Thermosphere densities derived from Swarm GPS observations

After the detection of many anomalies in the Swarm accelerometer data, an alternative method has been developed to determine thermospheric densities for the three-satellite mission. Using a precise orbit determination approach, non-gravitational and aerodynamic-only accelerations are estimated from the high-quality Swarm GPS data. The GPS-derived non-gravitational accelerations serve as a baseline for the correction of the Swarm-C along-track accelerometer data. The aerodynamic accelerations are converted directly into thermospheric densities for all Swarm satellites, albeit at a much lower temporal resolution than the accelerometers would have been able to deliver. The resulting density and acceleration data sets are part of the European Space Agency Level 2 Swarm products.To improve the Swarm densities, two modifications have recently been added to our original processing scheme. They consist of a more refined handling of radiation pressure accelerations and the use of a high-fidelity satellite geometry and improved aerodynamic model. These modifications lead to a better agreement between estimated Swarm densities and NRLMSISE-00 model densities. The GPS-derived Swarm densities show variations due to solar and geomagnetic activity, as well as seasonal, latitudinal and diurnal variations. For low solar activity, however, the aerodynamic signal experienced by the Swarm satellites is very small, and therefore it is more difficult to accurately resolve latitudinal density variability using GPS data, especially for the higher-flying Swarm-B satellite. Therefore, mean orbit densities are also included in the Swarm density product.     

CHAMP and GRACE accelerometer calibration by GPS-based orbit determination

Current and planned Earth observation missions are equipped with highly sensitive accelerometers. Before using the data, the instrument has to be calibrated by determining scale and bias parameters for each axis. Here, the accelerometer measurements are used in a GPS-based reduced-dynamic orbit determination approach, replacing the non-gravitational force models, and nominally daily calibration parameters are estimated. Additional empirical accelerations are estimated to account for deficiencies in the applied force models. This method is applied to 5 years of CHAMP and GRACE data, resulting in an orbit precision at the level of a few centimeters. In along-track direction the calibration parameters can be estimated freely, scale factors of 0.96 ± 0.014 and 0.95 ± 0.015 are obtained for GRACE A and B, and 0.85 ± 0.024 for CHAMP. A constant scale factor results in the smoothest bias series, with clear trends and occasional jumps. In radial and cross-track direction tight constraints to a priori biases have to be applied. Furthermore, the determined orbits are analyzed with respect to reference trajectories, and SLR, phase and KBR residuals are presented.     

Measuring atmospheric density using GPS–LEO tracking data

We present a method to estimate the total neutral atmospheric density from precise orbit determination of Low Earth Orbit (LEO) satellites. We derive the total atmospheric density by determining the drag force acting on the LEOs through centimeter-level reduced-dynamic precise orbit determination (POD) using onboard Global Positioning System (GPS) tracking data. The precision of the estimated drag accelerations is assessed using various metrics, including differences between estimated along-track accelerations from consecutive 30-h POD solutions which overlap by 6 h, comparison of the resulting accelerations with accelerometer measurements, and comparison against an existing atmospheric density model, DTM-2000. We apply the method to GPS tracking data from CHAMP, GRACE, SAC-C, Jason-2, TerraSAR-X and COSMIC satellites, spanning 12 years (2001–2012) and covering orbital heights from 400 km to 1300 km. Errors in the estimates, including those introduced by deficiencies in other modeled forces (such as solar radiation pressure and Earth radiation pressure), are evaluated and the signal and noise levels for each satellite are analyzed. The estimated density data from CHAMP, GRACE, SAC-C and TerraSAR-X are identified as having high signal and low noise levels. These data all have high correlations with anominal atmospheric density model and show common features in relative residuals with respect to the nominal model in related parameter space. On the contrary, the estimated density data from COSMIC and Jason-2 show errors larger than the actual signal at corresponding altitudes thus having little practical value for this study. The results demonstrate that this method is applicable to data from a variety of missions and can provide useful total neutral density measurements for atmospheric study up to altitude as high as 715 km, with precision and resolution between those derived from traditional special orbital perturbation analysis and those obtained from onboard accelerometers.     

