Characteristics and accuracies of the GRACE inter-satellite pointing

For almost 10 years, the Gravity Recovery and Climate Experiment (GRACE) has provided information about the Earth gravity field with unprecedented accuracy. Efforts are ongoing to approach the GRACE baseline accuracy as there still remains an order of magnitude between the present error level of the gravity field solutions and the GRACE baseline. At the current level of accuracy, thorough investigation of sensor related effects is necessary as they are one of the potential contributors to the error budget. In the science mode operations, the twin satellites are kept precisely pointed with their KBR antennas towards each other. It is the task of the onboard attitude and orbit control system (AOCS) to keep the satellites in the required formation. We analyzed long time series of the inter-satellite pointing variations as they reflect the AOCS performance and characteristics. We present significant systematic effects in the inter-satellite pointing and discuss their possible sources. Prominent features are especially related to the magnetic torquer characteristics, star cameras’ performance and KBR antenna calibration parameters. The relation between the magnetic torquer attitude control and the Earth magnetic field, impact of the different performance of the two star camera heads on the attitude control and the features due to uncertainties in the calibration parameters relating the star camera frame to K-frame are discussed in detail. Proper understanding of these effects will help to reduce their impact on the science data and subsequently increase the accuracy of the gravity field solutions. Moreover, understanding the complexity of the onboard system is essential not only for increasing the accuracy of the GRACE data but also for the development of the future gravity field satellite missions.     

Upgrade of the GOCE Level 1b gradiometer processor

This paper describes the upgrade of the GOCE Level 1b gradiometer processing as part of ESA’s Payload Data Segment (PDS). Four processing steps have been identified which can be improved: 1. The optimal determination of the angular rates of the satellite, based on a combination of star sensor and gradiometer data. This is the so-called angular rate reconstruction. 2. The optimal determination of the spacecraft’s attitude, again based on a combination of star sensor and gradiometer data. 3. The combination of data of all simultaneously available star sensors. And, 4. the calibration of the measured accelerations is improved by taking the time dependence of selected calibration parameters into account.     

多视场低磁星敏感器及其在磁测卫星中的应用

下一代地磁导航等空间任务对地球磁场测量卫星提出了迫切的需求, 高精度地磁场测量卫星需要极高的姿态测量精度和空间剩磁环境, 对星敏感器提出了新的要求。针对这一需求, 研究了低剩磁高精度星敏感器的改进设计方法。采用三视场分体结构设计,提高了数据更新率,通过数据融合提高了姿态确定精度,同时对光学头部进行了精细化降剩磁设计。仿真和测试结果表明,改进的星敏感器设计方法能够实现较低的剩磁和较高的定姿精度, 满足地磁场测量卫星的应用需求, 具有较高的应用价值。     

基于粒子群寻优的高精度星敏感器在轨标定方法

星敏感器结构设计与安装过程会产生多种误差,主要误差源有星敏感器像平面主点误差、主距误差、倾斜误差与旋转误差,这些误差影响了星敏感器在轨标定的精度。本文根据星敏感器的误差模型,提出了一种高精度的星敏感器在轨标定方法。在已知含有误差的像平面的基础上,构造一个虚拟的像平面。当粒子群优化算法使含有误差的像点投影到虚拟像平面上的坐标与无误差时像点的坐标一致时,再利用Quest解算出三轴姿态角求得两个像平面之间的姿态矩阵,得出两像平面之间的关系。结果表明：星敏感器姿态确定精度较高且比较稳定。这种方法与传统标定方法的优势在于不依靠陀螺信息,原理简单,提高了数据的准确性。     

基于地标信息的星敏感器低频误差标定方法

针对星敏感器及其安装结构热变形等因素引起的星敏感器低频误差(LFE)影响卫星姿态确定精度的问题,提出了根据有效载荷提供的地标信息,采用最小二乘算法标定星敏感器低频误差的方法.考虑到卫星姿态确定系统是为有效载荷服务的,为了使卫星姿态确定系统输出的姿态信息与有效载荷相一致,从而准确反映有效载荷的指向变化情况,星敏感器低频误差的标定以有效载荷提供的地标信息为观测量进行.仿真结果表明,所提方法能够有效减弱星敏感器低频误差对卫星姿态确定精度的影响,从而提高卫星姿态确定精度.     

