Analysis of radial orbit errors of ERS-1, and the development of super-tailored gravity models

The altimetry mission of the future ESA remote sensing satellite ERS-1 requires very accurate orbit solutions, of which in particular the radial position component should have an accuracy of approximately 10 cm. This paper presents some investigations into the possibility of reducing the radial position error due to the earth's gravity field, which is by far the largest contributing error source.With a detailed harmonic analysis of the ERS-1 orbit a number of gravity field model terms are identified which produce the major radial orbit perturbations. These dominant terms are adjusted in a least-squares orbit determination and parameter estimation procedure using actual SEASAT laser tracking observations and altimeter height measurements. The initial gravity model is the NASA GEM-L2 model derived from satellite tracking data only, with an emphasis on LAGEOS data. The resulting super-tailored model yields a significantly improved radial accuracy relative to GEM-L2, but fails to reach the accuracy of the SEASAT-tailored model PGS-S4.Finally, the SEASAT altimeter residuals and the residuals of the cross-over differences are analyzed in the frequency domain by applying a special filtering technique which separates the major radial orbit error and geoid error contributions.     

SPOT-2 and TOPEX/Poseidon precise orbit determination from DORIS doppler tracking

The French earth observation satellite SPOT-2 has served as a testbed for precise orbit determination from DORIS doppler tracking in anticipation of the TOPEX/Poseidon mission. Using the most up-to-data gravity field model, JGM-2, a radial orbit accuracy of about 2–9 cm was achieved, with an rms of fit of the tracking data of about 0.64 mm/s. Furthermore, it was found that the coordinates of the ground stations can be determined with an accuracy of the order of 2–5 cm after removal of common rotations, and translations.

Using a slightly different model for atmospheric drag, but the same gravity model, precise orbits of TOPEX/Poseidon from DORIS tracking data were determined with a radial orbit accuracy of the order of 4–5 cm, which is far within the 13 cm mission requirement. This conclusion is based on the analysis of 1-day overlap of successive 11-day orbits, and the comparisons with orbits computed from satellite laser tracking (SLR) and from the combination of SLR and DORIS tracking. Results indicate a consistency between the different orbits of 1–4 cm, 4–20 cm, and 6–13 cm in the radial, cross-track, and along-track directions, respectively. The residual rms is about 4–5 cm for SLR data and 0.56 mm/s for DORIS tracking. These numbers are roughly twice as large as the system noise levels, reflecting the fact that there are still some modeling errors left.     

Proposal of application of same beam VLBI measurements in precision orbit determination of lunar orbiter and return capsule and lunar gravity field simulation in Chang’E-3 mission

High accuracy differenced phase delay can be obtained by observing multiple point frequencies of two spacecraft using the same beam Very Long Baseline Interferometry (VLBI) technology. Its contribution in lunar spacecraft precision orbit determination has been performed during the Japanese lunar exploration mission SELENE. In consideration that there will be an orbiter and a return capsule flying around the moon during the Chinese lunar exploration future mission Chang’E-3, the contributions of the same beam VLBI in spacecraft precision orbit determination and lunar gravity field solution have been investigated. Our results show that the accuracy of precision orbit determination can be improved more than one order of magnitude after including the same beam VLBI measurements. There are significant improvements in accuracy of low and medium degree coefficients of lunar gravity field model obtained from combination of two way range and Doppler and the same beam VLBI measurements than the one that only uses two way range and Doppler data, and the accuracy of precision orbit determination can reach meter level.     

Precision orbit determination for TOPEX/Poseidon using TDRSS doppler tracking data

