in the GNSS working session, \(m\) is the number of \(uls\) in the GNSS working session, and \(tot_{offset}\) remains invariant. Correspondingly, the system's averaged ellipsoidal height \(\overline{h}_{sys}\) can be estimated by the following:  
\[\overline{h}_{sys}=\frac{1}{n}\sum_{i=1}^{n}h_{i}^{apc}-\frac{1}{m}\sum_{i=1}^ {m}uls_{i}+dev_{offset} \tag{10}\]  
Therefore, the parameter \( datum_{offset}\) can be also estimated by the averaged reference value \(\overline{w}l_{ref}\) as follows:  
\[ datum_{offset}=\overline{w}l_{ref}-\overline{h}_{sys} \tag{11}\]