The GRACE-type gravity satellites provide essential baseline geophysical data for the study of changes in Earth's mass and global climate by monitoring the global monthly time-varying gravity field variation. The inter-satellite ranging system, which is used to measure the distance variations between two satellites, is a key payload on the gravity satellites. GRACE/GRACE-FO and China's first pair of gravity satellites are both equipped with a K-Band Ranging system (KBR) with micrometer accuracy. The KBR relies on an Ultra-Stable Oscillator (USO) to generate the on-board time tag and carrier frequencies, and then uses the clock offset between the local clock (USO clock) and the GPS clock which estimated in the GPS precision orbit determination to synchronize the local clocks of the two satellites and precisely measure the USO's frequencies, so the accuracy of the USO/GPS clocks directly affects the ranging accuracy of the KBR. Based on GRACE-FO data, this paper deeply investigates the specific effects of different clock accuracies and the factors that influence the low-frequency characteristics of USO on the ranging accuracy of the KBR. Firstly, we evaluate the accuracy of the USO clock and the GPS clock and their effects on the calculation of the KBR biased range and the carrier Frequency Variation correction (FV correction), and then further analyze the influencing factors of the low-frequency accuracy of the USO clock, including relativistic effects and the temperature variations of the Instrument Processing Unit (IPU). The results show that: (1) Compared with the USO clock, the GPS clock can improve the low-frequency (< 1 mHz) accuracy of the KBR ranging by 1 similar to 2 orders of magnitude, which meets the requirements of the biased range calculation, but the high-frequency (1 similar to 6 mHz) noise of the GPS clock introduces noise higher than the KBR design noise level in the FV correction; (2) Among the influencing factors of the low-frequency accuracy of the USO clock, the relativistic effect is the main component of the clock error between the USO clock and the GPS clock at 1 cpr and 2 cpr for the case of single-satellite, while the relative clock error caused by the relativistic effect has a negligible influence on the measurement of the biased range, but it is still the main influencing factor on the FV correction at 1 cpr and 2 cpr. The correlation coefficients between the relative temperature variation of the two satellites and the relative clock error are higher than 0.6 for 70% of the period, indicating the temperature variation is a potential factor affecting the low-frequency accuracy of the USO clocks. In addition, the inter-annual variation of the USO frequency drift is highly correlated with the temperature variation of satellite IPU, but the error of the relative clock error does not exhibit a significant correlation with such temperature variations. This study provides a theoretical foundation for evaluating clock noise in KBR ranging and optimizing the data pre-processing algorithms.

Modeling sub-daily mass changes, dominated by the atmosphere and the oceans, is a fundamental requirement for nearly all existing terrestrial or space-borne geodetic observations to perform signal separation. Removing these high-frequency mass changes, through the usage of so-called de-aliasing products, is of particular interest for satellite gravity missions such as GRACE and GRACE-FO to prevent the aliasing of short-term mass changes into seasonal and long-term mass variability. Ongoing efforts focus on simulating this high-frequency signal by driving atmospheric/oceanic numerical models with specific climate-forcing fields and assimilating observational data. In this study, we establish China's first de-aliasing computation platform, achieved by using the recently released CRA-40 (China's first generation of atmospheric reanalysis) as forcing fields to drive our in-house 3-D atmospheric integration model and the LASG/IAP (State Key Laboratory of Numerical Modeling for Atmospheric Sciences and Geophysical Fluid Dynamics/Institute of Atmospheric Physics) Climate System Ocean Model 3.0 (LICOM3.0). With this new platform, we reproduce an alternative high-frequency atmospheric and oceanic gravity de-aliasing product, called CRA-LICOM, at 6 hourly and 50 km resolution, covering 2002-2024 at a global scale. The product is freely available at 10.11888/SolidEar.tpdc.302016 . Inter-comparisons with the products of GFZ (Helmholtz Centre for Geosciences) and validations against independent observations reveal: (i) the current version of CRA-LICOM satisfies the requirement of the state-of-the-art satellite gravity missions, as well as other geodetic measurements, and (ii) despite agreement across most areas, considerable uncertainty is found at marginal seas near continental shelves, particularly at high-latitude regions. Therefore, scientific applications that aim to understand the sub-daily atmospheric-oceanic water exchange, as well as mission design of future satellite gravity that seeks accurate gravity de-aliasing, can use our product as a reliable source. Nevertheless, the current platform has the potential to be improved in terms of modeling and data assimilation capacity, which will be outlined in this study.