Precision orbit determination on the TOPEX/Poseidon (T/P) altimeter satellite is now being routinely achieved with sub-5cm radial and sub-15 cm total positioning accuracy using state-of-the-art modeling with precision tracking provided by a combination of: (a) global Satellite Laser Ranging (SLR) and Doppler Orbitography and Radiopositioning Integrated by Satellite (DORIS), or (b) the Global Positioning System (GPS) Constellation which provides pseudo-range and carrier phase observations. The geostationary Tracking and Data Relay Satellite System (TDRSS) satellites are providing the operational tracking and communication support for this mission. The TDRSS Doppler data are of high precision (0.3 mm/s nominal noise levels). Unlike other satellite missions supported operationally by TDRSS, T/P has high quality independent tracking which enables absolute orbit accuracy assessments. In addition, the T/P satellite provides extensive geometry for positioning a satellite at geostationary altitude, and thus the TDRSS-T/P data provides an excellent means for determining the TDRS orbits. Arc lengths of 7 and 10 days with varying degrees of T/P spacecraft attitude complexity are studied. Sub-meter T/P total positioning error is achieved when using the TDRSS range-rate data, with radial orbit errors of 10.6 cm and 15.5 cm RMS for the two arcs studied. Current limitations in the TDRSS precision orbit determination capability include mismodeling of numerous TDRSS satellite-specific dynamic and electronic effects, and in the inadequate treatment of the propagation delay and bending arising from the wet troposphere and ionosphere.     

Dynamic and non-dynamic ERS-1 radial orbit improvement from ERS-1/TOPEX dual-satellite altimetry

Dual-satellite altimeter crossover differences between ERS-1 and TOPEX/Poseidon have been included as supplementary tracking data in ERS-1 orbit computations from SLR and single-satellite crossover differences. It was found that including the dual-satellite crossover differences slightly improves the ERS-1 radial orbit accuracy of about 12 cm for orbits computed with the JGM-2 gravity field and also leads to a better ‘centering’ of the ERS-1 orbit in the terrestrial reference frame defined for TOPEX/Poseidon. In addition to this dynamic orbit improvement technique, a non-dynamic technique has been investigated that removes the larger part of the ERS-1 radial orbit error from the dual-satellite crossover difference residuals. For ERS-1 orbits computed with the GEM-T2 gravity field, it was found that the non-dynamic technique could improve the radial orbit accuracy from 140 cm to the same level of accuracy as the ERS-1 JGM-2 orbits.     

Orbit determination of BDS-3 satellite based on regional ground tracking station and inter-satellite link observations

The BeiDou global navigation satellite system (BDS-3) has established the Ka-band inter-satellite link (ISL) to realize a two-way ranging function between satellites, which provides a new observation technology for the orbit determination of BDS-3 satellites. Therefore, this study presents a BDS satellite orbit determination model based on ground tracking station (GTS) observations and ISL ranging observations firstly to analyze the impact of the ISL ranging observations on the orbit determination of BDS-3 satellites. Subsequently, considering the data fusion processing, the variance component estimation (VCE) algorithm is applied to the parameter estimation process of the satellite orbit determination. Finally, using the measured data from China’s regional GTS observations and BDS-3 ISL ranging observations, the effects of ISL ranging observations on the orbit determination accuracy of BDS-3 satellites are analyzed. Moreover, the impact of the VCE algorithm on the fusion data processing is evaluated from the aspects of orbit determination accuracy, Ka-band hardware delay parameter stability, and ISL ranging observation residuals. The results show that for China’s regional GTSs, the addition of BDS-3 ISL ranging observations can significantly improve the orbit determination accuracy of BDS-3 satellites. The observed orbit determination accuracy of satellite radial component is improved from 48 cm to 4.1 cm. In addition, when the initial weight ratio between GTS observations and ISL ranging observations is not appropriate, the various indicators which include orbit determination accuracy, ISL hardware delay, and ISL observation residuals were observed to have improved after the adjustment of the VCE algorithm. These results validate the effectiveness of the VCE algorithm for the fusion data processing of the GTS observations and ISL ranging observations.     

Comparison analyses on the 150 × 150 lunar gravity field models by gravity/topography admittance,correlation and precision orbit determination

We analyzed the 150 × 150 lunar gravity field models, LP150Q, GLGM-3 and SGM150, using the power spectrum on the lunar nearside and farside, the lunar global and localized gravity/topography admittance and correlation, and Chang’E-2 precision orbit determination to investigate which model is a more effective tool to estimate geophysical parameters and determine the lunar satellite precision orbit. Results indicate that all gravity field models can be used to estimate the lunar geophysical parameters of the nearside of the Moon. However, SGM150 is better in such computation of the farside. Additionally, SGM150 is shown to be the most useful model for determining the lunar satellite orbit.     

