Contributions of Satellite Laser Ranging to Past and Future Radar Altimetry Missions

Satellite laser ranging (SLR) has proven avery efficient method for contributingto the tracking of altimetric satellites anddetermining accurately their orbitalthough hampered by the non-worldwide coverageand the meteorologicalconditions. Indeed, in some cases it is the onlymethod available to determinethe satellite orbit (e.g., the orbits of the ERS-1and Geosat-Follow-On missions).Moreover, any operational and non-weather dependenttechniques, like GPS,DORIS, PRARE, can exhibit systematic errors inpositioning and orbitography. Acomparison with SLR results allows to evidence sucherrors and vice versa. Fordoing that, two different approaches for determiningprecise orbits can beconsidered: one based on global orbit determination,the other on a short-arctechnique used to locally improve a global orbitdetermined by another trackingtechniques, such as DORIS or GPS. We can thusvalidate a global orbit andachieve orbit quality control to a level of2 to 3 centimeters at present and expectto achieve a level of 1 to 2 centimeters inthe near future. Errors induced bystation coordinates or by the gravity field(geographically correlated errors, forexample) can be estimated from SLR tracking data.Colocation experiments withdifferent techniques in the same geodetic siteplay also a key role to ensure preciserelationships between the geodetic referenceframes linked to each technique. Inparticular, the role of the SLR technique is tostrengthen the vertical component(including velocity) of the positioning, whichis crucial for altimetry missions.The role of SLR data in the modelling of the firstterms of the gravity field has finally to be emphasized,which is of primary importance in orbitography,whatever the tracking technique used.Another application of SLR technology is thesatellite altimeter calibration. Examples of past calibrationand future experiments are given, including theaccuracy we can expect from the Jason-1 and EnviSatspace oceanography missions.     

On precise orbit determination of HY-2 with space geodetic techniques

As the first radar altimetric satellite of China, HY-2 requires the precise orbit determination with a higher accuracy than that of other satellites. In order to achieve the designed radial orbit with the accuracy better than 10 cm for HY-2, the methods of precise orbit determination for HY-2 with the centimeter-level accuracy based on space geodetic techniques (DORIS, SLR, and satellite-borne GPS) are studied in this paper. Perturbations on HY-2 orbit are analyzed, in particular those due to the non-spherical gravitation of the earth, ocean tide, solid earth tide, solar and earth radiation, and atmospheric drag. Space geodetic data of HY-2 are simulated with the designed HY-2 orbit parameters based on the orbit dynamics theory to optimize the approaches and strategies of precise orbit determination of HY-2 with the dynamic and reduced-dynamic methods, respectively. Different methods based on different techniques are analyzed and compared. The experiment results show that the nonspherical perturbation modeled by GGM02C causes a maximum perturbation, and errors caused by the imperfect modeling of atmospheric drag have an increasing trend on T direction, but errors are relatively stable on the other two directions; besides, the methods with three space geodetic techniques achieve the radial orbit with the precision better than 10 cm.     

基于卫星数据和NRLMSISE-00模型的低轨道大气密度预报修正方法

NRLMSISE-00大气模型广泛应用于航天器定轨和预测等方面,但存在着较大的误差,尤其是在短期变化方面.为了提高低轨道大气密度短期预报的精度,我们提出了一种基于实测数据对NRLMSISE-00大气模型密度结果进行修正预报的方法:利用GRACE(Gravity Recovery and Climate Experiment)和CHAMP(Challenging Mini-Satellite Payload)卫星2002-2008年大气密度探测数据对NRLMSISE-00模型进行误差分析,获得模型的修正因子,再对模型的大气密度结果进行修正.采用该修正方法对GRACE-A和CHAMP卫星轨道上的大气密度进行3天短期预报试验验证,结果表明可显著提高大气密度的预报精度,在太阳活动低年,修正后的大气密度预报误差比NRLMSISE-00模型误差降低50%以上.     

