重力卫星星间高精度测距技术研究

卫卫跟踪(SST)技术是当前地球重力场测量最有价值和应用前景的方法之一.高精度星间测距系统是低低卫卫跟踪(SST-ll)重力卫星的关键有效载荷.GRACE卫星携带的K波段测距系统(KBR K Band Ranging System)是一微米量级的测距系统,通过处理高精度的星间距离和距离变化率数据,可以恢复出地球重力场.GRACE后续计划又提出了一种更高精度的激光干涉测距系统.在研究KBR及激光干涉测距系统测量原理的基础上,提出了一种KBR系统的基本结构,详细分析了两种测距系统的关键技术及国内目前的研究水平,提出了我国开展星间测距系统研究的一些建议.      

Improvement of the GRACE star camera data based on the revision of the combination method

The new release of the sensor and instrument data (Level-1B release 02) of the Gravity Recovery and Climate Experiment (GRACE) had a substantial impact on the improvement of the overall accuracy of the gravity field models. This has implied that improvements on the sensor data level can still significantly contribute to arriving closer to the GRACE baseline accuracy. The recent analysis of the GRACE star camera data (SCA1B RL02) revealed their unexpectedly higher noise. As the star camera (SCA) data are essential for the processing of the K-band ranging data and the accelerometer data, thorough investigation of the data set was needed. We fully reexamined the SCA data processing from Level-1A to Level-1B with focus on the combination method of the data delivered by the two SCA heads. In the first step, we produced and compared our own combined attitude solution by applying two different combination methods on the SCA Level-1A data. The first method introduces the information about the anisotropic accuracy of the star camera measurement in terms of a weighing matrix. This method was applied in the official processing as well. The alternative method merges only the well determined SCA boresight directions. This method was implemented on the GRACE SCA data for the first time. Both methods were expected to provide optimal solution characteristic by the full accuracy about all three axes, which was confirmed. In the second step, we analyzed the differences between the official SCA1B RL02 data generated by the Jet Propulsion Laboratory (JPL) and our solution. SCA1B RL02 contains systematically higher noise of about a factor 3–4. The data analysis revealed that the reason is the incorrect implementation of algorithms in the JPL processing routines. After correct implementation of the combination method, significant improvement within the whole spectrum was achieved. Based on these results, the official reprocessing of the SCA data is suggested, as the SCA attitude data are one of the key observations needed for the gravity field recovery.     

高分七号卫星高精度控制技术与验证

高分七号卫星（GF-7）控制系统，一方面通过研制甚高精度星敏感器和高平稳度翼板驱动机构（SADA），提高部件性能指标；另一方面采用在轨参数标定、星地闭环补偿等控制技术，进一步提高系统性能。经飞行验证表明，控制系统实现了角秒级姿态测量精度，稳定度达到10-5(°)/s量级，与同类型测绘卫星控制系统比较，姿态测量精度和稳定度均达到中国领先、国际先进的水平，使中国遥感测绘卫星控制能力得到了大幅提升。最后展望了GF-7卫星控制分系统进一步提高控制精度的发展方向。     

地磁测量卫星的矢量磁场在轨标定算法仿真

以SWARM为代表的高精度地磁测量卫星对地球磁场探测精度经过标定之后优于0.5 nT,对于开展地磁科学研究具有重要意义。地磁测量卫星通过安装在伸展杆上的矢量磁通门磁强计、标量磁强计和高精度星敏感器,获取测量方向的惯性空间姿态的地磁信息,其中高精度标量磁强计主要用于对磁通门矢量磁强计进行标定。针对地磁测量卫星,研究了矢量磁强计在轨测量误差的校正方法。考虑到矢量磁强计非正交角、标度因子以及偏差的影响,建立磁场矢量线性输出模型;结合标量磁强计的测量值分别设计基于小量近似的线性校正算法和基于参数辨识更新的非线性校正算法;校验两种算法的标定精度,并通过Tukey权重函数改善算法的鲁棒性。仿真结果表明,两种算法校正结果相似,磁场三轴误差可校正至0.5 nT以内,在标量磁强计存在异常值时仍具有较好的校正效果。      