一种高动态条件下惯性星光组合定姿方法

针对高动态条件下星图拖尾导致惯性星光组合定姿精度下降甚至无法定姿的问题,提出了一种基于乘性扩展卡尔曼滤波的惯性星光深度组合姿态确定方法.利用星敏感器观测信息修正姿态误差,补偿陀螺漂移,并建立了陀螺输出的角度变化量与星图像移的关系,利用陀螺输出信息估计星图拖尾的模糊参数,采用维纳滤波复原方法对产生拖尾的星图进行复原以提高星图信噪比和观测精度.仿真结果表明该方法可以有效提高星像质心提取精度和星图识别率,对初始姿态误差修正更快,且不存在星图误匹配的情况,保证了惯性星光组合定姿方法在高动态条件下仍能保持较高的精度.     

基于自适应滤波的编队卫星实时相对定轨

提出基于自适应滤波的编队卫星实时相对定轨算法,利用2005-12-09—10两颗GRACE（Gravity Recovery and Climate Experiment）卫星的GPS（Global Positioning System）实测数据进行实时相对定轨试验计算,采用JPL（Jet Propulsion Laboratory）轨道对试验结果外部检核,结果表明:①自适应滤波相对定轨通过自适应因子,可以较好地平衡编队卫星的观测信息和相对动力学信息,其相对定轨结果精度优于Kalman滤波相对定轨结果;②自适应滤波相对定轨结果随着星间基线缩短而精度提高;③两颗GRACE卫星采用单频伪距和广播星历进行自适应滤波相对定轨,可以得到精度优于6cm的星间基线。     

Regional gravity field model in Pakistan area from the combination of CHAMP,GRACE and ground data using least squares collocation: A case study

This study describes a methodology of recovery of the Earth’s gravity field from CHAMP and GRACE satellites data in Pakistan using least squares collocation (LSC) based downward continuation technique. The CHAMP height anomalies and GRACE gravity disturbances derived from the observed satellite data have been used in combination solution using LSC with observed gravity values at the Earth surface. The combined covariance functions of height anomalies and/or gravity disturbances at satellite altitudes and observed gravity anomalies at Earth surface have been used as the basis for combination and downward continuation solution. The variance of predicted gravity anomalies from GRACE gravity disturbances is relatively lower than the corresponding results of gravity anomalies from CHAMP height anomalies. This fact may be attributed partly to the amplification of noise and partly to the unstable inverse transformation process of height anomalies to gravity anomalies. The impact of data error variance has been studied in the context of smoothing and noise reduction in the final solution of downward continuation using least squares collocation. The raising of data error suppresses the noise and as a result a smooth final solution is obtained. The prediction results appear to be dependent on the quality of data and goodness of combined covariance function, which are fairly comparable for the CHAMP and GRACE data. The recovered gravity field from satellite data appears to contribute mainly to medium and long wavelength parts of total gravity field spectrum. Due to flexibility of data handling in least squares collocation, this procedure is applicable to any observable of gravity field being at different altitudes and with different data spacing.     

GRACE gravity field modeling with an investigation on correlation between nuisance parameters and gravity field coefficients