Gravity Recovery and Climate Experiment Follow‐On is equipped with two inter‐satellite ranging systems, notably the K‐Band ranging (KBR) and the more precise Laser Ranging Interferometer (LRI), which enable the detection of variations in Earth's gravity. Assessing the differences between KBR and LRI is beneficial for understanding the performance of future LRI‐only gravity satellite missions. However, due to limitations imposed by temporal aliasing errors, the advantages of LRI over KBR for monthly gravity field solutions are not clearly discernible. The along‐orbit range‐accelerations directly reflect the mass variations, providing a new way to evaluate the differences between LRI and KBR. Therefore, we selected different frequency bands and time scales to compare the along‐orbit range‐accelerations of KBR and LRI from 2019 to 2021. Analyzing the spatiotemporal‐averaged along‐orbit data, the results indicate a systematic difference between KBR and LRI, with a scale factor of about 0.977 over the selected 92 basins, while the scale factor is lower over oceanic regions. A comparison of the instantaneous along‐orbit data for KBR and LRI reveals that the noise level of LRI in the [15.8–21 mHz] band is at least one order of magnitude lower than that of KBR. After simulating instrument noise, model errors, and time‐variable signals, it was determined that KBR noise is likely the primary factor contributing to the systematic difference in capturing temporal signals between LRI and KBR. In addition, regions with a low signal‐to‐noise ratio (SNR) are more susceptible to noise, which diminishes the correlation between KBR and LRI along‐orbit data.

The gravity recovery and climate experiment (GRACE) and its successor GRACE follow-on (GRACE-FO) provide critical insights into global terrestrial water storage anomalies (TWSAs) by precisely measuring changes in intersatellite distances. However, various uncertainty sources cause geographically correlated noise in the GRACE/GRACE-FO Level-2 data, which is manifested as north-south striping noise in TWSA grids and complicates hydrological investigations. To address these challenges, we introduce a novel deep learning framework, the Bayesian optimization convolutional neural network with spatial attention mechanism (BO-CNN-SAM), which directly mitigates systematic errors and recovers TWSA from Level-2 data. The results are as follows: 1) The BO-CNN-SAM model architecture demonstrates superior predictive accuracy and robustness, with the root mean squared error (RMSE) reducing by 142%, 120%, and 93% during training, and 136%, 89%, and 74% during validation, compared to other deep learning structures such as BO-CNN, CNN-SAM, and CNN, respectively. 2) In terms of recovered TWSA, BO-CNN-SAM outperforms other CNN-based models, achieving the lowest RMSE (4.25, 4.40, and 5.50 cm) and the highest Nash-Sutcliffe Efficiency coefficients of 0.78, 0.64, and 0.60 during the training, validation, and testing phase, respectively. 3) The BO-CNN-SAM framework is successfully used to estimate ice sheet mass balance in Greenland and to accurately quantify prolonged drought in the Yangtze River Basin during 2022. Looking ahead, BO-CNN-SAM has the potential to directly recover TWSA from raw GRACE/GRACE-FO Level-1 data to gridded Level-3 TWSA products. This capability opens new opportunities for producing TWSA fields with low latency and enhancing our understanding of hydrological processes.

