The time-variable gravity field solutions from the Gravity Recovery and Climate Experiment (GRACE) and GRACE Follow-On (GRACE-FO) mission are generally contaminated by the correlation errors, specifically parameter correlation (strong parameter coupling) and observation noise correlation (colored instead of white noise). In this context, we propose a decorrelation approach to pursue an improved time-variable gravity solution following a step-wise processing. The step-wise decorrelation approach comprises three steps, standard, parameter decorrelation, and observation noise decorrelation processes. First, the standard process serves to establish a reliable signal reference for the following. Then, the parameter decorrelation is implemented through the separate estimation of orbit and gravity field parameters. Finally, to achieve the goal of observation noise decorrelation, the post-fit residuals obtained from the result of parameter decorrelation are used to estimate a colored noise model, which is considered to determine the final gravity field model, specifically termed the step-wise decorrelation solution. The basic idea is that under the regularization constraints of separate estimation for dynamic parameters, the reduced dynamic parameter space allows certain low-frequency perturbative errors to emerge in post-fit residuals, enabling comprehensive characterization of observation noise correlation. Using this step-wise decorrelation approach, we process monthly GRACE-FO gravity field time series and evaluate the performance of them from the aspects of signal and noise. Spectral and spatial domain analyses of noise levels confirm significant noise suppression in the final solution. For instance, it achieves 66

Compared to the traditional two-step method, the dynamic one-step method fully utilizes the raw information from the observation data and theoretically yields more accurate time-variable gravity field products. However, due to the problems with the complexity of parameter space and functional model, one-step method remains a key focus and challenge in current research. We study the dynamic one-step method, presents a reasonable data processing strategy, and obtain the 60-degree temporal gravity fields for the years 2021-2022 from GRACE Follow-On (GRACE-FO) GPS and K/Ka Band Ranging (KBR) rang rate data. For the technical details of the one-step method, we focus on analyzing the impact of a priori weighting and empirical parameter son orbit and gravity field determination. The study reveals that when using GPS data with a 30 s sampling, it is necessary to down weight the GPS data appropriately to avoid introducing excessive noise. The recommended a priori weight ratio for code, carrier phase, and rang rate data is 1:10(4):10(14). To ensure the quality of the orbit and the gravity field model, empirical parameters are suggested to be co-estimated with other parameters to absorb residual perturbative force errors. Among various empirical parameters (such as piecewise periodic accelerations and kinematic empirical parameters), piecewise constant accelerations are more effective in absorbing noise in the model while maintaining orbit accuracy. Furthermore, under the same dynamic parameter configuration, the time-variable gravity field model driven from the dynamic one-step method outperforms the two-step method interms of both consistency with the official model and precision. Finally, a comprehensive evaluation of the orbit and time-variable gravity field model over the entire time span is conducted. The results indicate that the orbits determined by the dynamic one-step method meet centimeter-level requirements, with a standard deviation of 1.6cm for the satellite laser ranging (SLR) residuals of twin satellites. The gravity field model exhibits good consistency with the latest RL06.1 models released by CSR (Center for Space Research), JPL (Jet Propulsion Laboratory), and GFZ (Geo Forschungs Zentrum Potsdam). While preserving the full characteristics of time-variable signals, the noise performance is comparable to the CSR model and better than the JPL and GFZ models.

The Gravity Recovery and Climate Experiment (GRACE) mission provides original observations to different institutions for the production of various monthly time-variable gravity field models (TVGFMs). Aiming to optimize the signal-to-noise ratio of TVGFMs, we determine to combine them in the spatial domain. This combination comprises two approaches: one combines spherical harmonic coefficient (SHC) solutions, and the other combines SHC and mascon (mass concentration) solutions together. For each approach, we employ four old weighting schemes and one new scheme named oceanic accuracy weighting. We then assessed the combined models through both internal and external validations. In external validation, we compare the Caspian Sea level changes derived from the combined models with those obtained from satellite altimeter. Our results reveal an improvement of the SHC combination using variance component estimation (VCE) weighting compared to any single SHC solution. Moreover, we found enhanced performance in the combined models with the incorporation of mascon solutions, particularly employing the oceanic accuracy weighting. These findings underscore the efficacy of model combination in improving performance, and emphasize the importance of selecting appropriate weighting strategies for integrating GRACE solutions. Specifically, we recommend VCE weighting scheme for combining SHC solutions only and oceanic accuracy weighting scheme for integrating mascon and SHC solutions.