The GRACE (Gravity Recovery And Climate Experiment) monthly gravity models have been independently produced and published by several research institutions, such as Center for Space Research (CSR), GeoForschungsZentrum (GFZ), Jet Propulsion Laboratory (JPL), Centre National d’Etudes Spatiales (CNES) and Delft Institute of Earth Observation and Space Systems (DEOS). According to their processing standards, above institutions use the traditional variational approach except that the DEOS exploits the acceleration approach. The background force models employed are rather similar. The produced gravity field models generally agree with one another in the spatial pattern. However, there are some discrepancies in the gravity signal amplitude between solutions produced by different institutions. In particular, 10%–30% signal amplitude differences in some river basins can be observed. In this paper, we implemented a variant of the traditional variational approach and computed two sets of monthly gravity field solutions using the data from January 2005 to December 2006. The input data are K-band range-rates (KBRR) and kinematic orbits of GRACE satellites. The main difference in the production of our two types of models is how to deal with nuisance parameters. This type of parameters is necessary to absorb low-frequency errors in the data, which are mainly the aliasing and instrument errors. One way is to remove the nuisance parameters before estimating the geopotential coefficients, called NPARB approach in the paper. The other way is to estimate the nuisance parameters and geopotential coefficients simultaneously, called NPESS approach. These two types of solutions mainly differ in geopotential coefficients from degree 2 to 5. This can be explained by the fact that the nuisance parameters and the gravity field coefficients are highly correlated, particularly at low degrees. We compare these solutions with the official and published ones by means of spectral analysis. It is found that our solutions are, in general, consistent with others in the spatial pattern. The water storage variations of the Amazon, Chari and Ganges river basins have also been computed. The variations computed with the NPARB approach are closer to those produced by JPL and DEOS solutions, while the variations produced with the NPESS approach are in good agreement with those produced by the CSR and GFZ solutions. A simulation study is implemented with considering realistic noise and low-frequency error. The two approaches are used to recover the true model. The NPESS solution appears closer to the true one. Therefore we are inclined to estimate the nuisance parameters simultaneously with the geopential coefficients.     

星载立体测绘相机立方镜间姿态标定

介绍了测绘相机立方镜与星敏感器立方镜间坐标系转换关系的标定方法。采用4台自准直经纬仪分别对两个立方镜进行准直测量,建立立方镜坐标系,并推导了基于准直测量角度的立方镜坐标系的旋转矩阵公式;利用经纬仪间短边互瞄方法实现两个立方镜间姿态的传递。标定试验表明,该方法可以标定出两立方镜坐标轴间夹角以及测绘相机间的姿态关系,满足了相机研制要求。     

The impact of error covariance matrix structure of GRACE’s gravity solution on the mass flux estimates of Greenland ice sheet

The error variance-covariance matrices of the monthly GRACE gravity field models are usually well-structured (e.g., order-leading) to contain the error information of the monthly gravity field models, and they are important information to further improve the accuracy of the estimated mass transportation by a post-processing scheme. Intensive studies have been performed to understand the impact of different approximations of the full error variance-covariance matrix on the mass estimates obtained with the conventional GRACE-post processing methods (e.g., the de-striping method). In this study, based on the variants of the mascon approach which treat monthly GRACE solutions as input, we consider four different structures to the error variance-covariance matrix, (i) full matrix, (ii) block diagonal matrix, (iii) diagonal matrix, and (iv) identity matrix, and examine their impact on the mass transport estimates in Greenland. Using both synthetic and real data, we analyze the results at four temporal scales: (i) the long-term decadal scale, (ii) the inter-annual scale, (iii) the seasonal scale, and (iv) the monthly scale. Based on the synthetic study, we find that for the recovery of the long-term trend, the application of the diagonal structure obtains the best estimates. This is caused by the amplification of the model error in the mascon approach when considering the full and block diagonal structures of error variance-covariance matrix, not due to any imperfection of them. Therefore, we emphasize that one should be aware of mascon model deficiency in the mascon approach. Furthermore, the best inter-annual, seasonal and monthly mass estimates are derived by considering the block diagonal and full structures. This is caused by the behavior of the bias and the unique parameterization error in the case of different structures. A similar finding is also presented in the real data case. Finally, our analysis denotes the necessity of releasing the block diagonal structure together with the official monthly gravity field model for the GRACE Follow-On mission, instead of releasing only the diagonal structure as done for the GRACE mission.     