Towards development of a consistent orbit series for TOPEX,Jason-1, and Jason-2

The TOPEX/Poseidon, Jason-1 and Jason-2 set of altimeter data now provide a time series of synoptic observations of the ocean that span nearly 17 years from the launch of TOPEX in 1992. The analysis of the altimeter data including the use of altimetry to monitor the global change in mean sea level requires a stable, accurate, and consistent orbit reference over the entire time span. In this paper, we describe the recomputation of a time series of orbits that rely on a consistent set of reference frames and geophysical models. The recomputed orbits adhere to the IERS 2003 standards for ocean and earth tides, use updates to the ITRF2005 reference frame for both the SLR and DORIS stations, apply GRACE-derived models for modeling of the static and time-variable gravity, implement the University College London (UCL) radiation pressure model for Jason-1, use improved troposphere modeling for the DORIS data, and apply the GOT4.7 ocean tide model for both dynamical ocean tide modeling and for ocean loading. The new TOPEX orbits have a mean SLR fit of 1.79 cm compared to 2.21 cm for the MGDR-B orbits. These new TOPEX orbits agree radially with independent SLR/crossover orbits at 0.70 cm RMS, and the orbit accuracy is estimated at 1.5–2.0 cm RMS over the entire TOPEX time series. The recomputed Jason-1 orbits agree radially with the Jason-1 GDR-C orbits at 1.08 cm RMS. The GSFC SLR/DORIS dynamic and reduced-dynamic orbits for Jason-2 agree radially with independent orbits from the CNES and JPL at 0.70–1.06 cm RMS. Applying these new orbits, and using the latest altimeter corrections for TOPEX, Jason-1, and Jason-2 from September 1992 to May 2009, we find a global rate in mean sea level of 3.0 ± 0.4 mm/yr.     

光压摄动对卫星姿态轨道耦合的影响分析

随着卫星对地测量精度要求的不断提高, 对卫星轨道的精度要求也随之提高. 目前Topex, Jason-1, Jason-2等一系列海洋测地卫星的轨道计算精度已经达到厘米量级, 相应对卫星动力学模型的要求也越来越精细. 以Topex海洋测地卫星为背景, 考虑卫星帆板有规律的运动, 将其几何形状简化为高精度轨道计算中比较通用的Boxing-Wing模型, 计算了Topex卫星的Boxing-Wing模型在轨运行中受到的太阳光压力及光压力矩. 考虑卫星姿态和轨道耦合的情况下, 计算了太阳光压力及光压力矩对Topex卫星轨道半长轴和卫星姿态的影响. 通过一个轨道周期的计算可知, 光压对卫星轨道半长轴的影响大约为9cm, 对卫星滚动角和俯仰角的影响在6°左右, 因此, 在高精度的轨道计算和姿态控制中这个影响是应该考虑的.      

Orbit determination of BeiDou navigation satellite system maneuvered satellites based on instantaneous velocity pulses parameters

The BeiDou navigation satellite system (BDS) comprises geostationary earth orbit (GEO) satellites as well as inclined geosynchronous orbit (IGSO) and medium earth orbit (MEO) satellites. Owing to their special orbital characteristics, GEO satellites require frequent orbital maneuvers to ensure that they operate in a specific orbital window. The availability of the entire system is affected during the maneuver period because service cannot be provided before the ephemeris is restored. In this study, based on the conventional dynamic orbit determination method for navigation satellites, multiple sets of instantaneous velocity pulses parameters which belong to one of pseudo-stochastic parameters were used to simulate the orbital maneuver process in the orbital maneuver arc and establish the observed and predicted orbits of the maneuvered and non-maneuvered satellites of BeiDou regional navigation satellite system (BDS-2) and BeiDou global navigation satellite system (BDS-3). Finally, the single point positioning (SPP) technology was used to verify the accuracy of the observed and predicted orbits. The orbit determination accuracy of maneuvered satellites can be greatly improved by using the orbit determination method proposed in this paper. The overlapping orbit determination accuracy of maneuvered GEO satellites of BDS-2 and BDS-3 can improve 2–3 orders of magnitude. Among them, the radial orbit determination accuracy of each maneuvered satellite is basically better than 1 m. simultaneously, the combined orbit determination of the maneuvered and non-maneuvered satellites does not have a great impact on the orbit determination accuracy of the non-maneuvered satellites. Compared with the multi GNSS products (indicated by GBM) from the German Research Centre for Geosciences (GFZ), the impact of adding the maneuvered satellites on the orbit determination accuracy of BDS-2 satellites is less than 9 %. Furthermore, the orbital recovery time and the service availability period are significantly improved. When the node of the predicted orbit is traversed approximately 3 h after the maneuver, the accuracy of the predicted orbit of the maneuvered satellite can reach that of the observed orbit. The SPP results for the BDS reached a normal level when the node of the predicted orbit was 2 h after the maneuver.     

