One of the key constraints for the accelerometer of GRACE-type gravity satellites to accurately measure the non-gravitational accelerations acting on the satellite is that the center of mass of the satellite and the proof mass of the accelerometer should maintain a coincidence. In addition, the accuracy requirement is that the center of mass offset (CM-offset) in the three directions is less than 100 microns. Since the center of mass (CoM) of the satellite will change with the consumption of cold-gas fuel in the tanks, it is necessary to regularly carry out the CoM calibration maneuver. Firstly, the observation equations consisting of the accelerometer linear acceleration, angular acceleration, and the CM-offset vector are established in order to estimate the amount of CM-offset. Then, according to the estimated CM-offset, the satellite mass trim mechanisms are used to change the satellite’s CoM, so that the satellite’s CoM always approaches the proof mass of the accelerometer, with an accuracy of 100 μm per axis. The CM-offset of the satellite of GRACE-FO is estimated by using the accelerometer, star camera, magnetic torquer, magnetometer, and the precision orbit data during the GRACE-C CM-offset calibration period on 1 February 2020. Four kinds of CM-offset results are obtained by four different angular accelerations as follows: the angular acceleration based on the attitude dynamics (“MTQ angular acceleration”), the accelerometer angular acceleration calibrated by MTQ, the accelerometer angular acceleration, and the angular acceleration calculated by the star camera. By comparing the four kinds of CM-offset results that are estimated by the four different methods, all four of the results are shown to have the same level of accuracy. Based on the accelerometer (calibrated) angular acceleration, the difference with the JPL result is 0.5 μm, while the difference between the conventional method and the JPL result is 6.0 μm. All four of the methods can achieve the requirement of 50 μm accuracy and using four CM-offset estimation methods simultaneously can improve the integrity of the calibration results. Subsequently, the CM-offset results of GRACE-C since its launch are estimated here. The calibration algorithm that is proposed in this paper can be used as a reference in the calibration of gravity satellites carrying an accelerometer payload.

To address the limitations in global seafloor topography model construction, a scheme is proposed that takes into account the efficiency of seafloor topography prediction, the applicability of inversion methods, the heterogeneity of seafloor environments, and the inversion advantages of sea surface gravity field element. Using the South China Sea as a study area, we analyzed and developed the methodology in modeling the seafloor topography, and then evaluated the feasibility and effectiveness of the modeling strategy. Based on the proposed modeling approach, the STO_IEU2020 global bathymetry model was constructed using various input data, including the SIO V29.1 gravity anomaly (GA) and vertical gravity gradient anomaly (VGG), as well as bathymetric data from multiple sources (single beam, multi-beam, seismic, Electronic Navigation Chart, and radar sensor). Five evaluation areas located in the Atlantic and Indian Oceans were used to assess the performance of the generated model. The results showed that 79%, 89%, 72%, 92% and 93% of the checkpoints were within the ±100 m range for the five evaluation areas, and with average relative accuracy better than 6%. The generated STO_IEU2020 model correlates well with the SIO V20.1 model, indicating that the proposed construction strategy for global seafloor topography is feasible.

Based on its unique sensitivity to Earth's temporal gravity and since 2002, the Gravity Recovery And Climate Experiment (GRACE) twin-satellite, and its successor, GRACE Follow On (GRACE-FO) missions have accumulated a twodecade-long and continuing Earth's mass change climate data record. Additionally, the Chinese Gravimetry Mission (ChiGaM) was launched as the last polar-pair satellite formation in 2021. With the opportunity of two Existing Polar-pair Gravity satellite Formations (EPGF) in operations, we explore the ideal configuration to launch a third-pair satellite formation to construct the Triple-pair Gravity Satellite Constellation (TGSC). Here we examine the selection of initial orbit parameters of the third satellite formation based on subcycles and orbit parameters of EPGF to augment TGSC. The simulation study explores the effectiveness of the monthly temporal gravity field from the TGSC in potential contributions to geosciences. Our study reveals that TGSC improves continental hydrological signal recovery by approximately 24% and 38% in large and small basins (above/below 106 km2), as compared to GRACE-FO which would be the polar-pair gravity satellite in operations. TGSC's effectiveness varies across drainage systems of the Greenland Ice Sheet (GrIS) due to different ground track coverage. Compared to GRACE-FO, TGSC enhances GrIS mass balance recovery by 37 ∼ 56%. Simulations for six mega earthquakes (above Mw 7.7) reveal that TGSC outperforms GRACE-FO by approximately 46 ∼ 58% in extracting co-seismic signals. Our study reveals the importance of incorporating existing on-orbit gravity missions into the design of future gravity satellite constellations. This strategy aims to not only accomplish the predefined objectives of gravity satellite missions but also potentially provide additional benefits to the field of geosciences.