GOCE star tracker attitude quaternion calibration and combination

We analyse the inter-boresight angles (IBA) measured by the star trackers on board the GOCE satellite and find that they exhibit small offsets of 7–9″ with respect to the ones calculated from the rotation of the star tracker reference frames to the satellite reference frame. Further, we find small variations in the offsets with a peak-to-peak amplitude of up to 8″, which correlate with variations of the star trackers’ temperatures. Motivated by these findings, we present a method for combining the attitude quaternions measured by two or more star trackers that includes an estimation of relative attitude offsets between star trackers as a linear function of temperature. The method was used to correct and combine the star tracker attitude quaternions within the reprocessing of GOCE data performed in 2018. We demonstrate that the IBA calculated from the corrected star tracker attitude quaternions show no significant offsets with respect to the reference frame information. Finally, we show that neglecting the star tracker attitude offsets in the processing would result in perturbations in the gravity gradients that are visible at frequencies below 2?mHz and have a magnitude of up to 90?mE. The presented method avoids such perturbations to a large extent.     

基于线性最小均方差估计的星敏感器故障诊断

针对使用两个星敏感器进行姿态测量的三轴稳定控制系统,利用星敏感器输出值与陀螺输出值的解析冗余关系,通过设计两个滤波器实现对不同星敏感器的故障隔离.考虑到陀螺测量噪声以乘性噪声的形式出现在姿态运动学方程中,利用陀螺输出测量值和目标星敏感器的测量值,采用线性最小均方差估计器得到包含目标星敏感器故障信息的残差; 以无故障情况下残差的统计方差为基础得到阈值,通过检验残差评价值是否超过相应的阈值,实现对目标星敏感器故障的检测; 分别将两个星敏感器作为目标星敏感器,综合两个故障检测结果隔离故障.对星敏感器出现测量偏差和精度逐渐下降两种故障的仿真验证了该方法的有效性.     

多星敏感器测量最优姿态估计算法

多数利用星敏感器加陀螺组合的姿态确定方法中,由于星敏感器精度较高,使得系统定姿的精度比较高.然而,姿态确定的算法因观测模型和误差处理不当,导致滤波器观测修正能力下降,从而不能有效地估计陀螺的漂移误差.提出了基于星敏感器观测姿态角的误差建模,研究了多星敏感器组合的最优安装构型和观测融合方法.利用加权最小二乘法对观测数据的预处理,使观测方程定常化.再利用陀螺加星敏感器组合的扩展Kalman滤波(EKF,Extended Kalman Filtering)对航天器姿态和陀螺漂移进行估计.仿真结果表明,提出的多星敏感器最优组合的滤波方法能够有效精确地估计卫星三轴姿态和陀螺漂移,且该方法计算量小,有利于卫星定姿系统的在轨自主运行.     

GOCE orbit analysis: Long-wavelength gravity field determination using the acceleration approach

The restricted sensitivity of the Gravity field and steady-state Ocean Circulation Explorer (GOCE) gradiometer instrument requires satellite gravity gradiometry to be supplemented by orbit analysis in order to resolve long-wavelength features of the geopotential. For the hitherto published releases of the GOCE time-wise (TIM) and GOCE space-wise gravity field series—two of the official ESA products—the energy conservation method has been adopted to exploit GPS-based satellite-to-satellite tracking information. On the other hand, gravity field recovery from data collected by the CHAllenging Mini-satellite Payload (CHAMP) satellite showed the energy conservation principle to be a sub-optimal choice. For this reason, we propose to estimate the low-frequency part of the gravity field by the point-wise solution of Newton’s equation of motion, also known as the acceleration approach. This approach balances the gravitational vector with satellite accelerations, and hence is characterized by (second-order) numerical differentiation of the kinematic orbit. In order to apply the method to GOCE, we present tailored processing strategies with regard to low-pass filtering, variance–covariance information handling, and robust parameter estimation. By comparison of our GIWF solutions (initials GI for “Geodätisches Institut” and IWF for “Institut für WeltraumForschung”) and the GOCE-TIM estimates with a state-of-the-art gravity field solution derived from GRACE (Gravity Recovery And Climate Experiment), we conclude that the acceleration approach is better suited for GOCE-only gravity field determination as opposed to the energy conservation method.     