GRACE accelerometer calibration by high precision non-gravitational force modeling

The precise modeling and knowledge of non-gravitational forces acting on satellites is of big interest to many scientific tasks and missions. Since 2002, the twin GRACE satellites have measured these forces in a low Earth orbit with highly precise accelerometers, for about 15?years. Besides the significance for the GRACE mission, these measurement data allow the evaluation of modeling approaches and the improvement of force models. Unfortunately, before any scientific usage, the accelerometer measurements need to be calibrated, namely scale factor and bias have to be regularly estimated.In this study we demonstrate an accelerometer calibration approach, solely based on high precision non-gravitational force modeling without any use of empirically or stochastically estimated parameters, using our in-house developed satellite simulation tool XHPS. The aim of this work is twofold, first we use the accelerometer data and the residuals resulting from the calibration to quantitatively analyze and validate different non-gravitational force model approaches. In a second step, we compare the calibration results to three different calibration methods from different authors, based on gravity field recovery, GPS-based precise orbit determination, and based on modeled accelerations.We consider atmospheric drag forces and winds, as well as radiation forces due to solar radiation pressure, albedo, Earth infrared and thermal radiation (TRP) of the satellite itself. For TRP, we investigate different transient temperature calculation approaches for the satellite surfaces with absorbed power from the aforementioned radiation sources. A detailed finite element model of the satellite is utilized for every force, considering orientation, material properties and shadowing conditions for each element.For cross-track and radial direction, which are mainly affected by the radiative forces, our calibration residuals are quite small when drag is not super dominant (1–3?$\text{nm}/{\text{s}}^2$ for total accelerations around $\pm$50?$\text{nm}/{\text{s}}^2$). For these directions the calibration seems to perform better than the other compared methods, where some bigger differences were found. For the drag dominated along-track direction it is vice versa, here our method is not sensitive enough because the difference between modeled and measured drag is bigger (e.g. residuals around 10?$\text{nm}/{\text{s}}^2$ for total accelerations around $\pm$70?$\text{nm}/{\text{s}}^2$ for low solar activity). In along-track direction the orbit determination based methods are more sensitive and produce more reliable results. Results for the complete GRACE mission time span from 2003 to 2017 are shown, covering different seasonal environmental conditions.     

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.     

基于双频GPS观测的简化动力学最小二乘批处理精密定轨

星载双频GPS载波相位和伪距观测量已成为低轨卫星获取精确三维位置和速度信息的主要方式. 本文以非差消电离载波相位和伪距组合作为观测量,应用简化动力学最小二乘批处理方法进行地球低轨卫星的精密定轨,并给出完整定轨流程. 采用逐段常量的经验加速度对动力学模型误差进行补偿,描述了经验加速度敏感矩阵及稀疏带状矩阵求逆的有效计算方法. 利用GRACE-A卫星GPS观测数据对定轨位置精度进行分析,结果显示,三维位置定轨精度优于5cm,经验加速度在径向、切向和法向上的补偿水平不超过40nm·s-2,大气阻力系数和辐射光压系数的估计值符合物理实际,星载接收机钟差大致呈线性并具有短周期小波动.      

A shadow function model based on perspective projection and atmospheric effect for satellites in eclipse

Accurate Solar Radiation Pressure (SRP) modelling is critical for correctly describing the dynamics of satellites. A shadow function is a unitless quantity varying between 0 and 1 to scale the solar radiation flux at a satellite’s location during eclipses. Errors in modelling shadow function lead to inaccuracy in SRP that degrades the orbit quality. Shadow function modelling requires solutions to a geometrical problem (Earth’s oblateness) and a physical problem (atmospheric effects). This study presents a new shadow function model (PPM_atm) which uses a perspective projection based approach to solve the geometrical problem rigorously and a linear function to describe the reduction of solar radiation flux due to atmospheric effects. GRACE (Gravity Recovery And Climate Experiment) satellites carry accelerometers that record variations of non-conservative forces, which reveal the variations of shadow function during eclipses. In this study, the PPM_atm is validated using accelerometer observations of the GRACE-A satellite. Test results show that the PPM_atm is closer to the variations in accelerometer observations than the widely used SECM (Spherical Earth Conical Model). Taking the accelerometer observations derived shadow function as the “truth”, the relative error in PPM_atm is ?0.79% while the SECM 11.07%. The influence of the PPM_atm is also shown in orbit prediction for Galileo satellites. Compared with the SECM, the PPM_atm can reduce the radial orbit error RMS by 5.6?cm over a 7-day prediction. The impacts of the errors in shadow function modelling on the orbit remain to be systematic and should be mitigated in long-term orbit prediction.     

