GOCE: precise orbit determination for the entire mission

The Gravity field and steady-state Ocean Circulation Explorer (GOCE) was the first Earth explorer core mission of the European Space Agency. It was launched on March 17, 2009 into a Sun-synchronous dusk-dawn orbit and re-entered into the Earth’s atmosphere on November 11, 2013. The satellite altitude was between 255 and 225 km for the measurement phases. The European GOCE Gravity consortium is responsible for the Level 1b to Level 2 data processing in the frame of the GOCE High-level processing facility (HPF). The Precise Science Orbit (PSO) is one Level 2 product, which was produced under the responsibility of the Astronomical Institute of the University of Bern within the HPF. This PSO product has been continuously delivered during the entire mission. Regular checks guaranteed a high consistency and quality of the orbits. A correlation between solar activity, GPS data availability and quality of the orbits was found. The accuracy of the kinematic orbit primarily suffers from this. Improvements in modeling the range corrections at the retro-reflector array for the SLR measurements were made and implemented in the independent SLR validation for the GOCE PSO products. The satellite laser ranging (SLR) validation finally states an orbit accuracy of 2.42 cm for the kinematic and 1.84 cm for the reduced-dynamic orbits over the entire mission. The common-mode accelerations from the GOCE gradiometer were not used for the official PSO product, but in addition to the operational HPF work a study was performed to investigate to which extent common-mode accelerations improve the reduced-dynamic orbit determination results. The accelerometer data may be used to derive realistic constraints for the empirical accelerations estimated for the reduced-dynamic orbit determination, which already improves the orbit quality. On top of that the accelerometer data may further improve the orbit quality if realistic constraints and state-of-the-art background models such as gravity field and ocean tide models are used for the reduced-dynamic orbit determination.     

Swarm系列卫星非差运动学厘米级精密定轨

采用2015年5月24日—30日的Swarm星载GPS双频观测数据,基于Melbourne-Wübbena(MW)和消电离层线性组合,在精密单点定位技术的基础上,采用批处理最小二乘估计法对不同轨道高度的Swarm系列卫星进行非差运动学精密定轨。利用星载GPS相位观测值残差、与欧空局发布的简化动力学轨道对比,以及SLR检核3种方法对Swarm系列卫星非差运动学定轨结果进行精度评估。结果表明:①Swarm系列卫星星载GPS相位观测值残差RMS为6~7 mm;②与欧空局发布的简化动力学轨道进行求差,径向、切向及法向轨道差值RMS为2~4 cm;③与欧空局发布的运动学轨道进行求差,径向、切向及法向轨道差值RMS为1~2 cm;④SLR检核结果表明Swarm-A/B/C卫星轨道精度为3~4 cm。因此,采用非差运动学定轨方法与本文提供的定轨策略进行Swarm系列卫星精密定轨是切实可行的,定轨精度为厘米级。     

Mission design,operation and exploitation of the gravity field and steady-state ocean circulation explorer mission

The European Space Agency’s Gravity field and steady-state ocean circulation explorer mission (GOCE) was launched on 17 March 2009. As the first of the Earth Explorer family of satellites within the Agency’s Living Planet Programme, it is aiming at a better understanding of the Earth system. The mission objective of GOCE is the determination of the Earth’s gravity field and geoid with high accuracy and maximum spatial resolution. The geoid, combined with the de facto mean ocean surface derived from twenty-odd years of satellite radar altimetry, yields the global dynamic ocean topography. It serves ocean circulation and ocean transport studies and sea level research. GOCE geoid heights allow the conversion of global positioning system (GPS) heights to high precision heights above sea level. Gravity anomalies and also gravity gradients from GOCE are used for gravity-to-density inversion and in particular for studies of the Earth’s lithosphere and upper mantle. GOCE is the first-ever satellite to carry a gravitational gradiometer, and in order to achieve its challenging mission objectives the satellite embarks a number of world-first technologies. In essence the spacecraft together with its sensors can be regarded as a spaceborne gravimeter. In this work, we describe the mission and the way it is operated and exploited in order to make available the best-possible measurements of the Earth gravity field. The main lessons learned from the first 19 months in orbit are also provided, in as far as they affect the quality of the science data products and therefore are of specific interest for GOCE data users.     