The Global Navigation Satellite System (GNSS) is vital for monitoring terrestrial water storage (TWS). However, effectively extracting hydrological load deformation from GNSS observations poses a significant challenge. This study proposes a novel strategy; the seasonal hydrological load signals are removed from the raw data, and the remaining signals use principal component analysis (PCA). Simulation results from Yunnan Province demonstrate that the spatial distribution of the root mean square error (RMSE) is improved by approximately 15 % compared with traditional PCA extraction from raw data. From January 2013 to December 2022, TWS was inverted from 24 GNSS stations in Yunnan Province. The spatial distribution and time series of TWS inverted from GNSS align well with those TWS inferred from the Gravity Recovery and Climate Experiment (GRACE), GRACE Follow-On (GFO), and the Global Land Data Assimilation System (GLDAS) land surface model. However, the amplitude of the GNSS-inverted TWS is slightly higher. Since GNSS ground stations are more sensitive to hydrological load signals, they show correlations with precipitation data that are 8.6 % and 6.0 % higher than those of GRACE and GLDAS, respectively. In the power spectral density analysis of GRACE/GFO, GLDAS, and GNSS, the signal strength of GNSS is much higher than that of GRACE/GFO and GLDAS in the June and February cycles. These findings suggest that the new data extraction strategy can capture higher frequency hydrological signals in TWS, and GNSS observations can help address limitations in GRACE/GFO observations. This study demonstrates the potential of GNSS TWS in capturing higher-frequency hydrological signals and climate extremes application.

The GRACE-like gravity satellites are designed to provide accurate measurements of the global time-varying gravity field, allowing to monitor the changes in the distribution of the Earth's mass caused, for example, by climate change. The gravity information is encoded in the line-of-sight vector, which is given by the position difference between the satellites. The key observable of GRACE and GRACE follow-on is the change in length of the LOS vector, measured by dedicated ranging instruments (K-band ranging system (KBR) or laser ranging interferometer (LRI)). However, the orientation of the LOS vector is measured with some precision using GNSS/GPS, which limits the accuracy of the gravity field maps. To overcome this problem, we propose the use of a dedicated angular velocity sensing (AVS) system that tracks the changes in the orientation of the line of sight with respect to the inertial frame. The angular velocity vector of the LOS has two independent components, yaw and pitch, which we introduce as additional observations in the gravity field recovery process. We firstly show how the AVS and range observables can be used to reconstruct the 3-dimensional differential acceleration vector. Then we find that the inversion results with AVS and regular ranging can mitigate the effect of AOD errors and significantly improve the accuracy of the gravity fields if more accurate AVS observations are available than currently provided by GNSS/GPS orbits. One potential way to achieve more accurate AVS observations is to use differential wavefront sensing (DWS) to accurately measure the orientation of the accelerometer test masses with respect to the platform, giving lower noise than the conventional star cameras, and combine these measurements with the DWS measurements from the inter-satellite laser interferometer to obtain the orientation of the LOS with respect to the inertial frame. With a DWS noise level of 0.1 nrad/√Hz, a single pair of GRACE satellites can achieve the same accuracy as a four-satellite Bender configuration. This study provides a promising alternative to the development of multiple satellite pairs to improve the accuracy of gravity missions.

The K-Band Ranging System (KBR) is the key payload for measuring inter-satellite distance variations with micrometer accuracy on the GRACE and GRACE Follow-On (GRACE-FO) missions. Alongside KBR, GRACE-FO includes a novel and more precise Laser Ranging Interferometer (LRI). The KBR observations not only support the gravity field recovery, but also play an irreplaceable role in estimating the LRI scale factor. Although recent analyses suggest that the KBR-LRI residuals at low frequencies are mainly limited by time-tag errors, this study investigates also smaller contributions in detail. We reprocess the KBR data from Level-1A to Level-1B in alternative ways, e.g. to study different approaches for gap-filling of missing phase observations and the impacts of clock offsets. We find that low-pass filtering the clock offset improves data quality, and additional smoothing at day boundaries reduces some jumps at these day-to-day transitions. In addition, carrier Frequency Variation Correction is applied in the phase-to-range conversion with amplitudes at a level close to KBR noise requirements. Other enhancements include the refinement of the Light Time Correction and the consideration of satellite center-of-mass motion in the Antenna Offset Correction. These updates have been incorporated into our new KBR1B v50 dataset, which is publicly available for the GRACE-FO period (2018–2024). While these changes have little effect on the Level-2 gravity field maps at the current level of precision, they do improve the Level-1B KBR data for GRACE missions and are partially applicable to LRI processing, which has potential applications for future more accurate missions.