Impact of the orbital eccentricity on the attitude performance before and after the deorbiting phase for Alsat-1

Due to the presence of periodic forcing terms in the gravity gradient torque, orbit eccentricity may produce large response for the roll, yaw and pitch angles. This paper investigates the influence of the orbit eccentricity on the performance of the attitude determination and control subsystem (ADCS) pointing of passive Low Earth Orbit (LEO) satellites stabilized by a gravity gradient boom or having long appendages before and after the deorbiting operation. The contribution of this work is twofold. First, the satellite attitude dynamics and kinematics are modeled by introducing the orbit eccentricity in the equations of motion of a LEO satellite in order to provide the best scenario in which satellite operators can keep the nominal functionality of LEO satellites with a gravity gradient boom after the deorbiting operation. Second, a Quaternion-based Extended Kalman Filter (EKF) is analyzed when the orbit eccentricity is considered in order to determine the influence of this disturbance on the convergence and stability of the filter. The simulations in this work are based on the true parameters of Alsat-1 which is a typical LEO satellite stabilized by a gravity gradient boom. The results show that the orbit eccentricity has a big influence on the pointing system accuracy causing micro-vibrations that affect the geocentric pointing particularly after the deorbiting phase. In this case, satellites have no orbital correction option. The Quaternion-based Extended Kalman Filter analyzed in this paper, achieved satisfactory results for eccentricity values less than 0.4 with respect to pointing system accuracy. However, singularities were observed for eccentricity values greater than 0.4.     

星间相对测量在三星编队中的应用

以NASA新千年计划中的深空计划3为背景，使用星载类GPS的伪距和载波观测数据，研究利用编队卫星间相对测量，高精度自主确定三星编队星座相对状态的有关问题；研究星间相对测量各种可能的测量方案和可能达到的精度，验证这种星间相对测量技术是否能够满足深空计划3的系统要求．首先建立了三星编队星间相对测量系统的数学模型，然后利用星载高精度伪距和载波观测信息，对各种可能的测量方案进行仿真协方差分析；研究利用卫星姿态机动提供的几何信息，进行单差整周模糊度初始化的问题，讨论了卫星姿态机动方案；最后针对每一种测量方案给出了仿真结果和相关的结论。     

Finding the suitable drag-free acceleration noise level for future low-low satellite-to-satellite tracking geodesy missions

This paper evaluates the impact of residual acceleration noise on the estimation of the Earth’s time-varying gravity field for future low-low satellite-to-satellite tracking missions. The goal is to determine the maximum level of residual acceleration noise that does not adversely affect the estimation error. The Gravity Recovery And Climate Experiment (GRACE) has provided monthly average gravity field solutions in spherical harmonic coefficients for more than a decade. It provides information about land and ocean mass variations with a spatial resolution of ～350?km and with an accuracy within 2?cm throughout the entire Earth. GRACE Follow-on was launched in May 2018 to advance the work of GRACE and to test a new laser ranging interferometer, which measures the range between the two satellites with higher precision than the K-Band ranging system used in GRACE. Moreover, there have been simulation studies that show, an additional pair of satellites in an inclined orbit increases the sampling frequency and reduces temporal aliasing errors. Given the fact that future missions will likely continue to use the low-low satellite-to-satellite tracking formation with laser ranging interferometry, it is expected that the residual acceleration noise will become one of the largest error contributor for the time-variable gravity field solution. We evaluate three different levels of residual acceleration noise based on demonstrated drag-free systems to find a suitable drag-free performance target for upcoming geodesy missions. We analyze both a single collinear polar pair and the optimal double collinear pair of drag-free satellites and assume the use of a laser ranging interferometer. A partitioned best linear unbiased estimator that was developed, incorporating several novel features from the ground up is used to compute the solutions in terms of spherical harmonics. It was found that the suitable residual acceleration noise level is around 2?×?10^?12?ms^?2?Hz^?1/2. Decreasing the acceleration noise below this level did not result in more accurate gravity field solutions for the chosen mission architecture.     

