# Sea Level Estimation Based on GNSS Dual-Frequency Carrier Phase Linear Combinations and SNR
## 4 Discussion  
The use of GNSS reflection signals for remote sensing was proposed in 1988 [40] and is now popular in the field of remote sensing. GNSS-R has its own advantages, such as all-weather and all-day \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & & **SNR1** & **SNR2** & **L4d** & **L4-Model** & **S2-Model** \\ \hline \multirow{2}{*}{5\({}^{\circ}\)–12\({}^{\circ}\)} & RMSE(cm) & 19.32 & 14.01 & 14.68 & 18.30 & 17.63 \\  & Corr-coeff\({}^{\circledR}\) & 0.9753 & 0.9822 & 0.9822 & 0.9701 & 0.9696 \\ \multirow{2}{*}{5\({}^{\circ}\)–15\({}^{\circ}\)} & RMSE(cm) & 14.69 & 12.36 & 13.81 & 13.67 & 13.17 \\  & Corr-coeff\({}^{\circledR}\) & 0.9778 & 0.9831 & 0.9810 & 0.9810 & 0.9831 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Statistical analysis of residual data between sea level changes derived from the GPS multipath effect and tide gauge (TG) observations over the one month period of 1-31 January 2015 with different elevations ranges. Figure 9: Residuals of sea surface height differences compared between SNR and geometry-free phase estimations for the elevation range 5–15\({}^{\circ}\) and tide gauge (TG) observations. observation, multi-signal sources, wide coverage, and high spatiotemporal resolution, which has provided it wide scope in the field of ocean altimetry. In this paper, the first known use of the L4 carrier phase dual-frequency combination from GNSS data to obtain sea surface height has been presented. The L4_d method also obtained very similar accuracy results to the L4_ model method, indicating that the L1 quantity in \(dL4\) has no significant impact on the L2 quantity in spectral analysis. This is probably because of the frequency difference between carrier phases L1 and L2. In future work, it is anticipated that we will focus on researching a new method with which to distinguish these two quantities in \(dL4\). If this can be achieved, the L4_d method will be able to achieve higher measurement accuracy, thus avoiding the low precision caused by inaccuracy of the linear model when using the L4_model. Ionospheric error is an important quantity that affects the accuracy of the L4_model method. Although the L4 carrier phase geometry-free linear combinations of GNSS dual-frequency signals contain ionospheric delays, it has been shown here that the residual error from the ionospheric effect after high-order polynomial fitting will not strongly impact the L4 data, provided the order of the polynomial is appropriate. Although high-order polynomial fitting is used to weaken its influence, the remaining error still affects the accuracy of the solutions. In future research, the proper order of polynomials that can satisfy the accuracy of the L4_model method will be investigated. Moreover, ionospheric error will be calculated in advance using geodetic positioning methods, and this error will be subtracted in L4 observations to see if the accuracy of L4_model method can be improved. The correctness of the linear model is also an important element when determining the measurement accuracy of the L4_model and SNR2_model methods. The linear model was obtained from a forward model of the multipath effect in this paper. The forward model takes into account many influences when considering the multipath effect reflected from the ocean surface, such as water temperature, salinity and surface roughness. However, because of the lack of on-site observation of these quantities, and the fact that all quantities adopted in this paper are commonly used values, the forward model cannot really simulate the multipath effect. This is especially true for surface roughness, which has a significant impact on the scattering of GPS signals on the ocean surface and therefore needs detailed study in the future. Additionally, although the forward model simulates multipath effects as much as possible, there are inevitably still errors. Seeking a more accurate multipath simulation model is also a way to improve accuracy.