## 4 Retrieval of Sea Surface Height
### Code Delay Sea Surface Altimetry
The reflection waveforms of GPS L1, Galileo E1, and Beidou-3 B1 signals were generated through processing and the delay was estimated using three algorithms, which were converted into sea surface height measurements. Using the raw IF data collected by the CYGNSS satellite and using bistatic geometry [2] to calculate the ellipsoidal height \(H_{e}^{\text{obs}}\) of the sea surface above the WGS84 ellipsoid, the following was derived:  
\[H_{e}^{\text{obs}}=-\frac{c\tau_{\text{trk}}^{\text{obs}}-(\delta\rho_{\text{ iono}}+\delta\rho_{\text{tropo}}+\delta\rho_{\text{b1}})}{2\cos i} \tag{6}\]  
where \(\tau_{\text{trk}}^{\text{obs}}\) is the residual bistatic delay derived from different re-trackers, \(\delta\rho_{\text{iono}}\) is the ionospheric delay correction term, \(\delta\rho_{\text{tropo}}\) is the two-way slant troposphere delay, \(\delta\rho_{\text{b1}}\) is the antenna baseline correction, and \(i\) is the incident angle. Research has found that the bidirectional ranging accuracy can reach 3.9 m and 2.5 m, but there is a dispersion of inter orbit delay, mainly due to orbit errors of the receiver and ionospheric correction residuals. The study provided important references for the development of GNSS-R ocean altimetry missions and pointed out key considerations for updating CYGNSS mission configurations and future mission development. Figure 6 shows the process flow of code phase height retrieval, where the phase height retrieval process begins with the coherent processing of the raw IF signal. Firstly, the code phases of the direct and reflected signals are separated, and after denoising and MSS model correction, path delay and orbit error are jointly compensated for. The geometric calculation module synchronously processes L1 observation data, GNSS position, and Sp3 ephemeris, and finally outputs surface elevation through the code phase difference  
height measurement method. [PERSON] et al. (2018) explored the application of spaceborne GNSS-R technology in determining sea-level height based on raw IF data from the TDS-1 satellite, particularly analyzing reflection signals from sea ice and rough sea surfaces. By combining the MSS model and orbit error correction, the accuracy of altitude measurement was improved. The study also found that direct signals may interfere with reflected signals, and attention should be paid to data processing. These achievements provide important references and validation for the application of GNSS-R in the field of ocean altimetry. Faced with the challenges of delayed re-tracking, ionospheric correction, and receiver positioning, [PERSON] et al. (2018) proposed a delayed re-tracking method based on reflection models, which uses the raw count DDM subtracted from the background noise from the Level 1 data product. Three re-tracking methods (P70, VZ18 WAVE and VZ18 DDM) were selected from some data in the surrounding waters of Indonesia to retrieve the ocean surface height. The results showed that, without additional time averaging (1 s comprehensive observation from CYGNSS), the VZ18 DDM method was superior to the other two methods, and the standard deviations of surface height retrieval based on single-sample and Gaussian smoothing were 5.8 m and 1.9 m, respectively. When averaging for 10 s, the time-averaged results in all cases were significantly better than those achieved with 1 s. At this point, the VZ18 DDM method was based on single-sample and Gaussian smoothing with standard deviations of 3.8 m and 1.3 m, respectively. Despite the existence of systematic errors, these methods produced advanced altitude retrieval results, providing important references for the design of future GNSS-R altimetry missions. In the future, the use of GNSS-R instruments and strategies with wider-bandwidth signals and dual-frequency observations is expected to further improve height measurement accuracy and effectively monitor mesoscale ocean topography.