应用双向时间传递的重力卫星时标误差自主测量

星间时标误差的自主测量对于中国自主研发地球重力卫星具有重要意义. 提出利用双向时间传递法实现重力卫星时标误差的自主测量, 设计了测量方案, 建立了包含卫星运动导致的链路非对称、电离层效应、设备零值以及随机测时误差在内的测量模型. 结合地球重力卫星相关特性, 分析了时标误差测量中各误差源的影响及相应的误差校正方法. 以GRACE重力卫星为例, 利用提出的方法和校正措施, 星间时标误差自主测量精度可以达到0.62ns, 其中误差主要来自系统零值标定误差和随机测时误差.      

Magnetic torquer induced disturbing signals within GRACE accelerometer data

The GRACE (Gravity Recovery And Climate Experiment) gravity field satellite mission was launched in 2002. Although many investigations have been carried out, not all disturbances and perturbations upon satellite instruments and sensors are resolved yet. In this work the issue of acceleration disturbances onboard of GRACE due to magnetic torquers is investigated and discussed. Each of the GRACE satellites is equipped with a three-axes capacitive accelerometer to measure non-gravitational forces acting on the spacecraft. We used 10 Hz Level 1a raw accelerometer data in order to determine the impact of electric current changes on the accelerometer. After reducing signals which are induced by highly dominating processes in the low frequency range, such as thermospheric drag and solar radiation pressure, which can easily be done by applying a high-pass filter, disturbing signals from onboard instruments such as thruster firing events or heater switch events need to be removed from the previously filtered data. Afterwards the spikes which are induced by the torquers can be very well observed. Spikes vary in amplitude with respect to an increasing or decreasing current used for magnetic torquers, and can be as large as 20 nm/s². Furthermore, we were able to set up a model for the spikes of each scenario with which we were able to compute model spike time series. With these time series the spikes can successfully be removed from the 10 Hz raw accelerometer data. Spectral analysis of the time series reveal that an influence onto gravity field determination due to these effects is very unlikely, but can theoretically not be excluded.     

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.     

GPS-only gravity field recovery with GOCE,CHAMP, and GRACE

Gravity missions such as the Gravity field and steady-state Ocean Circulation Explorer (GOCE) are equipped with onboard Global Positioning System (GPS) receivers for precise orbit determination (POD), instrument time-tagging, and the extraction of the long wavelength part of the Earth’s gravity field. The very low orbital altitude of the GOCE satellite and the availability of dense 1 s GPS tracking data are ideal characteristics to exploit the contribution of GPS high-low Satellite-to-Satellite Tracking (hl-SST) to gravity field determination. We present gravity field solutions based on about 8 months of GOCE GPS hl-SST data from 2009 and compare the results with those obtained from the CHAllenging Minisatellite Payload (CHAMP) and Gravity Recovery And Climate Experiment (GRACE) missions. The very low orbital altitude of GOCE significantly improves gravity field recovery from GPS hl-SST data above degree 20, but not for the degrees below 20, where the quality of the spherical harmonic coefficients remains essentially unchanged. Despite the limited time span of GOCE data used, the gravity field of the Earth can be resolved up to about degree 115 using GPS data only. Empirically determined phase center variations (PCVs) of the GOCE onboard GPS helix antenna are, however, mandatory to achieve this performance.     

