# Sea Level Estimation Based on GNSS Dual-Frequency Carrier Phase Linear Combinations and SNR
## 5 Conclusions  
Previous research has shown that ground-based GNSS-R altimetry based on SNR and triple-frequency combinations from a single GPS station can be achieved. However, the SNR data in dB and triple-frequency carrier phase measurements are not usually provided in their RINEX observation files. However, the carrier phase measurements from two signals with different frequencies are always obtainable from permanent GNSS stations. In this paper, the reflector heights from the sea surface were retrieved using dual-frequency carrier phase linear combinations, and the precision of the solutions were similar to those derived from SNR data. The geometry-free linear combinations of GPS carrier phase observations were used to estimate the snow depth by [PERSON] and [PERSON], in 2012, for the first time [25]. We successfully used their method to retrieve changes in sea level. Data processing and reflector height calculation methods have been described, including analysis of the remaining errors for methods based on L4 measurements. Peak frequencies from L4 measurements contain some errors because of the interaction between the two series of signals with different frequencies, but the methods are suitable for use with other GNSS signals from BDS, Galileo and GLONASS. Five reflector height determination strategies were proposed to process the 10-day GPS data. SNR data and L4 measurements can all be used to solve the reflector heights separately, and a comparison with sea level changes observed from TG showed that the five strategies produce valid results. However, the solutions derived from phase combinations were not as good as those based on SNR data, and although there were some remaining ionospheric errors in the L4 measurements, their solutions can still achieve good accuracy. The L4 and SNR analyses were performed using two different methods, respectively: a direct use of the formula method, using Equation (8), and a linear model method to obtain sea surface height after obtaining the peak frequency from spectral analysis. However, the use of L4 should be discussed under low or high solar activities with longer-period observation data, because L4 is influenced by ionospheric changes, which are due to the periodic activity of sunspots. In summary, this paper has shown that the geometry-free linear combinations of GPS carrier phase observations can be used to estimate sea level changes, which were previously considered to have poor accuracy because of ionospheric error. However, when the appropriate polynomial fit is used to remove the ionospheric error, the measurement results achieve good accuracy. Here, double-frequency phase combination with a 10-order polynomial fit was used to remove this error to allow for estimation of sea level changes at station SC02. SNR data were also processed at the same time to provide a comparison. The results of the phase combination are not as good as that of SNR data when compared with TG observations, but they still maintain a certain degree of accuracy. All the results show good agreement with TG observations with correlation coefficients of 0.97-0.98 and RMSEs of 12-20 cm. From this study it can be concluded that, in the absence of SNR data and triple-frequency phase data, the dual-frequency phase combination method can be used to reliably monitor sea level changes. This is, of course, not surprising, since this method has been used to estimate snow depth and soil moisture. However, sea level fluctuates considerably more than snow depth and soil moisture over time and space, particularly over a duration of approximate 20 min. There are also significant changes in spatial coverage by measurement points because of changes in the elevation angle during multipath analysis, resulting in inevitably lower retrieval accuracy of sea surface height. However, the analysis presented in this paper shows that sea level changes can be measured with considerable accuracy using the double-frequency phase combination method.