The high-precision inter-satellite laser interferometer is the key payload of the TianQin mission satellite, and the raw data processing of laser interferometric measurements is a crucial step in achieving its scientific objectives. Based on the measurements from the GRACE-FO gravity satellite, this study investigated the characteristics of laser ranging interferometer (LRI) measurements and raw data processing procedures. To validate the reliability of the data processing techniques, this study compares the processing results with RL04 product form NASA JPL and V50 product form AEI in terms of phase jump processing, scale factor estimation, biased range, and gravity field recovery results. The results show that the LRI product processed in this study demonstrates a precision of 1 nm/s/√Hz at 0.1 Hz, which is comparable to the V50 and better than RL04. Moreover, the geoid degree variance of gravity field based on the product in this study is superior to JPL's results for degrees above 30, and shows a good consistency with AEI’s results. The LRI raw data processing algorithm and software shown in this study can effectively process the raw LRI measurements, providing a foundation for the future LRI data processing work of TianQin 2, while also offering experience for TianQin 3.

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 (CSs), single event upsets (SEUs), 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, 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 pm/root Hz@1 Hz 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 7 nm/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 article provides a high precision and concise approach for processing phase anomalies.

The Laser Ranging Interferometer (LRI) on GRACE-FO gravity satellite can provide the distancevariations of inter-satellite with a nanometer precision, possessing great potential for high-precision characterization of earth ' s gravity field variations, the migration and distribution of surface materials on medium- and long-spatial scales. Due to the accuracy of ranging measurements converted from phase measurements is directly affected by time-tag errors, phase jumps and ranging system errors in the raw LRI phase measurements, and which would propagate into subsequent gravity field solutions and scientific applications, thus meticulous data processing method is necessary for LRI phase measurements. This paper, based on GRACE-FO measured data, thoroughly investigates the characteristics of LRI measurements, the raw data processing procedures and the corresponding key technologies, resulting an independently developed laser ranging product (LRI1B SYSU S10). Focusing on the limitations in the existing phase jump processing algorithm developed by the Jet Propulsion Laboratory of the United States that cannot accurately process phase jumps, we verified that combining the phase jump template method with the phase jump smoothing method can effectively eliminate various types of phase jumps. The results show that the biased range rate of the LRI1B product developed in this paper achieves a precision of 1 nm.s(-1).Hz(-1/2) at 0.1 Hz, which surpasses JPL's RL04 (Release 04) product (5 similar to 10 nm.s(-1).Hz(-1/2)) and comparable to the similar product of the Albert Einstein Institution (AEI), Germany. The geoid degree variance derived from our product is superior to JPL's results for degrees beyond 30 and demonstrates strong consistency with AEI's results. The LRI raw data processing method developed in this study can effectively eliminate various errors in the raw phase measurements, providing significant implications for the data processing, gravity field recovery and surface material migration research for future GRACE-like gravity satellite missions utilizing LRI (e.g., TianQin 2).

The Gravity Recovery and Climate Experiment (GRACE) satellites have observed mass migrations caused by megathrust earthquakes. Extracting earthquake-related signals from GRACE data is still a challenge due to the interference from non-earthquake sources such as terrestrial hydrology. Instead of reducing hydrological signals by potentially biased hydrological models, in this study we apply a model-free technique of independent component analysis (ICA), to separate earthquake and non-earthquake signals from non-Gaussian GRACE data. We elucidate the principles and mechanisms of ICA for the separation of earthquake and hydrology signals, employing simulated data to demonstrate the process. Our findings demonstrate that both spatial ICA and temporal ICA are highly effective in discerning earthquake related to 2004 Mw 9.2 event and hydrological signals from GRACE data in the Sumatra region. This stands in stark contrast to principal component analysis, which often encounters challenges with signal intermingling. The utility of ICA is evident in its ability to distinctly delineate coseismic and post-seismic behaviours associated with megathrust events, including the 2004 Sumatra, the 2010 Maule, and the 2011 Tohoku earthquakes. ICA effectively mitigates the potential for misestimation of earthquake signals, an issue that can carry substantial implications. Therefore, employing ICA facilitates the accurate extraction of earthquake-related data from satellite gravity observations-a critical process for refining earthquake source parameters and understanding Earth's rheological properties, especially when non-earthquake signals are significant and cannot be disregarded.