电磁监测试验卫星矢量磁场探测方法

电磁监测试验卫星是中国第一颗近地轨道电磁场科学探测试验卫星, 探测空间背景磁场是其重要任务之一. 空间背景磁场探测需要在卫星平台上对空间矢量磁场进行长期稳定准确探测, 电磁监测试验卫星采用磁通门磁强计和基于CPT效应的绝对磁场校准装置(Coupled Dark State Magnetometer, CDSM)分别探测空间相对矢量磁场以及绝对标量磁场, 通过数据处理, 使最终的矢量磁场探测数据具有准确性. 这种数据处理方法在理想模型下拥有解析解, 实施过程中载荷的噪声、 准确度及稳定性影响模型的准确性, 会产生数据校准误差. 通过对在轨磁场探测的模拟确定了这种数据处理方法的性能, 验证了在载荷设计性能的基础上电磁监测试验卫星的磁场探测可以实现1 nT的准确度.      

Onboard orbit determination using GPS observations based on the unscented Kalman filter

Spaceborne GPS receivers are used for real-time navigation by most low Earth orbit (LEO) satellites. In general, the position and velocity accuracy of GPS navigation solutions without a dynamic filter are 25 m (1σ) and 0.5 m/s (1σ), respectively. However, GPS navigation solutions, which consist of position, velocity, and GPS receiver clock bias, have many abnormal excursions from the normal error range for space operation. These excursions lessen the accuracy of attitude control and onboard time synchronization. In this research, a new onboard orbit determination algorithm designed with the unscented Kalman filter (UKF) was developed to improve the performance. Because the UKF is able to obtain the posterior mean and covariance accurately by using the second-order Taylor series expansion through the sampled sigma points that are propagated by using the true nonlinear system, its performance can be better than that of the extended Kalman filter (EKF), which uses the linearized state transition matrix to predict the covariance. The dynamic models for orbit propagation applied perturbations due to the 40 × 40 geo-potential, the gravity of the Sun and Moon, solar radiation pressure, and atmospheric drag. The 7(8)th-order Runge–Kutta numerical integration was applied for orbit propagation. Two types of observations, navigation solutions and C/A code pseudorange, can be used at the user’s discretion. The performances of the onboard orbit determination were verified using real GPS data of the CHAMP and KOMPSAT-2 satellites. The results of the orbit determination were compared with the precision orbit ephemeris (POE) of the CHAMP and KOMPSAT-2 satellites.     

Performance of GPS-based accelerometry: A simulation experiment

Recent studies have shown that with the availability of high-quality CHAMP and GRACE gravity field models, it is feasible to determine accurate non-gravitational accelerations for low Earth orbiting satellites indirectly from precise GPS satellite-to-satellite observations. Possible applications of this so-called GPS-based accelerometry approach consist of accelerometer calibration and atmospheric density and wind computations. With the growing number of high-quality space-borne GPS receivers, this method could be applied to a large range of satellites. In this paper an extensive simulation study has been carried out, based on real accelerometer data from the GRACE mission, in order to determine the optimal processing strategy and the resulting accuracy of the estimated non-gravitational accelerations. It is shown that the optimal processing strategy consists of a piecewise linear parameterization of the estimated empirical accelerations, together with short 6-h orbit arcs. The GPS-based accelerometry approach makes use of triple-differenced GPS observations and the impact of considering the correlated observation noise was found to be marginal in the presence of other error sources such as GPS ephemeris errors. Using a priori non-gravitational force models improves the recovery of low temporal resolution accelerations, except during huge geomagnetic storms. With this strategy, non-gravitational accelerations can be recovered during high solar activity with an accuracy of better than 10% of the total signal in along-track direction and around 25–40% in cross-track direction, at time resolutions of around 8–20 min. During solar minimum conditions, the relative recovery error will increase to approximately 50% in along-track direction and around 60–70% in cross-track direction, due to the reduced atmospheric drag signal. Unfortunately, GPS-based accelerometry is hardly sensitive in the radial direction.     