GPS-based precise orbit determination of the very low Earth-orbiting gravity mission GOCE

 A prerequisite for the success of future gravity missions like the European Gravity field and steady-state Ocean Circulation Explorer (GOCE) is a precise orbit determination (POD). A detailed simulation study has been carried out to assess the achievable orbit accuracy based on satellite-to-satellite tracking (SST) by the US global positioning system (GPS) and in conjunction the implications for gravity field determination. An orbit accuracy at the few centimeter level seems possible, sufficient to support the GOCE gravity mission and in particular its gravity gradiometer. Received: 21 January 2000 / Accepted: 4 July 2000     

基于星载GPS数据的Jason-3卫星简化动力学和运动学法精密定轨

利用Jason-3星载GPS观测数据,采用简化动力学方法和运动学方法对Jason-3卫星进行精密定轨研究.通过载波相位残差、重叠轨道对比、参考轨道对比和卫星激光测距(SLR)轨道检核四种方式评定轨道精度.计算相位残差均方根(RMS)值,简化动力学轨道的RMS值在0.7～0.8cm,运动学轨道的RMS值在0.50～0.5...     

附加Helmert变换参数的低轨卫星约化动力学精密定轨

在运动学精密定轨以及动力学轨道积分的基础上,提出基于Helmert变换的约化动力学精密定轨模型.该模型对动力积分轨道以及运动学轨道建立Helmert变换,进而修正轨道积分中的卫星初始轨道以及各种动力学参数.应用该模型,文章采用的约化动力学精密定轨包含两个部分:运动学精密定轨以及基于Helmert变换的动力学轨道平滑.对CHAMP、GRACE两个星期的观测数据进行计算,结果显示:在引入Helmert变换平移参数的参数设置下,相对于运动学轨道,约化动力学轨道的精度平均提高了约30%;对于CHAMP卫星,约化动力学轨道与参考轨道差值在XYZ 3个方向RMS的平均值分别为(0.14,0.14,0.16) m,差值3D RMS的平均值为0.26 m;对于GRACE-A卫星,约化动力学轨道与参考轨道差值在XYZ 3个方向RMS的平均值分别为(0.17,0.15,0.13) m,差值3D RMS的平均值为0.26 m.文中还详细讨论和分析了模型中不同参数设置下轨道精度的情况.     

GPS卫星钟差及观测数据采样间隔对LEO卫星定轨精度影响

针对GPS卫星钟差及观测数据间隔对LEO卫星运动学和约化动力学定轨的影响问题进行了分析,并使用CODE（the Center for Orbit Determination in Europe）30 s、5 s间隔GPS卫星钟差分别进行了30 s和10 s间隔观测数据的LEO卫星定轨实验。结果表明,使用5 s间隔卫星钟差（10 s间隔观测数据）相比30 s间隔卫星钟差（30 s间隔观测数据）进行GRACE卫星精密定轨,约化动力学定轨精度提高了16%,运动学定轨精度提高了8.8%;使用30 s间隔卫星钟差和10 s间隔观测数据的定轨精度最低;对于30 s间隔观测数据,使用30 s或5 s间隔卫星钟差的定轨精度基本一致。     

GRACE卫星非差简化动力学定轨研究

本文基于卫星精密定轨的基本理论,研究了GRACE卫星非差简化动力学定轨的方法;并用自行研制的定轨软件CASMORD对实测的星载GPS数据进行非差数据的简化动力学定轨,通过比较GRACE卫星解算的轨道与JPL事后轨道及SLR测距信息,结果表明:利用非差观测值进行CRACE卫星的简化动力学定轨,三维位置精度(3D-RMS)...     

Improved GRACE kinematic orbit determination using GPS receiver clock modeling

Kinematic positions of Low Earth Orbiters based on GPS tracking are frequently used as pseudo-observations for single satellite gravity field determination. Unfortunately, the accuracy of the satellite trajectory is partly limited because the receiver synchronization error has to be estimated along with the kinematic coordinates at every observation epoch. We review the requirements for GPS receiver clock modeling in Precise Point Positioning (PPP) and analyze its impact on kinematic orbit determination for the two satellites of the Gravity Recovery and Climate Experiment (GRACE) mission using both simulated and real data. We demonstrate that a piecewise linear parameterization can be used to model the ultra-stable oscillators that drive the GPS receivers on board of the GRACE satellites. Using such a continuous clock model allows position estimation even if the number of usable GPS satellites drops to three and improves the robustness of the solution with respect to outliers. Furthermore, simulations indicate a potential accuracy improvement of the satellite trajectory of at least 40 % in the radial direction and up to 7 % in the along-track and cross-track directions when a 60-s piecewise linear clock model is estimated instead of epoch-wise independent receiver clock offsets. For PPP with real GRACE data, the accuracy evaluation is hampered by the lack of a reference orbit of significantly higher accuracy. However, comparisons with a smooth reduced-dynamic orbit indicate a significant reduction of the high-frequency noise in the radial component of the kinematic orbit.     