Determination of polar motion from satellite observations

Doppler observations of U.S. Navy Navigation Satellites have been used to determine the Earth's pole position for the period 1967 to July 1972. Recent results are competitive in accuracy with astronomic results and exhibit about 0".02 agreement with astronomic pole positions. The differences are no larger than those between independent calculations of pole positions based on astronomic data (BIHvs. ILS). For a two-day span of observations made by 18 Doppler stations the uncertainty in computed pole position corresponding to random errors in observation is 0".002. However, the results have systematic errors with various frequencies which are primarily due to uncertainties in the gravity coefficients. Since these errors are independent of those producing systematic errors in astronomic results, the two techniques are complementary. Recent results of computation of polar motion based on laser observations of artificial Earth satellites have also produced results having accuracies comparable to Doppler and astronomic results. The analysis of the laser observations is based on the effect of pole position on the apparent inclination of satellite orbits; on the other hand, since the Doppler observations are made on polar orbiting satellites, they are more sensitive to errors in the component of pole position which lies in the orbit plane. As a result of this difference, biases in Doppler and laser results may be different in size or character.     

Centimeter-level precise orbit determination for the HY-2A satellite using DORIS and SLR tracking data

The HY-2A satellite is the first ocean dynamic environment monitoring satellite of China. Centimeter-level radial accuracy is a fundamental requirement for its scientific research and applications. To achieve this goal, we designed the strategies of precise orbit determination (POD) in detail. To achieve the relative optimal orbit for HY-2A, we carried out POD using DORIS-only, SLR-only, and DORIS + SLR tracking data, respectively. POD tests demonstrated that the consistency level of DORIS-only and SLR-only orbits with respect to the CNES orbits were about 1.81 cm and 3.34 cm in radial direction in the dynamic sense, respectively. We designed 6 cases of different weight combinations for DORIS and SLR data, and found that the optimal relative weight group was 0.2 mm/s for DORIS and 15.0 cm for SLR, and RMS of orbit differences with respect to the CNES orbits in radial direction and three-dimensional (3D) were 1.37 cm and 5.87 cm, respectively. These tests indicated that the relative radial and 3D accuracies computed using DORIS + SLR data with the optimal relative weight set were obviously higher than those computed using DORIS-only and SLR-only data, and satisfied the requirement of designed precision. The POD for HY-2A will provide the invaluable experience for the following HY-2B, HY-2C, and HY-2D satellites.     

基于星载GPS的HY-2卫星高精度精密定轨模拟研究(英文)

HY-2卫星是我国第一颗测高卫星,其径向定轨精度要求厘米量级,搭载了星载GPS接收机。目前HY-2还处于测试阶段,没有公布观测数据。为了确定基于星载GPS的HY-2精密定轨流程及其定轨精度,本文模拟了HY-2卫星星载GPS观测数据,结果表明HY-2星载GPS天线每个历元至少观测7颗GPS卫星。给出了基于星载GPS的精密定轨流程,分别采用简化动力学方法和动态几何法进行了精密定轨实验。对于相位1mm和3mm随机误差的相位观测数据,简化动力学法和动态几何法定轨都能够实现厘米量级的径向精密定轨,几何法定轨精度略低于简化动力定轨。地球重力场模型是影响HY-2卫星精密定轨的重要因素,本文对不同阶次的重力场模型EIGEN2、EGM96、TEG4和GEMT3进行了简化动力学定轨实验,高于50阶次的重力场模型都能够实现厘米级径向精密定轨,主要原因在于大量的高精度星载GPS观测数据和重力场模型精度的提高。     