The flex power technology in satellite navigation systems enhances anti-jamming capabilities but can impact the quality of GPS observations and the accuracy of low Earth orbit determination, such as GRACE Follow-On (GRACE-FO) mission. This study investigates the influence of GPS flex power on Hatch-Melbourne-Wübbena (HMW) linear combinations and GRACE-FO kinematic orbits from January 1 to September 30, 2020. Epoch-differenced K-Band Ranging (KBR) data is introduced in orbit determination during the flex power period to improve both absolute and inter-satellite relative accuracy. The analysis indicates that the influence of early flex power (before February 13, 2020) on HMW combinations and orbits is minimal, whereas the effect of later flex power (after February 14, 2020) is significant: (1) HMW combinations exhibit notable systematic discontinuities even with elevation angles greater than 50 degrees, causing the fixing rate of wide-lane ambiguities to drop from 96% to 80%. (2) Kinematic absolute orbits show significant deteriorations of approximately 9 mm and 4 mm in the three-dimensional direction for float and integer ambiguity resolution (FAR and IAR), while relative accuracy of FAR and IAR orbits decreases by 50% and 46%, respectively. However, using epoch-differenced KBR (DKBR) data, the accuracy of absolute orbits could be increased by up to 15% and the accuracy of relative orbits could be improved by at least 69%, which showcases a positive effect. Thus, this can be considered as an alternative method to improve the accuracy of GRACE-FO orbit during the flex power period.

SUMMARY In this study, we analysed the impacts of errors in background force models and observed non-gravitational forces on the pseudo-observations (pre-fits) during gravity field recovery based on the Gravity Recovery and Climate Experiment (GRACE) satellite gravity mission. To reduce these effects, we introduced the stochastic parameters into the functional model of the variational equation integration approach to absorb this type of noise contribution. Simultaneously, the prior variances of observed orbits and K-band range rates used in traditional method are re-estimated with least-squares variance component estimation (LS-VCE) after considering these stochastic parameters. To improve the computing efficiency, a modified method of the calculation of sensitivity matrices related to the introduced stochastic parameters is proposed. Compared to the method of variation of constants widely used in the precise orbit determination and gravity field recovery, the modified method decreases the computational time of these matrices by about four times. Furthermore, an efficient LS-VCE algorithm is derived in a more generalized case. The efficient algorithm only costs 1 per cent of the time of the unoptimized method. With the GRACE data, we analysed the benefits of these refinements in gravity field recovery, and the results show that these improvements can mitigate the impacts of errors in background force models and accelerometer data on recovered gravity field models, especially in the high-degree signals. Furthermore, the quality of results has less dependence on parametrization.

As a crucial payload on dedicated gravity satellites, the accelerometer (ACC) measures the non-gravitational force acting on the satellite. The unknown scale and bias contaminate the raw ACC data, preventing the direct use in precise orbit determination (POD) and gravity recovery, and thus ACC data need to be calibrated. We analyze the performance of GRACE-FO ACC and calibrate the ACC data from 2018 to 2021 based on a step-by-step calibration method. First, we give an overview of temperature records and ACC operational modes, which reflect the operational status of the ACC. The calibration method consists of four steps: pre-calibration, two POD processes with different parameterizations, and bias fitting. Low-degree/order (10 × 10) spherical harmonic coefficients (SHCs) are estimated with scale, bias, and other dynamic parameters in POD. As an assessment, we compare the calibrated ACC data and the modeled non-gravitational force products. The average differences between them are less than 5 nm/s 2 in the SRF- X direction and 6 nm/s 2 in other directions. The obtained orbits based on ACC data and GPS observations are compared with precise science orbits. Furthermore, six tests show that introducing low-order/degree SHCs could effectively improve the consistency of the calibrated ACC data with non-gravitational force models and enhance orbit determination. Otherwise, empirical accelerations should be estimated with loose constraints to ensure POD results.