Accurate Digital Elevation Models (DEMs) are essential for precise terrain gravity field calculations, which are critical in gravity field modeling, airborne gravimeter and gradiometer calibration, and geophysical inversion. This study evaluates the accuracy of various satellite DEMs by comparing them with a LiDAR DEM at the Wudalianchi test site, a location requiring ultra-accurate terrain gravity fields. Major DEM error sources, particularly those related to vegetation, were identified and corrected using a least squares method that integrates canopy height, vegetation cover, NDVI, and airborne LiDAR DEM data. The impact of DEM vegetation errors on terrain gravity anomalies and gravity gradients was quantified using a partitioned adaptive gravity forward-modeling method at different measurement heights. The results indicate that the TanDEM-X DEM and AW3D30 DEM exhibit the highest vertical accuracy among the satellite DEMs evaluated in the Wudalianchi area. Vegetation significantly affects DEM accuracy, with vegetation-related errors causing an impact of approximately 0.17 mGal (RMS) on surface gravity anomalies. This effect is more pronounced in densely vegetated and volcanic regions. At 100 m above the surface and at an altitude of 1 km, vegetation height affects gravity anomalies by approximately 0.12 mGal and 0.07 mGal, respectively. Additionally, vegetation height impacts the vertical gravity gradient at 100 m above the surface by approximately 4.20 E (RMS), with errors up to 48.84 E over vegetation covered areas. The findings underscore the critical importance of using DEMs with vegetation errors removed for high-precision terrain gravity and gravity gradient modeling, particularly in applications such as airborne gravimeter and gradiometer calibration.

The GRACE-FO satellite's laser ranging interferometer (LRI) measurements suffer from a significant number of phase anomalies, which can directly affect the gravity field recovery. To address this issue, we proposed an improved difference method (ImDFM) for phase anomaly processing, which enhances the traditional difference method (DFM) through two improvements: (1) combine the phase smoothing technique to handle cycle slips, single event upsets, and Mega phase jumps (PJs) which DFM hard to process; and (2) propose a novel time-tag synchronization offsets estimation method based on PJs to rectify the accuracy degradation caused by time-tag synchronization anomalies. Compared to the mainstream template method (TPM), ImDFM offers a significant advantage in conciseness. We evaluated the accuracy of ImDFM and residual spike characteristics by comparing the ImDFM product (S11) with the template-based product (S10) and the official JPL RL04 product in phase anomaly, LRI1B and gravity field results. The results show that (1) ImDFM can process phase anomalies with an accuracy better than 600 \boldmath $ \mathrm{pm/\sqrt{Hz}@1Hz}$ and the residual spikes mainly affect frequency band above 2 Hz; (2) the accuracy of estimated time-tag synchronization offset is better than 4 $\mu$ s, which can effectively correct the loss of accuracy; (3) the residual spikes in S11 are below 7nm/s, which does not affect the accuracy of gravity field recovery. The RL04 is still affected by phase anomalies, resulting in relatively higher noise above degree 30. In summary, the ImDFM proposed in this paper provides a high precision and concise approach for processing phase anomalies.

The coordinates of the KBR (K-band ranging system) antenna phase center of GRACE-type gravity satellites in the satellite Science Reference Frame should be precisely known, and the determination accuracy should reach 0.3 mrad in the Y (pitch) and Z (yaw) directions. Due to the precision limitation of ground measurement and the change of space environment during orbit, the KBR antenna phase center changes. In order to obtain more accurate KBR antenna phase center coordinates, it is necessary to maneuver the satellite to achieve the on-orbit calibration of the KBR antenna phase center. Based on the in-orbit calibration data of KBR of GRACE-FO satellites, a new method is proposed to estimate the antenna phase center of KBR using the inter-satellite range acceleration as the observation value. The antenna phase center of KBR is solved by the robust estimation method, and the obtained calibration results are better than 72 μm in the Y and Z directions and better than 1.3 mm in the X direction, which is 50% better than the least squares estimation algorithm. The accuracy of KBR calibration results obtained by using the data of positive maneuvers or mirror (negative) maneuvers, respectively, does not meet 0.3 mrad. It is shown that mirror maneuvers are required for KBR calibration of a GRACE-type gravity satellite to obtain antenna phase center estimation results that meet the accuracy requirements. The calibration algorithm proposed in this paper can provide reference for KBR antenna phase center calibration of Chinese GRACE-type gravity satellites.