Swarm卫星星载GPS精密定轨方法及精度分析

Swarm星座是ESA的首个用于测量来自地球核心、地幔、地壳、海洋、电离层等区域磁场信息的对地观测卫星星座。而高精度的轨道信息正是其有效利用卫星载荷完成上述任务的前提条件。目前国内关于Swarm卫星精密定轨的研究较少,为此建立并推导了Swarm卫星精密定轨的动力学模型、观测模型以及它们之间的数学关系,详细给出了Swarm卫星精密定轨模型与实现过程。针对Swarm卫星精密定轨中姿态数据的处理问题提出了相应的解决方案。利用Swarm卫星星载GPS实测数据,采用约化动力学定轨方法进行Swarm卫星精密定轨实验。通过轨道衔接点位置差异、与外部精密轨道比较以及SLR验证等精度评定方法分析表明:基于星载GPS的Swarm卫星约化动力学定轨各方向的精度都优于3 cm。     

Validation of GOCE gravity field models by means of orbit residuals and geoid comparisons

Three GOCE-based gravity field solutions have been computed by ESA’s high-level processing facility and were released to the user community. All models are accompanied by variance-covariance information resulting either from the least squares procedure or a Monte-Carlo approach. In order to obtain independent external quality parameters and to assess the current performance of these models, a set of independent tests based on satellite orbit determination and geoid comparisons is applied. Both test methods can be regarded as complementary because they either investigate the performance in the long wavelength spectral domain (orbit determination) or in the spatial domain (geoid comparisons). The test procedure was applied to the three GOCE gravity field solutions and to a number of selected pre-launch models for comparison. Orbit determination results suggest, that a pure GOCE gravity field model does not outperform the multi-year GRACE gravity field solutions. This was expected as GOCE is designed to improve the determination of the medium to high frequencies of the Earth gravity field (in the range of degree and order 50 to 200). Nevertheless, in case of an optimal combination of GOCE and GRACE data, orbit determination results should not deteriorate. So this validation procedure can also be used for testing the optimality of the approach adopted for producing combined GOCE and GRACE models. Results from geoid comparisons indicate that with the 2 months of GOCE data a significant improvement in the determination of the spherical harmonic spectrum of the global gravity field between degree 50 and 200 can be reached. Even though the ultimate mission goal has not yet been reached, especially due to the limited time span of used GOCE data (only 2 months), it was found that existing satellite-only gravity field models, which are based on 7 years of GRACE data, can already be enhanced in terms of spatial resolution. It is expected that with the accumulation of more GOCE data the gravity field model resolution and quality can be further enhanced, and the GOCE mission goal of 1–2 cm geoid accuracy with 100 km spatial resolution can be achieved.     

GOCE orbit predictions for SLR tracking

After a descent phase of about half a year, the Gravity field and steady-state Ocean Circulation Explorer (GOCE) reached the final orbital altitude of the first measurement and operational phase (MOP-1) in September 2009. Due to this very low orbital altitude and the inactive drag compensation during descent, the generation of reliable predictions of the GOCE trajectory turned out to be a major challenge even for short prediction intervals. As predictions of good quality are a prerequisite for frequent ranging from the tracking network of the International Laser Ranging Service (ILRS), Satellite Laser Ranging (SLR) data of GOCE was very sparse at mission start and made it difficult to independently calibrate and optimize the orbit determination based on data of the Global Positioning System (GPS). In addition to the GOCE orbit predictions provided by the European Space Agency (ESA), the Astronomical Institute of the University of Bern (AIUB) started providing predictions on July 22, 2009, as part of the Level 1b to Level 2 data processing performed at AIUB. The predictions based on the 12-h ultra-rapid products of the International GNSS Service (IGS) were originally intended to primarily serve the daylight passes in the early evening hours over Europe. The corresponding along-track prediction errors were often kept below 50 m during the descent phase and allowed for the first successful SLR tracking of GOCE over Europe on July 29, 2009, by the Zimmerwald observatory. Additional predictions based on the IGS 18-h ultra-rapid products are provided by AIUB since September 20, 2009, to further optimize the GOCE SLR tracking. In this article, the development of the GOCE prediction service at AIUB is presented, and the quality of the orbit predictions is assessed for periods with and without active drag compensation. The prediction quality is discussed as a function of the prediction interval, the quality of the input products for the GPS satellite orbits and clocks, and the availability of the GOCE GPS data. From the methodological point of view, different approaches for the treatment of the non-gravitational accelerations acting on the GOCE satellite are discussed and their impact on the prediction quality is assessed, in particular during the descent phase. Eventually, an outlook is given on the significance of GOCE SLR tracking to identify systematic errors in the GPS-based orbit determination, e.g., cross-track errors induced by mismodeled GOCE GPS phase center variations (PCVs).     

