# First In-Orbit Validation of Interferometric GNSS-R Altimetry: Mission Overview and Initial Results
## 2 Mission Overview
### iGNSS-R Sea Surface Height Retrieval
#### 2.4.3 The Process of iGNSS-R SSH Retrieval  
The flowchart of the iGNSS-R SSH inversion is depicted in Figure 9, and encompasses the following steps:  
Figure 8: Waveform matching cases for BDS iGNSS-R DMs: (**a**) BDS B1 iGNSS-R DM, (**b**) BDS B2 iGNSS-R DM.  
Data Parsing: Dual-frequency iGNSS-R DMs and auxiliary information are extracted from raw data packets.
2. Geophysical Path Delay Calculation: Utilizing the preliminary geolocation of the specular point calculated onboard, the SSH reference model is computed, incorporating the mean sea surface height, ocean tide, solid Earth tide, polar tide, and DAC. The specular point position is recalculated using the SSH reference model, precise GNSS ephemeris, and precise orbit determination files. Phase center corrections are applied to direct and reflected GNSS signals using satellite attitude information, and the geometry model delay difference between the GNSS reflected and direct signals is calculated.
3. Measuring Time Delay: The waveform-matching method is employed to determine the measured delay difference between GNSS reflected and direct signals. Corrections are applied, using a hardware delay lookup table, to the measured time delay difference between the reflected and direct GNSS signals.
4. Calculating the Delay Difference: The difference between the geophysical path delay and the measured time delay is calculated.
5. \(SSH_{ori}\) Error Correction and Calibration: The instantaneous sea surface height (SSHori) is calculated using (1). To eliminate the impact of ionospheric bias, a dual-frequency combination technique is employed. The dry and wet tropospheric delays are computed using the European Centre for Medium-Range Weather Forecasts (ECMWF) reanalysis data (temperature, humidity, and air pressure) through ray-tracing techniques that account for atmospheric variations along the reflection path. In [47; 48], [PERSON] et al. utilized numerical simulations to calculate the electromagnetic (EM) bias of L-band waves using the physical optics (PO) method under the Kirchhoff approximation (KA). They examined the impacts of several factors, including the incidence angle, wind speed, rain, swell, and surface currents. Their findings indicate that significant wave height, sea surface wind speed, and the incidence angle are the main contributors to EM bias, with the effect of the incidence angle being well-described by a cosine function. Based on these results, we developed an EM bias lookup table to correct for sea state bias. After correcting for the aforementioned errors, the residual error compared with radar altimeter data are modeled according to the cosine function of the incidence angle to calibrate the SSHori.
6. Calculation of 5 Hz SSH: After \(SSH_{ori}\) error correction and calibration, the GOT4.10 model is used to correct for ocean tides. Polar tides, which are tidal phenomena caused by the centrifugal effect due to the motion of the Earth's poles, are corrected using the International Earth Rotation and Reference Systems Service (IERS) polar tide model. Solid Earth tides are corrected using the tidal response analysis proposed in [49]. DAC is applied using the DAC data released by AVISO ([[https://www.aviso.altimetry.fr/en/data.html](https://www.aviso.altimetry.fr/en/data.html)]([https://www.aviso.altimetry.fr/en/data.html](https://www.aviso.altimetry.fr/en/data.html)) (accessed on 20 May 2025)).
7. 40 km SSH Moving Average Processing: Utilizing the 5 Hz SSH data, 40 km along-track averaging is implemented to achieve the final SSH products. The main steps of the along-track averaging are as follows: First, the difference between the 5 Hz sea surface height measurements and the corresponding mean sea surface height model is calculated. Next, this difference is smoothed to a 40 km resolution. Finally, the smoothed difference is added back to the mean sea surface height model value to obtain the 40 km sea surface height product.