A part of the pre-processed Beta Ka-band Radar Interferometer (KaRIn) data (September 7 – November 21, 2023) for the Surface Water and Ocean Topography (SWOT) mission has been released. To validate the performance of SWOT L2 KaRIn Beta Pre-Validated data (Beta data), this study conducted various experiments, including inverting the ocean gravity field and seafloor topography from these data. Validating the accuracy of deflections of the vertical (DOV) by DOV products of Scripps Institution of Oceanography (SIO). The RMS of differences of north-south and east-west components is about 1.83 urad and 2.71 urad, respectively. The precision of gravity anomaly (SWOT_GA) is about 5.07 mGal compared with shipborne gravity. The results derived from 1-cycle data are comparable to those obtained from a substantial dataset accumulated by traditional nadir altimeters. The accuracy of seafloor topography inverted from SWOT_GA is about 68 m validated by shipborne depth, which is almost the same as the topography obtained from SIO_GA and SDUST2021GRA. The results of multiple experiments have demonstrated that Beta data can be used to compute high-precision ocean gravity fields and seafloor topography products. This proves the success of the first operational run of KaRIn and the capability of SWOT to support studies related to ocean science. The current evaluation results are based on Beta data. The Pre-Validated data will be more accurate after further calibration, which will lead to higher accuracy of the inverted gravitational field products in the future.

As the first in-orbit formation satellites equipped with a Laser Ranging Interferometer (LRI) instrument, Gravity Recovery and Climate Experiment Follow-on (GRACE-FO) satellites are designed to evaluate the effective ability of the new LRI ranging system applied to satellite-to-satellite tracking. To evaluate the application of LRI in GRACE-FO, a relative kinematic orbit determination scheme for formation satellites integrating Kalman filters and GPS/LRI is proposed. The observation equation is constructed by combining LRI and spaceborne GPS data, and the intersatellite baselines of GRACE-FO formation satellites are calculated with Kalman filters. The combination of GPS and LRI techniques can limit the influence of GPS observation errors and improve the stability of orbit determination of the GRACE-FO satellites formation. The linearization of the GPS/LRI observation model and the process of the GPS/LRI relative kinematic orbit determination are provided. Relative kinematic orbit determination is verified by actual GPS/LRI data of GRACE-FO-A and GRACE-FO-B satellites. The quality of relative kinematic orbit determination is evaluated by reference orbit check and K-Band Ranging (KBR) check. The result of the reference orbit check indicates that the accuracy of GRACE-FO relative kinematic orbit determination along X, Y, and Z (components of the baseline vector) directions is better than 2.9 cm. Compared with the relative kinematic orbit determination by GPS only, GPS/LRI improves the accuracy of the relative kinematic orbit determination by approximately 1cm along with X, Y and Z directions, and by about 1.8 cm in 3D directions. The overall accuracy of relative kinematic orbit determination is improved by 25.9%. The result of the KBR check indicates that the accuracy of the intersatellite baseline determination is about +/−10.7 mm.

Haiyang-2D (HY-2D) is the fourth satellite in the marine dynamic satellite series established by China. It was successfully launched on 19 May 2021, marking the era of the 3-satellite network in the marine dynamic environment satellite series of China. The satellite’s precision orbit determination (POD) and validations are of great significance for ocean warning and marine altimetry missions. HY-2D is equipped with a laser reflector array (LRA), a satellite-borne Doppler Orbitography and Radiopositioning Integrated by Satellite (DORIS) receiver, and a satellite-borne dual-frequency GPS receiver named HY2 that was independently developed in China. In this paper, the quality of GPS data collected by the HY2 is analyzed based on indicators such as the multipath effect, cycle slips, and data completeness. The results suggest that the receiver can be used in POD missions involving low-Earth-orbit (LEO) satellites. The precise orbits of HY-2D are determined by the reduced-dynamics (RD) method. Apart from POD, validation of orbit accuracy is another important task for LEO POD. Therefore, two external validation methods are proposed, including carrier differential validation using one GPS satellite and inter-satellite differential validation using two GPS satellites. These are based on space-borne carrier-phase data, and the GPS satellites used for POD validation do not participate in orbit determination. The results of SLR range validation cannot illustrate the orbit accuracy in x, y, and z directions particularly, so to make validation results more intuitive, the SLR three-dimensional (3D) validation is proposed based on SLR range validation, and the RMSs in x, y, and z directions are 2.66, 3.32, and 2.69 cm, respectively. The results of SLR 3D validation are the same as those of SLR range validation, which proves that the new external validation method provided by SLR 3D is reliable. The RMSs of carrier differential validation and inter-satellite differential validation are 0.68 and 1.06 cm, respectively. The proposed validation methods are proved to be reliable.