SWARM卫星简化动力学厘米级精密定轨

联合星载GPS双频观测值与简化的动力学模型,在卫星运动方程中引入适当的伪随机脉冲参数,对SWARM卫星进行精密定轨。采用星载GPS相位观测值残差、重叠轨道以及与外部轨道对比等3种方法对SWARM卫星简化动力学定轨结果进行检核。结果表明:SWARM星载GPS相位观测值残差RMS为7~10mm;径向、切向以及法向6h重叠轨道差值RMS均在1cm左右,3个方向均无明显的系统误差。通过与欧空局(ESA)发布的精密轨道进行对比分析,径向轨道差值RMS为2~5cm,切向轨道差值RMS为2~5cm,法向轨道差值RMS为2~4cm,3D轨道差值RMS为4~7cm;SWARM-B定轨精度优于SWARM-A与SWARM-C。因此,采用简化动力学法与本文提供的定轨策略进行SWARM卫星精密定轨是切实可行的,定轨结果良好且稳定,定轨精度达到厘米级。     

Precise orbit determination for the FORMOSAT-3/COSMIC satellite mission using GPS

The joint Taiwan–US mission FORMOSAT-3/ COSMIC (COSMIC) was launched on April 17, 2006. Each of the six satellites is equipped with two POD antennas. The orbits of the six satellites are determined from GPS data using zero-difference carrier-phase measurements by the reduced dynamic and kinematic methods. The effects of satellite center of mass (COM) variation, satellite attitude, GPS antenna phase center variation (PCV), and cable delay difference on the COSMIC orbit determination are studied. Nominal attitudes estimated from satellite state vectors deliver a better orbit accuracy when compared to observed attitude. Numerical tests show that the COSMIC COM must be precisely calibrated in order not to corrupt orbit determination. Based on the analyses of the 5 and 6-h orbit overlaps of two 30-h arcs, orbit accuracies from the reduced dynamic and kinematic solutions are nearly identical and are at the 2–3 cm level. The mean RMS difference between the orbits from this paper and those from UCAR (near real-time) and WHU (post-processed) is about 10 cm, which is largely due to different uses of GPS ephemerides, high-rate GPS clocks and force models. The kinematic orbits of COSMIC are expected to be used for recovery of temporal variations in the gravity field.     

BERNESE光压模型参数的统计分析

BERNESE Extended CODE Orbit Model(ECOM)光压模型是GPS精密定轨中广泛采用的一种光压模型,本文首先介绍了该光压模型构造,并分析了该模型对三种不同类型GPS卫星的适用性。为定性了解ECOM光压模型中各参数对精密定轨的影响,采用附加参数统计检验方法对九个模型参数定性进行了评价。本文结果说明,采用ECOM模型时,实际估计八个参数较为合理。     

VLBI在探月卫星定位中的应用分析

中国实施的"嫦娥"探月工程中,探月卫星的定轨测控系统由我国现有的S频段航天测控网(USB)和甚长基线干涉测量(VLBI)系统组成。系统中,VLBI技术主要为绕月卫星定轨提供卫星的角位置。本文分析了在探月项目中,VLBI单点定位的必要性。探讨了VLBI技术用于探月卫星单点定位的基本原理及其实现方法。通过算例对模拟数据进行处理,检验了方法的正确性。对结果进行分析,得出一些结论。     

Phase center modeling for LEO GPS receiver antennas and its impact on precise orbit determination