In recent two decades, GRACE/GRACE-FO has continuously monitored the earth's time-variable gravity field (TVG). However, limited by a single-polar orbit configuration, background model errors and the accuracy of satellite payloads, the spatio-temporal resolution and accuracy of TVG are insufficient to detect short-term, small-scale mass change signals. The next-generation gravity missions (NGGMs), represented by ESA’s MAGIC (Mass Change and Geoscience International Constellation) and SYSU’s “TianQin”, will improve the accuracy of the recovered TVG through multi-pair satellite constellations and the new generation of high-precision satellite payloads. Considering the possibility of synergistic observation for future gravity missions, GRACE-FO and the Chinese gravity mission, this paper performed closed-loop simulations based on four constellations: 2Polar, Bender, Polar+Bender and 2Bender with the dynamic method. The solutions based on these different simulations are evaluated on one-day, two-day, three-day and monthly time scales. The results show that compared with the single-polar, the accuracy of monthly TVG for 2Polar, Bender, Polar+Bender and 2Bender is increased by 30.7%, 85.7%, 85.9% and 89.5%, respectively. The multi-pair satellite constellations can recover short-term TVG with high spatial resolution and retain the high-frequency part of the geophysical signals in time series. Among them, in terms of 40 degrees in spherical harmonics, 2Bender, Polar+Bender and Bender can recover 1-day, 2-days, and 3-days TVG, respectively.

The development of Cold-Atom Interferometry (CAI) provides new measurement ideas for future satellite gradiometry missions. Current simulation studies based on this mission concept have only demonstrated the ability of the CAI gradiometer to observe the Earth's gravity field on a single pointing mode. In this paper, numerical closed-loop simulations are conducted to evaluate the effect of different pointing modes of the CAI gradiometer on the gravity field recovery in the context of the GOCE mission. The simulation results show that in the nadir pointing mode, the accuracy of the gravity field solution of the CAI gradiometer is better than that of the GOCE within 50 d/o (d/o=degree and order) only, which is due to the influence of the satellite rotation angular velocity. When the satellite is equipped with the orbital rotation compensation scheme, the influence of the satellite rotation on the CAI gradiometer can be effectively attenuated, and then the accuracy of the gravity field solution can be improved. The combined accuracy of the three main diagonal components of the gravity gradient tensor is better than the results from the GOCE satellite in the full frequency band by a factor of 1.5 to 6. In the inertial pointing mode and considering only the effect of satellite residual angular velocity, the solution of the CAI gradiometer is less accurate than the GRADIO gradiometer on board the GOCE satellite after 30 d/o. Taking into account the residual angular velocity of the satellite and the rotation of the satellite orbital plane, the CAI gradiometer solves the gravity field with better accuracy than the GOCE satellite solution within 100 d/o. We further compared the results of the two pointing modes based on single-axis, dual-axes and tri-axes observations, respectively. It can be found that the overall accuracy of the two modes is comparable for tri-axes observations and outperform the result of the GRADIO gradiometer at all degrees and orders. However, when the observations are based on single-axis, the accuracy of the Vzz component in the nadir pointing mode is higher. While the accuracy of the combined solution ( Vxx+ Vzz and Vyy+ Vzz) in the inertial pointing mode is higher in the case of two-axis observations. The findings of this study on the effects of different pointing modes of the CAI gradiometer on gravity field recovery can provide guidance for the new spatial quantum Earth's gravity field measurements based on CAI gradiometers.