Grim4-C1, -C2p: combination solutions of the global earth gravity field

On the basis of the GRIM4-S1 satellite-only Earth gravity model, being accomplished in a common effort by DGFI and GRGS, a combination solution, called GRIM4-C1, has been derivcd using 1° × 1° mean gravity anomalies and 1° × 1° Seasat altimeter derived mean geoid undulations. In the meantime improvements could be achieved by incorporating more tracking data (GEOSAT, SPOT2-DORIS) into the solution, resulting in the two new parallel versions, the satellite-only gravity model GRIM4-S2 and the combined solution GRIM4-C2p (preliminary). All GRIM4 Earth gravity models cover the spectral gravitational constituents complete up to degree and order 50.In this report the emphasis is on the discussion of the combined gravity models: combination and estimation techniques, capabilities for application in precise satellite orbit computation and accuracies in long wavelength geoid representation. It is shown that with the new generation of global gravity models general purpose satellite-only models are no longer inferior to combination solutions if applied to satellite orbit restitution.     

基于GRACE星载加速度计数据的热层密度反演

本文主要研究了利用GRACE星载加速度计数据反演热层密度.首先联合采用GRACE卫星2007—2009年星载加速度计数据和星载GPS数据进行动力学定轨并同时估计加速度计校正参数,依此对加速度计数据进行了校正.根据Sentman稀薄空气动力学方程计算卫星空气动力系数,对校正后的加速度计数据进行处理,反演得到了该时期沿轨热层大气密度.为分析反演密度的精度,将本文反演得到的GRACE-A卫星沿轨密度与Doornbos的解算结果,以及经验密度模型NRLMSISE00,HASDM模型进行比较分析.统计结果表明,本文反演结果比Doornbos系统性偏大约5%~8%,二者间的标准差(STD,standard deviation)在10%以内,具有较好的符合性.其差异主要是由于采用了不同的加速度标校以及空气动力系数计算策略.本文反演得到的热层密度较HASDM模型表现为正的系统性偏差且幅度在4%以内,而Doornbos的结果较HASDM模型约系统性偏小4%~7%,二者与HASDM模型的标准差均为30%左右.另外,本文反演密度与NRLMSISE00模型之间存在约30%~40%的系统性bias,其STD也在30%左右.     

A methodology for using optimal MSIS parameters retrieved from SSULI data to compute satellite drag on LEO objects

A key application to be derived from Space Weather research will be to forecast atmospheric drag on low Earth orbit (LEO) satellites with significantly better accuracy than is attainable today. The recently launched STP P91-1 ARGOS mission will serve as a testbed for the use of future operational ultraviolet remote-sensing data to achieve such an improvement. This paper describes the associated methodology, which uses discrete inverse theory in conjunction with the data to derive correction factors in near real time for the MSISE-90 empirical thermospheric model. To simulate the application of this technique to orbit prediction, we use the Jacchia-71 operational model to generate an evolving “ground truth” upper atmospheric state over a 48 h time period. This permits a state-of-the-art Satellite Tool Kit orbit propagator to synthesize a corresponding “ground truth” orbit on a standard LEO test object at 350 km altitude. Our tests show that, for orbit prediction, the “data-enhanced” MSIS density specification can provide significant improvement over the uncorrected MSIS specification. However, for orbit prediction, the results are sensitive to the strategy selected for applying the correction factors. We contrast our results for orbit prediction with those of Marcos et al. (1998. Astrodynamics. Vol. 97(1). AAS, San Diego, pp. 501–513) for precision orbit determination. An important result in the context of Space Weather is that the Jacchia and MSIS models can show significant point-to-point disagreement, which has major implications for operational specification of thermospheric drag.     

Derivation of the CHAMP-only global gravity field model TUG-CHAMP04 applying the energy integral approach