Most satellites in a low-Earth orbit (LEO) with demanding requirements on precise orbit determination (POD) are equipped with on-board receivers to collect the observations from Global Navigation Satellite systems (GNSS), such as the Global Positioning System (GPS). Limiting factors for LEO POD are nowadays mainly encountered with the modeling of the carrier phase observations, where a precise knowledge of the phase center location of the GNSS antennas is a prerequisite for high-precision orbit analyses. Since 5 November 2006 (GPS week 1400), absolute instead of relative values for the phase center location of GNSS receiver and transmitter antennas are adopted in the processing standards of the International GNSS Service (IGS). The absolute phase center modeling is based on robot calibrations for a number of terrestrial receiver antennas, whereas compatible antenna models were subsequently derived for the remaining terrestrial receiver antennas by conversion (from relative corrections), and for the GNSS transmitter antennas by estimation. However, consistent receiver antenna models for space missions such as GRACE and TerraSAR-X, which are equipped with non-geodetic receiver antennas, are only available since a short time from robot calibrations. We use GPS data of the aforementioned LEOs of the year 2007 together with the absolute antenna modeling to assess the presently achieved accuracy from state-of-the-art reduced-dynamic LEO POD strategies for absolute and relative navigation. Near-field multipath and cross-talk with active GPS occultation antennas turn out to be important and significant sources for systematic carrier phase measurement errors that are encountered in the actual spacecraft environments. We assess different methodologies for the in-flight determination of empirical phase pattern corrections for LEO receiver antennas and discuss their impact on POD. By means of independent K-band measurements, we show that zero-difference GRACE orbits can be significantly improved from about 10 to 6 mm K-band standard deviation when taking empirical phase corrections into account, and assess the impact of the corrections on precise baseline estimates and further applications such as gravity field recovery from kinematic LEO positions.     

单星模糊度固定的整数相位钟法及在低轨卫星定轨中的应用

单星GPS相位模糊度固定可以显著提升低轨卫星的定轨精度.目前,CNES/CLS、武汉大学和CODE 3家机构都已公开发布用于单星模糊度固定的GPS整数相位钟产品.本文首先利用整数相位钟方法实现单星模糊度固定,并应用于低轨卫星精密定轨中;然后,对比分析了不同机构提供的整数相位钟产品在低轨卫星单星模糊度固定和精密定轨中的应...     

First GOCE gravity field models derived by three different approaches

Three gravity field models, parameterized in terms of spherical harmonic coefficients, have been computed from 71 days of GOCE (Gravity field and steady-state Ocean Circulation Explorer) orbit and gradiometer data by applying independent gravity field processing methods. These gravity models are one major output of the European Space Agency (ESA) project GOCE High-level Processing Facility (HPF). The processing philosophies and architectures of these three complementary methods are presented and discussed, emphasizing the specific features of the three approaches. The resulting GOCE gravity field models, representing the first models containing the novel measurement type of gravity gradiometry ever computed, are analysed and assessed in detail. Together with the coefficient estimates, full variance-covariance matrices provide error information about the coefficient solutions. A comparison with state-of-the-art GRACE and combined gravity field models reveals the additional contribution of GOCE based on only 71 days of data. Compared with combined gravity field models, large deviations appear in regions where the terrestrial gravity data are known to be of low accuracy. The GOCE performance, assessed against the GRACE-only model ITG-Grace2010s, becomes superior at degree 150, and beyond. GOCE provides significant additional information of the global Earth gravity field, with an accuracy of the 2-month GOCE gravity field models of 10?cm in terms of geoid heights, and 3?mGal in terms of gravity anomalies, globally at a resolution of 100?km (degree/order 200).     

Earth’s gravity field modelling based on satellite accelerations derived from onboard GPS phase measurements

GPS data collected by satellite gravity missions can be used for extracting the long-wavelength part of the Earth’s gravity field. We propose a new data processing method which makes use of the ‘average acceleration’ approach to gravity field modelling. In this method, satellite accelerations are directly derived from GPS carrier phase measurements with an epoch-differenced scheme. As a result, no ambiguity solutions are needed and the systematic errors that do not change much from epoch to epoch are largely eliminated. The GPS data collected by the Gravity Field and Steady-State Ocean Circulation Explorer (GOCE) satellite mission are used to demonstrate the added value of the proposed method. An analysis of the residual accelerations shows that accelerations derived in this way are more precise, with noise being reduced by about 20 and 5% at the cross-track component and the other two components, respectively, as compared to those based on kinematic orbits. The accelerations obtained in this way allow the recovery of the gravity field to a slightly higher maximum degree compared to the solution based on kinematic orbits. Furthermore, the gravity field solution has an overall better performance. Errors in spherical harmonic coefficients are smaller, especially at low degrees. The cumulative geoid height error is reduced by about 15 and 5% up to degree 50 and 150, respectively. An analysis in the spatial domain shows that large errors along the geomagnetic equator, which are caused by a high electron density coupled with large short-term variations, are substantially reduced. Finally, the new method allows for a better observation of mass transport signals. In particular, sufficiently realistic signatures of regional mass anomalies in North America and south-west Africa are obtained.