This paper studies the data preprocessing and analysis methods of the key microwave ranging system for the low-low satellite-to-satellite tracking gravity mission, and achieve the efficient suppression of the key carrier frequency noise, as well as the elimination and correction of the related interference and deviation. According to the theoretical analysis results, relevant processing and analysis procedures are developed. The residual between the dual one-way ranging data product completed by this research and the official product of GRACE Follow-On is much smaller than the design requirement of the payload, which meets the accuracy requirements of gravity field inversion. Evaluation and analysis methods for electronic noise, system noise and other noise in the final data product are discussed. In this paper, by introducing the frequency-domain analysis method of the spatial inhomogeneity of the ionospheric free electron content, and using the inter-satellite microwave ranging data, the ability to analyse the variation behaviour of free electron content at different spatial scales and its global distribution characteristics is realized, providing data support for the in-depth study of the ionosphere. This research can provide relevant technical accumulation and reference for the data preprocessing and analysis of the microwave ranging system for low-low satellite-to-satellite tracking missions of China.

在详细分析非差运动学精密定轨原理和步骤基础上,采用平滑卡尔曼滤波算法,通过自主研发的精密定轨软件对 GRACE-FO卫星进行非差运动学精密定轨.结果表明,与官方科学轨道相比,平滑滤波不仅能提高定轨开始阶段的精度,而且整体上定轨精度也得到提升,GRACE-FO C 星轨道残差为 2～4 cm,GRACE-FO D星轨道残差为 3～5 cm.

Drought is a prolonged dry period in the natural climate cycle, and is one of the most costly weather events. The Gravity Recovery and Climate Experiment (GRACE) derived terrestrial water storage anomalies (TWSA) have been widely used to assess drought severity. However, the relatively short cover period of GRACE and GRACE Follow-On limit our knowledge about the characterization and evolution of drought over decades time scale. This study proposes a standardized GRACE reconstructed TWSA index (SGRTI) to assess the drought severity based on a statistical reconstruction method calibrated by GRACE observations. Results show that the SGRTI correlates well with 6-month scale SPI and SPEI, with correlation coefficients reaching 0.79 and 0.81 in the YRB from 1981 to 2019. Soil moisture can capture drought condition like the SGRTI, while cannot further reflect deeper water storage depletion. The SGRTI is also comparable to the SRI and in-situ water level. As a case study for the Yangtze River Basin, its three sub-basins experience more frequent droughts, shorter drought duration, and lower severity drought, as identified by SGRTI during 1992-2019 relative to 1963-1991. The presented SGRTI in this study can provide a valuable supplement to the drought index before the GRACE era.

The terrestrial water storage anomaly (TWSA) observed by the Gravity Recovery and Climate Experiment (GRACE) satellite and its successor GRACE Follow-On (GRACE-FO) provides a new means for monitoring floods. However, due to the coarse temporal resolution of GRACE/GRACE-FO, the understanding of flood occurrence mechanisms and the monitoring of short-term floods are limited. This study utilizes a statistical model to reconstruct daily TWS by combining monthly GRACE observations with daily temperature and precipitation data. The reconstructed daily TWSA is utilized to monitor the catastrophic flood event that occurred in the middle and lower reaches of the Yangtze River basin in 2020. Furthermore, the study compares the reconstructed daily TWSA with the vertical displacements of eight Global Navigation Satellite System (GNSS) stations at grid scale. A modified wetness index (MWI) and a normalized daily flood potential index (NDFPI) are introduced and compared with in situ daily streamflow to assess their potential for flood monitoring and early warning. The results show that terrestrial water storage (TWS) in the study area increases from early June, reaching a peak on 19 July, and then receding till September. The reconstructed TWSA better captures the changes in water storage on a daily scale compared to monthly GRACE data. The MWI and NDFPI based on the reconstructed daily TWSA both exceed the 90th percentile 7 days earlier than the in situ streamflow, demonstrating their potential for daily flood monitoring. Collectively, these findings suggest that the reconstructed TWSA can serve as an effective tool for flood monitoring and early warning.