A global gravity field model TUG-CHAMP04, derived from CHAMP (CHAllenging Minisatellite Payload) satellite-to-satellite GPS tracking observations in the high-low mode (SST-hl) in combination with CHAMP accelerometry, is presented and described in detail in this paper. For this purpose the energy integral approach was applied to precise kinematic orbits and accelerometer data. The advantage of these kinds of orbits is that they are derived from purely geometrical information, hence no external gravity field information is used for the determination of the positions. The disadvantage of precise kinematic orbit information is, that no velocities are delivered and hence a procedure has to be elaborated to deduce the velocities from kinematic positions. This work is done in preparation for ESA’s GOCE (Gravity field and steady state Ocean Circulation Explorer) satellite mission (scheduled launch November 2006), aiming at a high precision and high-resolution gravity field model on a global scale. This paper concentrates on the CHAMP data processing, where, in contrast to the usual standard method (processing in the Earth fixed frame), an approach in the inertial frame is chosen. Focus is taken on the data preprocessing of both accelerometer and orbit data, emphasising on the correct treatment of data-gaps and outlier detection. Furthermore an arc-wise weighting strategy is introduced and the advantages/disadvantages of this approach are discussed. Finally, the TUG-CHAMP04 model, calculated from one year of CHAMP data is compared with the official CHAMP gravity field model EIGEN-3p and terrestrial data (GPS levelling data).     

APOD mission status and preliminary results

On September 20 th, 2015, twenty satellites were successfully deployed into a near-polar circular orbit at 520 km altitude by the Chinese CZ-6 test rocket, which was launched from the Tai Yuan Satellite Launch Center. Among these satellites, a set of 4 Cube Sats conform the atmospheric density detection and precise orbit determination(APOD) mission, which is projected for atmospheric density estimation from in-situ detection and precise orbit products. The APOD satellites are manufactured by China Spacesat Co. Ltd. and the payload instruments include an atmospheric density detector(ADD), a dual-frequency dualmode global navigation satellite system(GNSS) receiver(GPS and Beidou), a satellite laser ranging(SLR) reflector, and an S/Xband very long baseline interferometry(VLBI) beacon. In this paper, we compare the GNSS precise orbit products with colocated SLR observations, and the 3 D orbit accuracy shows better than 10 cm RMS. These results reveal the great potential of the onboard micro-electro-mechanical system(MEMS) GNSS receiver. After calibrating ADD density estimates with precise orbit products, the accuracy of our density products can reach about 10% with respect to the background density. Density estimates from APOD are of a great importance for scientific studies on upper atmosphere variations and useful for model data assimilation.     

天体运行轨道的背景介质理论导引与自相似分形测度计算的分维微积分基础

通过讨论天体运行背景介质理论的连续轨道及离散轨道这二个研究方向的基础假设,介绍了天体运行轨道的具体方程形式及理论框架概要;进一步地通过讨论天体运行轨道Binet方程的一般形式及其行星近日点进动角的解,给出了连续轨道理论与Newton理论及Einstein广义相对论的联系与区别;通过讨论天体运行轨道的分维扩展方程,给出了包括太阳系行星、天王星卫星、地球卫星、绕月航天器等在内的离散轨道（稳定性轨道）方程及其预言数据.特别地,作为对天体在较为广泛区域作用曲线的初步探讨推论,指出仅由天体引力难以形成质量密度趋于无穷大的理想黑洞.通过讨论一般函数的分维导数的位置假设及幂函数的分维导数的形式假设,进一步明晰了幂函数的分维导数、分维微分及分维积分的具体方程形式,给出分维导数与分数阶导数的区别,随后讨论了基于一般分形测度的分维微积分形式定义导出的自相似分形的测度计算方程具体形式,给出了其与目前Hausdorff测度方法（覆盖方法）的区别,并对包括三分Cantor集合、Koch曲线、Sierpinski垫片及正交十字星形等自相似分形在内的测度进行了计算分析.     

