# Sea Level Estimation Based on GNSS Dual-Frequency Carrier Phase Linear Combinations and SNR
## 3 Experiment and Analysis of Results
### Data Processing Strategies  
As described in Section 2, the methods used to retrieve the reflector heights can be divided into two steps: spectral analysis and reflector height calculation. In the second step, the reflector heights can be calculated directly using Equation (8) and can also be solved using the theoretical model described in Section 2.3.  
For spectral analysis, the daily SNR and carrier phases were clustered into ascending or descending sections according to satellite elevation. SNR and L4 geometry-free linear combinations of carrier phase observations were arranged according to the values of the sine of the elevation angles. Spectral analysis based on L1 SNR, L2 SNR and L4 carrier phase combinations were performed separately using the methods mentioned in Section 2 and the peak frequencies for each spectral analysis can be obtained. For reflector height calculation, the reflector height between the ARP of the GPS antenna and the sea surface can be retrieved using Equation (8) or Equation (17).  
We proposed five strategies to retrieve the reflector height to evaluate the different methods. The reflector heights were then calculated using Equation (8) based on the peak frequency from the SNR of L1 signals and L2 signals separately, and their solutions are denoted by SNR_L1 and SNR_L2, respectively. The reflector heights were calculated using Equations (8) and (17) with the peak frequencies from L4 carrier phase combinations, and their solutions are denoted by L4_d and L4_model, respectively. As stated in Section 2.2, L4 is the combination of L1 and L2, and L2 peaks were usually used for the analysis. The reflector heights were also calculated using Equation (17)  
Figure 5: Photograph showing GPS station SC02 and the surrounding environment at Friday Harbor Port in Washington State, USA (image from [[http://www.sonel.org/spip.php?page=gps&idStation=2689](http://www.sonel.org/spip.php?page=gps&idStation=2689)]([http://www.sonel.org/spip.php?page=gps&idStation=2689](http://www.sonel.org/spip.php?page=gps&idStation=2689))).  
based on SNR of L2 signals to compare the capability of L4 and SNR. The solutions are denoted by the SNR_L2_model.  
The precision of the solutions is elevated by using measurements from a TG near the GPS station, such as with the co-located Friday Harbor TG near the GPS station SC02. However, the GPS-derived reflector heights are relative to the antenna phase center, whereas the TG sea level observations are relative to the TG benchmark. There is a fixed difference between the antenna phase center and the TG benchmark, as shown in Figure 1. For convenience, the letter 'C' is used to represent this difference here. After removing the reflector height from C, the sea level heights can be deduced from the TG benchmark based on GNSS observations. The values of C can be estimated by using the least squares match between the estimated sea level and that determined from the TG.  
When comparing the GPS-derived sea level changes with TG measurements, we noted that they have different sampling rates. The co-located TG observations are sampled every 6 min, while the GPS-derived sea surface heights are estimated for a chosen elevation interval (between 5\({}^{\circ}\) and 12\({}^{\circ}\) or between 5\({}^{\circ}\) and 15\({}^{\circ}\)), which is generally about 20 min. Thus, the TG measurements are averaged over each 20-minute period and at the same time as the GPS measurements.