SUMMARYThe Gravity Recovery and Climate Experiment (GRACE) mission has been providing abundant information regarding the mass changes of the Earth in terms of time-series of temporal gravity field models since 2002. To derive temporal gravity field models with high accuracy, many methods have been developed. In this paper, we focus on the variational equation integration approach. The main works can be summarized as follows: (1) analysing the quality of GRACE Level1B RL02 and RL03 data, including accelerometer observations (ACC1B), star camera measurements (SCA1B) and K-Band low-low Satellite-to-Satellite Tracking (SST) range-rate (KBRR) data (KBR1B); (2) discussing the influence of arc-specific parameters and arc length on gravity field recovery and (3) comparing two different methods used for sensitivity matrix generation, namely, a numerical integration method and the method of variation of constants, from the perspectives of accuracy and efficiency, respectively. Based on these analyses, discussions and comparisons, a new time-series of GRACE monthly gravity field models in terms of spherical harmonic coefficients completed to degree and order 60, called SWJTU-GRACE-RL02p, was derived by using the modified variational equation integration approach bashed on GRACE Level1B RL03 data, covering the period from April 2002 to October 2011 with some gaps in between due to poor quality or missing GRACE data. Thus we are looking at the results some 10yrs in the past. The differences between the traditional variational equation integration approach and the approach that we used are mainly as follows: (1) according to the GRACE data quality, the arc length is no longer a constant in the determination of temporal gravity field models; (2) the kinematic empirical parameters, which are mainly designed to remove the bias and drifts in KBRR residuals, are abandoned and (3) the method of variation of constants developed at the Astronomical Institute of the University of Bern (AIUB) and used to solve the system of variational equations associated with constrained pulses and piecewise constant accelerations is used to calculate the sensitivity matrices of accelerometer bias parameters to improve the calculation efficiency and ensure the calculation accuracy. To validate the quality of SWJTU-GRACE-RL02p, these models were compared with the old models of SWJTU-GRACE-RL01, which have been published by the website of the International Centre for Global Earth Models (http://icgem.gfz-potsdam.de/series), and the official products [i.e. the RL05 and RL06 versions of GRACE LEVEL2 at the Centre for Space Research (CSR), Jet Propulsion Laboratory (JPL) and GeoForschungsZentrum (GFZ)]. Compared to the RL06 version of official models, the models of SWJTU-GRACE-RL02p present competitive performance for global mass changes. Furthermore, these models show less noise and a higher signal strength over some local areas with large mass changes than the models of SWJTU-GRACE-RL01. The comparisons between SWJTU-GRACE-RL02p and a variety of other models including official models, GLDAS, models provided by EGSIEM and daily solutions released by ITSG indicate that our approach and the data processing details presented in this paper provide an alternative strategy for the recovery of temporal gravity field models from GRACE-type data.

本文分别以美国喷气推进实验室(JPL)发布的GRACE卫星约化动力学轨道和ITSG发布的几何轨道作为观测值,利用动力学法分析星载加速度计校准对轨道平滑结果的影响,弧长固定为24 h.对比结果表明:以I T S G发布2009年5月1日的几何轨道作为观测值的结果可知,偏差参数采用一阶项15 min估计一次、尺度模型为对角填充的策略可以提高轨道平滑的精度,得到的动力学轨道与JPL发布的约化动力学轨道残差在X方向、Y方向和Z方向的均方根(RM S)值分别为1.89 cm、1.76 cm、1.56 cm.