The Use of Resonant Orbits in Satellite Geodesy: A Review

Dynamic resonance, arising from commensurate (orbital or rotational) periods of satellites or planets with each other, has been a strong force in the development of the solar system. The repetition of conditions over the commensurate periods can result in amplified long-term changes in the positions of the bodies involved. Such resonant phenomena driven by the commensurability between the mean motion of certain artificial Earth satellites and the Earth’s rotation originally contributed to the evaluation and assessment of the Stokes parameters (harmonic geopotential coefficients) that specify the Earth’s gravitational field. The technique constrains linear combinations of the harmonic coefficients that are of relevant resonant order (lumped coefficients). The attraction of the method eventually dwindled, but the very accurate orbits of CHAMP and GRACE have recently led to more general insights for commensurate orbits applied to satellite geodesy involving the best resolution for all coefficients, not just resonant ones. From the GRACE mission, we learnt how to explain and predict temporary decreases in the resolution and accuracy of derived geopotential parameters, due to passages through low-order commensurabilities, which lead to low-density ground-track patterns. For GOCE we suggest how to change a repeat orbit height slightly, to achieve the best feasible recovery of the field parameters derived from on-board gradiometric measurements by direct inversion from the measurements to the harmonic geopotential coefficients, not by the way of lumped coefficients. For orbiters of Mars, we have suggestions which orbits should be avoided. The slow rotation of Venus results in dense ground-tracks and excellent gravitational recovery for almost all orbiters.     

基于多颗低轨卫星的SLR台站坐标几何解算方法

卫星激光测距（SLR）技术作为卫星精密定轨手段和轨道检核重要方法,激光反射器已经成为重力卫星和测高卫星等低轨卫星的基本载荷.经典的SLR台站坐标是使用动力学方法计算的,本文根据多颗低轨卫星（LEO）多历元的激光观测数据,采用几何方法开展地面SLR测站坐标计算.通过组建低轨卫星群实现对全球激光站的动态观测,为了合理配置不同低轨卫星间观测值权重,削弱低轨卫星群可能存在的系统性偏差,提出采用方差分量估计组合的最小二乘法进行解算.实测结果显示,解算出SLR台站坐标框架解与SLRF2014差异平均值在25.1 mm,外符合精度达到1~2 cm.该方法避免了复杂动力学模型,SLR台站坐标的几何计算方法既可以作为激光测站框架解算手段之一,同时将LEO卫星群作为空间并址站实现不同技术地球参考框架间的融合.     

TEMPORAL MONITORING OF SOIL MOISTURE USING ERS-1 SAR DATA

Multi-temporal synthetic aperture radar (SAR) imagery from the European Remote Sensing Satellite (ERS-1) was evaluated for monitoring soil moisture at the Romney Marsh test site as part of the UK SAR Calibration and Crop Backscatter Experiment. A total of 18 C-band (5.3 GHz) ERS-1 SAR images were acquired during the three day orbit and co-registered. Accurate calibration of the backscatter measurements was achieved using calibration constants derived from an analysis of corner reflector target responses. Mean backscatter measurements were recorded for each field and compared with field data on soil moisture, surface roughness and rainfall patterns. A comparison of daily and hourly rainfall and soil moisture measurements with backscatter for different cover types showed that the observed trends in backscatter are dominated by moisture effects. A high positive correlation between volumetric soil moisture in the range 10–40% was observed for bare soil fields. A much weaker positive relationship between soil moisture and backscatter was observed for grassland fields.     

基于卫星轨道扰动理论的重力反演算法

为了更充分利用低轨重力卫星的高精度观测数据,根据卫星轨道的扰动理论,导出了应用卫星轨道与星间距离观测值联合反演地球重力场模型的算法.该算法的实质是将牛顿运动方程在卫星轨道处进行展开,转化为第二类Volterra积分方程,并采用基于移动窗口的9次多项式内插公式进行数值求解.给出了该算法的观测方程,用QR分解法消去局部参数矩阵,最后采用预条件共轭梯度法求解法方程.利用GRACE卫星2008-01-01~2008-08-01时间段内的轨道及星间距离观测数据,解算了120阶次的地球重力场模型SWJTU-GRACE01S,该模型在120阶处的阶方差为1.58×10^-8,大地水准面差距累计误差为22.29 cm,与美国GPS水准网比较的标准差为0.793 m,结果表明:SWJTU-GRACE01S模型精度介于EIGEN-GRACE01S与EIGEN-GRACE02S模型之间,从而验证了该算法的有效性.     