基于机动力模型的GEO卫星恢复期间定轨

北斗卫星导航系统(BDS)中GEO卫星频繁的轨道机动对高精度、实时不间断的导 航服务需求提出了更高要求, 如何在短弧跟踪条件下提高GEO卫星轨道快速 恢复能力, 是提升导航系统服务精度的关键因素. 针对该问题, 本文提出了基 于机动力模型的动力学定轨方法, 尝试利用高精度的C波段转发式测距数据, 辅 以机动期间的遥测遥控信息建立机动力模型, 联合轨控前后的观测数据进行动 力学长弧定轨. 利用BDS中GEO卫星实测数据进行了定轨试验与分析, 结果表明, 恢复期间需要采用解算机动推力的定轨方法, 联合机动前、机动期间和机 动后4h数据定轨的轨道位置精度在20m量级, 径向精度优于2.5m. 该方 法克服了短弧跟踪条件下动力学法定轨和单点定位中的诸多问题, 提供了解决 GEO卫星机动后轨道快速恢复问题的技术方法.      

Modeling and analysis of Earth’s gravity field measurement performance by inner-formation flying system

The Earth’s gravity field can be measured with high precision by constructing the purely gravitational orbit of the inner-satellite in Inner-formation Flying System (IFS), which is independently proposed by Chinese scholars and offers a new way to carry out gravity field measurement by satellite without accelerometers. In IFS, for the purpose of quickly evaluating the highest degree of recovered gravity field model and geoid error as well as analyzing the influence of system parameters on gravity field measurement, an analytical formula was established by spectral analysis method. The formula can reflect the analytical relationship between gravity field measurement performance and system parameters such as orbit altitude, the inner-satellite orbit determination error, the inner-satellite residual disturbances, data sampling interval and total measurement time. This analytical formula was then corrected by four factors introduced from numerical simulation of IFS gravity field measurement. By comparing computation results from corrected analytical formula and the actual gravity field measurement performance by CHAMP, the correctness and rationality of this analytical formula were verified. Based on this analytical formula, the influences of system parameters on IFS gravity field measurement were analyzed. It is known that gravity field measurement performance is a monotone decreasing function of orbit altitude, the inner-satellite orbit determination error, the inner-satellite residual disturbances, data sampling interval and the reciprocal of total measurement time. There is a match relationship between the inner-satellite orbit determination error and residual disturbances, in other words, the change rate of gravity field measurement performance with one of them is seriously restricted by their relative size. The analytical formula can be used to quantitatively evaluate gravity field measurement performance fast and design IFS parameters optimally. It is noted that the analytical formula and corresponding conclusions are applied to any gravity satellite which measures gravity field by satellite perturbation orbit.     

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。     

基于经验加速度的低轨卫星轨道预报新方法

研究将定轨过程中的经验加速度应用于地球低轨卫星轨道预报的新方法. 利用GPS伪距观测数据和简化动力学最小二乘批处理方法对地球低轨卫星定 轨, 其中卫星位置、速度及大气阻力系数和辐射光压系数可以直接用于轨道预报. 作为简化动力学最重要特征的经验加速度呈现准周期、余弦曲线特点, 可通过 傅里叶级数拟合建模. 确定性动力学模型与补偿大气阻力模型误差的切向经验 加速度级数拟合模型组成增强型动力学模型用于提高轨道预报精度. 应用 GRACE-A星载GPS伪距观测数据和IGS超快星历定轨并进行轨道预报, 结果表明 轨道预报初值位置精度达到0.2m, 速度精度达到1×10-4m·s-1, 预报3天位置精度优于60m, 比只利用确定性动力学模型进行预报精度平 均提高2.3倍. 先定轨后预报的模式可用在星上自主精确导航系统中.      