Haiyang-2C (HY-2C) is a dynamic, marine-monitoring satellite that was launched by China and is equipped with an onboard dual-frequency GPS receiver named HY2_Receiver, which was independently developed in China. HY-2C was successfully launched on 21 September 2020. Its precise orbit is an important factor for scientific research applications, especially for marine altimetry missions. The performance of the HY2_Receiver is assessed based on indicators such as the multipath effect, ionospheric delay, cycle slip and data utilization, and assessments have suggested that the receiver can be used in precise orbit determination (POD) missions involving low-Earth-orbit (LEO) satellites. In this study, satellite-borne GPS data are used for POD with a reduced-dynamic (RD) method. Phase centre offset (PCO) and phase centre variation (PCV) models of the GPS antenna are established during POD, and their influence on the accuracy of orbit determination is analysed. After using the PCO and PCV models in POD, the root mean square (RMS) of the carrier-phase residuals is around 0.008 m and the orbit overlap validation accuracy in each direction reaches approximately 0.01 m. Compared with the precise science orbit (PSO) provided by the Centre National d’Etudes Spatiales (CNES), the RD orbit accuracy of HY-2C in the radial (R) direction reaches 0.01 m. The accuracy of satellite laser ranging (SLR) range validation is better than 0.03 m. Additionally, a new method is proposed to verify the accuracy of the RD orbit of HY-2C by using space-borne Doppler orbitography and radiopositioning integrated by satellite (DORIS) data directly. DORIS data are directly compared to the result calculated using the accurate coordinates of beacons and the RD orbit, and the results indicate that the external validation of HY-2C RD orbit has a range rate accuracy of within 0.0063 m/s.

Full tensor of gravity gradients contains extremely large amounts of information, which is one of the most important sources for research on recovery seafloor topography and underwater matching navigation. The calculation and accuracy of the full tensor of gravity gradients are worth studying. The Ka-band interferometric radar altimeter (KaRIn) of surface water and ocean topography (SWOT) mission enables high spatial resolution of sea surface height (SSH), which would be beneficial for the calculation of gravity gradients. However, there are no clear accuracy results for the gravity gradients (the gravity gradient tensor represents the second-order derivative of the gravity potential) recovered based on SWOT data. This study evaluated the possible precision of gravity gradients using the discretization method based on simulated SWOT wide-swath data and investigated the impact of instrument errors. The data are simulated based on the sea level anomaly data provided by the European Space Agency. The instrument errors are simulated based on the power spectrum data provided in the SWOT error budget document. Firstly, the full tensor of gravity gradients (SWOT_GGT) is calculated based on deflections of the vertical and gravity anomaly. The distinctions of instrument errors on the ascending and descending orbits are also taken into account in the calculation. The precision of the T_zz component is evaluated by the vertical gravity gradient model provided by the Scripps Institution of Oceanography. All components of SWOT_GGT are validated by the gravity gradients model, which is calculated by the open-source software GrafLab based on spherical harmonic. The T_zz component has the poorest precision among all the components. The reason for the worst accuracy of the T_zz component may be that it is derived by T_xx and T_yy, T_zz would have a larger error than T_xx and T_yy. The precision of all components is better than 6 E. Among the various errors, the effect of phase error and KaRIn error (random error caused by interferometric radar) on the results is greater than 2 E. The effect of the other four errors on the results is about 0.5 E. Utilizing multi-cycle data for the full tensor of gravity gradients recovery can suppress the effect of errors.

Conventional methods for bathymetry inversion based on gravity field data usually adopt gravity anomaly and vertical gravity gradient. Indeed, a gravity gradient tensor (GGT) has six components. Besides the commonly used vertical gravity gradient, the other five components can also contribute to bathymetry inversion, which is investigated in this article. The formulas for the inversion are derived based on the Parker’s formula. In order to provide GGT data for the inversion, vertical deflections and gravity anomalies of Scripps Institution of Oceanography, including north_SWOT_02 (1’), east_SWOT_02 (1’) and grav_SWOT_02 (1’) are firstly used to derive GGT in the study region, i.e., Bay of Bengal. And then, six bathymetric grid models are derived using the six components of the gravity gradients, respectively. The results show that within the study area, the ${{{\bm{T}}}_{{\bm{yz}}}}$ component exhibits the best performance among the bathymetric inversion results derived from the single components of GGT. Combining the inversion results of the six GGT components yields a new bathymetric model—one with higher accuracy than that derived from the single ${{{\bm{T}}}_{{\bm{yz}}}}$ component. Evaluations using ship-borne depth data indicate that, at the test points, the root mean square error of the combined model is 5.24 meters less than that of the ${{{\bm{T}}}_{{\bm{yz}}}}$-derived model. When GEBCO_2024 depths are treated as the reference (true values), the RMS error of the combined bathymetric model is 14.31 meters less than that of the ${{{\bm{T}}}_{{\bm{yz}}}}$-derived model.