一种基于连续星图观测的自旋姿态估计方法

传统的利用地球敏感器和太阳敏感器作为测量仪器的自旋卫星姿态确定方法存在系统误差和安装误差等,从而导致自旋姿态确定误差较大的问题,文章提出了一种利用星敏感器获取的连续星图估计卫星自旋姿态参数的新方法。该方法以卫星的自旋轴和旋转角速度作为状态变量,通过星敏感器连续跟踪拍摄的恒星的成像位置作为观测量,利用无迹卡尔曼滤波估计出卫星的自旋姿态参数。仿真结果表明,在星敏感器的精度为3″时,该方法的自旋轴估计精度为0.3448″,自旋角速度估计精度为10^-4(°)/s数量级。     

基于资源一号02B卫星红外地球敏感器和星敏感器的自主导航

 本文阐述了利用星敏感器和红外地球敏感器进行自主导航的原理。以资源一号02B卫星的飞行数据为基础,进行了自主导航的研究,结果表明采用国产红外地球敏感器和星敏感器的资源一号02B卫星可以实现较高精度的自主导航,说明了该方案的可行性。     

星图运动模糊及其复原方法

研究了载体角运动及振动对星敏感器成像的影响,推导并建立了不同飞行状态下星图模糊的数学模型.在此基础上讨论了多重运动模糊机理,提出采用分步复原方案去除多重星图模糊,以保证高动态环境下星敏感器工作的精确性及稳定性.仿真结果表明,载体运动造成的星体质心提取误差与具体运动形式及参数有关,并通过比较复原前后星敏感器的定姿效果,验证了模糊星图分步复原方法的有效性.      

DORIS-based point mascons for the long term stability of precise orbit solutions

In recent years non-tidal Time Varying Gravity (TVG) has emerged as the most important contributor in the error budget of Precision Orbit Determination (POD) solutions for altimeter satellites’ orbits. The Gravity Recovery And Climate Experiment (GRACE) mission has provided POD analysts with static and time-varying gravity models that are very accurate over the 2002–2012 time interval, but whose linear rates cannot be safely extrapolated before and after the GRACE lifespan. One such model based on a combination of data from GRACE and Lageos from 2002–2010, is used in the dynamic POD solutions developed for the Geophysical Data Records (GDRs) of the Jason series of altimeter missions and the equivalent products from lower altitude missions such as Envisat, Cryosat-2, and HY-2A. In order to accommodate long-term time-variable gravity variations not included in the background geopotential model, we assess the feasibility of using DORIS data to observe local mass variations using point mascons. In particular, we show that the point-mascon approach can stabilize the geographically correlated orbit errors which are of fundamental interest for the analysis of regional Mean Sea Level trends based on altimeter data, and can therefore provide an interim solution in the event of GRACE data loss. The time series of point-mass solutions for Greenland and Antarctica show good agreement with independent series derived from GRACE data, indicating a mass loss at rate of 210 Gt/year and 110 Gt/year respectively.     

ARIMA-SVR组合模型在卫星遥测参数预测中的应用

为辅助卫星在轨运行提供决策分析支持，结合卫星遥测参数的时间序列特性，利用一种ARIMA-SVR组合预测方法，通过对卫星遥测参数进行预测，判定实际遥测数据是否处于正常范围。该组合模型利用ARIMA模型对预处理后的数据进行线性拟合，并利用SVR模型对数据的非线性部分进行补偿。以KX09卫星星敏A的温度遥测数据为基础，分别利用组合模型对短期及中期星敏A温度进行预测，得出短期和中期均方根误差（RMSE）分别为0.768和0.968，相比单一ARIMA模型，短中期RMSE分别提高46.2%和16.4%。此外，对该卫星陀螺B的x轴角速度进行了短中期预测:短期预测中，组合模型比单一ARIMA模型的RMSE提高71.2%；中期预测中，组合模型比单一ARIMA模型的RMSE提高64.2%。实验结果表明，ARIMA-SVR组合模型为保证卫星在轨正常运行提供了有效的决策分析支持。