The electrostatic gravity gradiometer carried by the Gravity field and steady-state Ocean Circulation Explorer (GOCE) satellite is affected by accelerometer noise and other factors; hence, the observation data present complex error characteristics in the low-frequency domain. The accuracy of the recovered gravity field will be directly affected by the design of the filters based on the error characteristics of the gradient data. In this study, the applicability of various filters to different errors in observation is evaluated, such as the 1/f error and the orbital frequency errors. The experimental results show that the cascade filter (DARMA), which is formed of a differential filter and an autoregressive moving average filter (ARMA) filter, has the best accuracy for the characteristic of the 1/f low-frequency error. The strategy of introducing empirical parameters can reduce the orbital frequency errors, whereas the application of a notch filter will worsen the final solution. Frequent orbit changes and other changes in the observed environment have little impact on the new version gradient data (the data product is coded 0202), while the influence cannot be ignored on the results of the old version data (the data product is coded 0103). The influence can be effectively minimized by shortening the length of the arc. By analyzing the above experimental findings, it can be concluded that the inversion accuracy can be effectively improved by choosing the appropriate filter combination and filter estimation frequency when solving the gravity field model based on the gradient data of the GOCE satellite. This is of reference significance for the updating of the existing models.

近20年来,利用重力卫星研究地球系统的质量分布得到了广泛的发展,使人类对发生在大气、水圈、海洋、极地冰盖等地球圈层的动态过程有了更为深刻的理解.现阶段重力卫星主要包括挑战性小卫星有效载荷计划、地球重力场恢复及气候探测计划(gravity recovery and climate experiment,GRACE),地球重力场稳态海洋环流探测计划和GRACE后续任务,回顾其发展历程,简要说明其在地球重力场解算的研究进展及存在的问题.为了改善现阶段重力卫星的缺点,国际上各研究机构为下一代重力卫星任务(next generation gravity mission,NGGM)提出众多远景规划和模拟分析,梳理了国际上提出的12种下一代重力卫星任务的任务概念、预期精度及任务状态.为了更加清晰介绍NGGM和整体把握其进展,根据星座构型和卫星栽荷技术将其划分为4类,即Sharifi型重力卫星星座、Bender型重力卫星星座、星链型重力卫星星座和量子型重力卫星星座,并综合分析其性能,尝试性地给出相应的参考性实施建议.

The linearized Stokes boundary value problem is taken as a case to study the relationship between the accuracy of the observation data and the degree of the ultra-high degree gravity filed model.The linearized Stokes boundary value problem was first derived,and the corresponding spherical harmonic series solutions were gave according to the spherical approximation and ellipsoidal approximation of the boundary surface respectively.Then through the simulation,the linearized boundary value problem and the influence of different the accuracy of the observation data for the construction of the ultra-high degree gravity field model were analyzed,respectively. From the simulation,the linearized boundary value problem has met the requirements of the construction of the ultra-high degree gravity model within 2 159 degree,and the accuracy of the potential coefficients can be improved by one order of magnitude through ellipsoid correction compared with the solution of the spherical approximation.Then,the 1 and 3 mGal random errors were added to the gravity anomaly respectively.The maximum degree of the recovered gravity field model is about 1 600 and 1 400 through the Stokes spherical boundary value problem,and the maximum degree of the recovered gravity field model is about 2 000 and 1 450 through the Stokes ellipsoid boundary value problem.The accuracy of the middle and low-degree of the potential coefficients solved by Stokes ellipsoid boundary value problem is better than the solution of the Stokes spherical boundary value problem. However,the accuracy of the middle and high-degree of the potential coefficients solved by Stokes ellipsoid boundary value problem is lower. In other words,the ellipsoidal boundary value problem has worse anti-error interference ability than the spherical boundary value problem,and this is mainly due to the existence of nε~2 term in the spherical harmonic coefficients solution of the ellipsoidal boundary value problem.