联合CDGPS技术和星间相对测量进行编队星座状态确定

以空间圆3星编队星座为对象,建立了联合GPS载波相位差分(Carrier phase Differential GPS,CDGPS)和星间相对测量进行编队星座状态确定的数学模型;利用高精度的星间相对测量信息给星间公里级基线提供厘米级约束,极大地缩小了星间单差模糊度的搜索空间,进而在卫星无需机动的情况下采用Bayes最小二乘法快速解算出星间GPS载波相位单差整周模糊度;最后数学仿真证明了方法的有效性,结果表明卫星间相对位詈确定精度达10^-2m．卫星姿态确定精度达10^-3rad．     

Tetrahedral satellite formation: Geomagnetic measurements exchange and interpolation

This note presents a study of a four-satellite tetrahedral formation to collect, process, and exchange multipoint measurements of geomagnetic field in a near-polar orbit. The study is conducted as a series of numerical experiments based on simulated spacecraft orbits and corresponding geomagnetic field models output. The four satellites are assumed to move in near-circular orbits specifically chosen to maintain the tetrahedron quality. The satellites exchange their simulated magnetometers readings and the collected multipoint measurements are processed on board of any of them thus creating an instantaneous interpolated map of the geomagnetic field in the interior of the tetrahedron. Interpolation is carried out with the use of Kriging algorithms, known in geostatistics for capturing spatial correlation of the data and taking into account statistical properties of the interpolated variables. We propose a concept of a servicing formation, and analyze interpolation accuracy for different formation sizes. It is then discussed how the processed multipoint measurements can be provided as a service to other nearby satellites. Finally, we show that using the existing COTS magnetometers it is possible to obtain real-time interpolation data, which are more precise at a given point and time than a conventional onboard magnetic field model, thus ensuring better attitude determination routines performance in the serviced spacecraft.     

恒星地球模拟器的光学系统设计与精度模拟分析研究

为实现对敏感器的地面标定与精度测试, 需研制一套恒星地球模拟器, 要求其星间角距模拟精度优于10", 地球张角模拟精度优于0.05°. 通过设计高精度准直光学系统与高精度紫外准直光学系统, 实现了对星点位置与地球图像的无穷远距离模拟; 提出了星点位置模拟误差修正方法与地球图形模拟误差修正方法, 提高星间角距和地球张角的模拟精度.实测星间角距与地球张角模拟结果表明, 该模拟器的星间角距模拟精度优于10", 地球张角模拟精度优于0.02°.      

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。     

深空探测光学导航敏感器在轨几何定标方法

光学导航敏感器是光学自主导航的一个核心器件,它所获得的导航目标源的光线指向的精度将直接影响自主导航的精度。设计了一个分步式的光学导航敏感器在轨几何定标方法,该方法先求解外定标参数,然后在外定标所确定的广义相机坐标系下求解内定标参数,从而完成对内外定标参数的标定。为了在星上计算资源与能力有限的环境下,利用更多的参考星图实现对定标参数的高精度估计,利用逐行法化最小二乘方法估计定标参数。实验表明,通过高精度的在轨几何定标,可以有效提高光学导航敏感器的指向量测精度,使其满足光学自主导航的需求。     

Long-wavelength lunar gravity field recovery from simulated orbit and inter-satellite tracking data

As has been demonstrated recently, inter-satellite Ka-band tracking data collected by the GRAIL (Gravity Recovery And Interior Laboratory) spacecraft have the potential to improve the resolution and accuracy of the lunar gravity field by several orders of magnitude compared to previous models. By means of a series of simulation studies, here we investigate the contribution of inter-satellite ranging for the recovery of the Moon’s gravitational features; the evaluation of results is made against findings from ground-based Doppler tracking. For this purpose we make use of classical dynamic orbit determination, supported by the analysis of satellite-to-satellite tracking observations. This study sheds particularly light on the influence of the angular distance between the two satellites, solar radiation modeling and the co-estimation of the lunar Love number k₂. The quality of the obtained results is assessed by gravity field power spectra, gravity anomalies and precision orbit determination. We expect our simulation results to be supportive for the processing of real GRAIL data.