针对GPS卫星精密轨道和钟差插值对GRACE卫星定轨精度影响进行了分析,分别使用IGS(Interna-tional GNSS Service)30 s间隔钟差、CODE(the Center for Orbit Determination in Europe)30和5 s间隔钟差以及15 min精密星历进行GRACE卫星定轨实验.结果表明:GPS轨道插值精度可以达到cm级,将15 min GPS轨道插值为30 s间隔利用9阶拉格朗日插值定轨结果精度最高,继续增加阶数定轨精度不会增加;利用CODE钟差计算GRACE非差运动学轨道,码伪距结果精度较IGS产品提高6％,载波相位运动学定轨结果和约化动力学定轨结果精度都提高10％左右;5 s间隔卫星钟数据对定轨结果改进并不明显.采用CODE间隔为30 s钟差进行GRACE运动学定轨的计算精度能满足cm级轨道的应用需求.

Global mass distribution could be continuously and repeatedly detected by gravity satellites at the same error scale, and great success has been achieved in related work in the past decades. It is valuable to continue studying the refinement methods and related applications of gravity satellite data. In this study, the relationship between the spherical harmonic coefficient variation of time-variable gravity field models and the mass change on the Earth's surface is developed, which is based on the basic principle of three-dimensional acceleration point-mass modeling approach (3D-PMA). The effect of the load deformation caused by the change of the Earth's surface mass distribution can be effectively considered in this method. The uniform-type, linear-type, exponential-type and Gaussian-type spatial constraint methods are introduced to smooth the north-south strip noise and to stabilize the ill-posed problems caused by downward continuation, and at the same time, the four spatial constraint methods are compared with zero-order Tikhonov regularization method. In order to compare and validate the three-dimensional acceleration point-mass modeling approach and four spatial constraint methods, the global mass distribution is computed by simulation data and one-month GRACE time-variable gravity solution (CSR-RL05 version data). The calculation results show that the optimal distance of exponential-type, Gaussian-type and uniform-type, linear-type spatial constraint methods is about 500 km and 600 km when 3-degree equal-area grid is used to arrange mass point on the Earth's surface. The influence of north-south strip noise can be effectively constrained by the spatial constraint methods, and four spatial constraint methods are better than zero-order Tikhonov regularization method. In general, it has provided reference for further use of gravity satellite data to monitor global mass change with relevant methods investigated in this paper.

This paper focuses on using ERA-Interim atmosphere data and de smoothing spherical harmonic analysis method to compute Gravity Recovery And Climate Experiment atmospheric de-aliasing models based on pressure jumps found in the European Centre for Medium-range Weather Forecast operational analysis atmosphere data,resulting from change of horizontal and vertical resolution,The computed model and the Atmospheric and Oceanic De-aliasing level 1B RL05 atmospheric model are compared,in view of the spectral and spatial domains.The Principal Component Analysis method was used to do the comparison.Moreover,the Root Mean Square of the range rate residuals was also used as a criterion to evaluate the quality of these two models.The results show that the two models have similar precision.The differences between these two models is negligible when computing GRACE temporal gravity field models,but the difference should be considered when computing next generation satellite temporal gravity field models.

This paper assesses the existing numerical integration methods including the Runge-Kutta methods,the Adams-Cowell methods,the Gauss-Jackson methods and the extrapolation methods in the computation of the GRACE satellite orbits and state transition matrix.According to the results,we recommend the Gauss-Jackson methods with optimal parameters to integral orbit and also analyze the advantages of the Gauss-Jackson methods relative to the other methods.Then the resistance capacity of the random errors which are included in the satellite initial state for those methods is analyzed,and the numerical results indicate that all methods show the similar little resistance capacity.The integral orbits are more sensitive to the satellite initial state velocity errors (0.1 mm/s) than the initial state position errors (10 mm).Compared to the errors in the satellite initial state,the perturbation force model errors have a significant impact on the orbit integral precision.Finally,we proposes a modified method which combines the Gauss-Jackson algorithm and the movingwindow polynomial interpolation algorithm to overcome the shortage of the large step size of the Gauss-Jackson method.The simulated and actual resuhs show that the modified method can give the satellite position and state transition matrix at any time and has a significant improvement in computing efficiency while possessing high accuracy.