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.     

The challenges in long-term altimetry calibration for addressing the problem of global sea level change

Long-term change of the global sea level resulting from climate change has become an issue of great societal interest. The advent of the technology of satellite altimetry has modernized the study of sea level on both global and regional scales. In combination with in situ observations of the ocean density and space observations of Earth’s gravity variations, satellite altimetry has become an essential component of a global observing system for monitoring and understanding sea level change. The challenge of making sea level measurements with sufficient accuracy to discern long-term trends and allow the patterns of natural variability to be distinguished from those linked to anthropogenic forcing rests largely on the long-term efforts of altimeter calibration and validation. The issues of long-term calibration for the various components of the altimeter measurement system are reviewed in the paper. The topics include radar altimetry, the effects of tropospheric water vapor, orbit determination, gravity field, tide gauges, and the terrestrial reference frame. The necessity for maintaining a complete calibration effort and the challenges of sustaining it into the future are discussed.     

基于光学测角数据的风云四号同步轨道卫星精密定轨

针对风云四号同步卫星的精密定轨和精度评估需求,首先利用地面光学测角数据对FY-4A卫星进行精密定轨,定轨后方位角和高度角的残差rms分别为0.25＂和0.45＂。与基于测距数据的轨道相比,位置精度在有测角数据的弧段内小于50m。进一步联合测角数据和测距数据对FY-4A卫星进行联合定轨,定轨后轨道重叠精度优于15m。利用联合定轨结果评估了基于测距数据的实时轨道产品精度,可以明显发现轨道精度随着测距数据的积累而逐步提高。     

New improved orbit solutions for the ERS-1 and ERS-2 satellites

Improved orbit solutions of the European Remote Sensing Satellites ERS-1 and ERS-2 have been computed in the ITRF2005 terrestrial reference frame using the recent models based mainly on IERS Conventions 2003. These solutions cover the periods 3 August 1991 to 8 July 1996 for ERS-1, and 3 May 1995 to 4 July 2003 for ERS-2. For each satellite, the final orbit solution is based on a combination of three separate orbit solutions independently computed at the Delft Institute of Earth Observation and Space Systems (DEOS) of the Delft University of Technology (The Netherlands), the Navigation Support Office of the European Space Operations Centre (ESOC, Germany) and the Helmholtz Centre Potsdam GFZ German Research Centre for Geosciences (Germany) using three different software packages for precise orbit determination, but using the same models in the same terrestrial reference frame within the European Space Agency (ESA) project ‘Reprocessing of Altimeter Products for ERS (REAPER)’. Validation using radar altimeter data indicates that the new combined orbits of ERS-1 and ERS-2 computed by us are significantly more accurate, approaching the 2–3 cm level in radial direction, than previously available orbit solutions.     

An alternative computation of a gravity field model from GOCE

GOCE is the first satellite with a gravitational gradiometer (SGG). This allows to determine a gravity field model with high spatial resolution and high accuracy. Four of the six independent components of the gravitational gradient tensors (GGT) are measured with high accuracy in the so-called measurement band (MB) from 5 to 100 mHz by the GOCE gradiometer. Based on more than 1 year of GOCE measurements, two gravity field models have been derived. Here, we introduce a strategy for spherical harmonic analysis (SHA) from GOCE measurements, with a bandpass filter applied to the SGG data, combined with orbit analysis based on the integral equation approach, and additional constraints (or stabilization) in the polar areas where no observation is available due to the orbit geometry. In addition, we combined the GOCE SGG part with a set of GRACE normal equations. This improves the accuracy of the gravity field in the long-wavelength parts, due to the complementarity of GOCE and GRACE. Comparison with other models and with external data shows that our results are rather close to the GPS-levelling data in well-selected test regions, with an uncertainty of 4–7 cm, for truncation at degree 200.