Comparisons of recent data of density scale height at 544–877 km with CIRA model

In order to obtain the observed scale height at high altitude a calculation method has been derived for determining density scale height from the difference between two satellite’s heights. Two balloon satellites, Chinese DQ-1A and DQ-1B, were launched together into a nearly circular orbit at a height near 900 km and they were together in orbit for 190 days. According to the difference of the orbital heights of these two balloon satellites from 19 September 1990 to 9 March 1991, 67 values of density scale height at heights of about 544–877 km were determined. In comparison with CIRA model the results show that: (1) the trend of the variation of the scale height with height is in agreement with CIRA; (2) the determined scale height values present an oscillatory variation with time and height; and (3) the mean of the observed scale height is 3.7% lower than the mean of corresponding values from CIRA-72 and 0.8% lower than CIRA-86.     

基于GRACE卫星重力数据确定地球重力场模型WHU-GM-05

基于卫星轨道运动的能量积分方程,可导出利用卫星跟踪卫星数据求解地球重力场的实用公式.本文在Jekeli给出的公式基础上导出了基于能量守恒方程利用两颗低-低卫星跟踪的扰动位差求解重力位系数的严密关系式.基于两颗GRACE卫星的观测数据,采用本文导出的严密能量积分方法求解得到120阶的GRACE地球重力场模型,命名为WHU-GM-05;将WHU-GM-05模型与国际上同类重力场模型EIGEN-GRACE系列和GGM02S分别在阶方差和大地水准面高等方面作了比较,并与美国和中国的部分地区GPS水准观测值进行了精度分析.结果表明基于本文推导的严密双星能量守恒方程得到的WHU-GM-05重力场模型精度与国际上同类重力场模型的精度相当.     

适用于重力任务的卫星编队轨道参数研究

从满足重力卫星编队的轨道根数条件出发, 通过全过程动力法仿真实验, 计算得出了满足串联编队(GRACE-type)、 钟摆编队(Pendulum-type)和车轮编队(Cartwheel-type)这三种卫星编队模式稳定在轨的轨道参数, 并验证了其稳定性。 同时, 深入分析了各种卫星编队模式对于重力卫星任务的适用性, 结果表明, 同时包含两个方向观测量的Pendulum-type编队和Cartwheel-type编队, 能够在一定程度上克服GRACE-type编队中存在的由单一星间观测量的强相关性导致的重力场各向异性敏感度问题, 是理论上更适合重力探测任务的卫星编队模式。     

Sub-Daily Earth Rotation Parameters and the International GPS Service Orbit/Clock Solution Products

Tidally induced sub-daily Earth Rotation Parameters (ERP) variations, when not properly accounted for, can cause apparent orbit and ERP rate errors, which can significantly exceed the IGS solution errors. All International GPS Service (IGS) Analysis Centers currently apply the conventional sub-daily ERP model in their transformations from ITRF (International Terrestrial Reference Frame) to ICRF (International Celestial Reference Frame), both of which are used for IGS global analyses. However, some IGS Analysis Centers did not apply the sub-daily ERP model when transforming ICRF orbit solutions to ITRF, which is used for IGS orbit/clock products. This transformation inconsistency can cause significant orbit RMS differences that could exceed the 5-cm level. Independent ERP rate solutions are sensitive even to small errors in the sub-daily ERP model, and can be used to verify the sub-daily ERP model at, or below 0.1 mas/day precision level.The Precise Point Positioning (PPP) via precise station position solutions with the IGS orbit/clock combined products, provides an ideal interface to access the IGS realization of ITRF. PPP also yields precise station clock and tropospheric zenith delays (TZD) solutions, all at the sub-cm precision level. However, when using IGS orbit/clock products it is important that the same convention be used with respect to sub-daily ERP. Otherwise, the solutions of station navigation positions, station clocks and TZD's will be affected by significant errors that could exceed the 1-cm level.