GSFC DORIS contribution to ITRF2008

The NASA GSFC DORIS analysis center has provided weekly DORIS solutions from November 1992 to January 2009 (839 SINEX files) of station positions and Earth Orientation Parameters for inclusion in the DORIS contribution to ITRF2008. The NASA GSFC GEODYN orbit determination software was used to process the orbits and produce the normal equations. The weekly SINEX gscwd10 submissions included DORIS data from Envisat, TOPEX/Poseidon, SPOT-2, SPOT-3, SPOT-4, SPOT-5. The orbits were mostly seven days in length (except for weeks with data gaps or maneuvers). The processing used the GRACE-derived EIGEN-GL04S1 gravity model, updated modeling for time-variable gravity, the GOT4.7 ocean tide model and tuned satellite-specific macromodels for SPOT-2, SPOT-3, SPOT-4, SPOT-5 and TOPEX/Poseidon. The University College London (UCL) radiation pressure model for Envisat improves nonconservative force modeling for this satellite, reducing the median residual empirical daily along-track accelerations from 3.75 × 10⁻⁹ m/s² with the a priori macromodel to 0.99 × 10⁻⁹ m/s² with the UCL model. For the SPOT and Envisat DORIS satellite orbits from 2003 to 2008, we obtain average RMS overlaps of 0.8–0.9 cm in the radial direction, 2.1–3.4 cm cross-track, and 1.7–2.3 cm along-track. The RMS orbit differences between Envisat DORIS-only and SLR & DORIS orbits are 1.1 cm radially, 6.4 cm along-track and 3.7 cm cross-track and are characterized by systematic along-track mean offsets due to the Envisat DORIS system time bias of ±5–10 μs. We obtain a good agreement between the geometrically-determined geocenter parameters and geocenter parameters determined dynamically from analysis of the degree one terms of the geopotential. The intrinsic RMS weekly position repeatability with respect to the IDS-3 combination ranges from 2.5 to 3.0 cm in 1993–1994 to 1.5 cm in 2007–2008.     

Generating precise and homogeneous orbits for Jason-1 and Jason-2

Driven by the GMES (Global Monitoring for Environment and Security) and GGOS (Global Geodetic Observing System) initiatives the user community has a strong demand for high-quality altimetry products. In order to derive such high-quality altimetry products, precise orbits for the altimetry satellites are a necessity. With the launch of the TOPEX/Poseidon mission in 1992 a still on-going time series of high-accuracy altimetry measurements of ocean topography started, continued by the altimetry missions Jason-1 in 2001 and Jason-2/OSTM in 2008. This paper contributes to the on-going orbit reprocessing carried out by several groups and presents the efforts of the Navigation Support Office at ESA/ESOC using its NAPEOS software for the generation of precise and homogeneous orbits referring to the same reference frame for the altimetry satellites Jason-1 and Jason-2. Data of all three tracking instruments on-board the satellites (beside the altimeter), i.e. GPS, DORIS, and SLR measurements, were used in a combined data analysis. About 7 years of Jason-1 data and more than 1 year of Jason-2 data were processed. Our processing strategy is close to the GDR-C standards. However, we estimated slightly different scaling factors for the solar radiation pressure model of 0.96 and 0.98 for Jason-1 and Jason-2, respectively. We used 30 s sampled GPS data and introduced 30 s satellite clocks stemming from ESOC’s reprocessing of the combined GPS/GLONASS IGS solution. We present the orbit determination results, focusing on the benefits of adding GPS data to the solution. The fully combined solution was found to give the best orbit results. We reach a post-fit RMS of the GPS phase observation residuals of 6 mm for Jason-1 and 7 mm for Jason-2. The DORIS post-fit residuals clearly benefit from using GPS data in addition, as the DORIS data editing improves. The DORIS observation RMS for the fully combined solution is with 3.5 mm and 3.4 mm, respectively, 0.3 mm better than for the DORIS-SLR solution. Our orbit solution agrees well with external solutions from other analysis centers, as CNES, LCA, and JPL. The orbit differences between our fully combined orbits and the CNES GDR-C orbits are of about 0.8 cm for Jason-1 and at 0.9 cm for Jason-2 in the radial direction. In the cross-track component we observe a clear improvement when adding GPS data to the POD process. The 3D-RMS of the orbit differences reveals a good orbit consistency at 2.7 cm and 2.9 cm for Jason-1 and Jason-2. Our resulting orbit series for both Jason satellites refer to the ITRF2005 reference frame and are provided in sp3 file format on our ftp server.     

NRLMSISE-00大气模型与GRACE和CHAMP卫星大气密度数据的对比分析

利用GRACE(Gravity Recovery And Climate Experiment)和CHAMP(Challenging Mini-Satellite Payload)卫星2002-2008年的大气密度数据与NRLMSISE-00大气模型密度结果进行比较,分析了模型密度误差及其特点.结果显示,NRLMSISE-00大气模型计算的密度值普遍偏大,其相对误差随经纬度变化,在高纬度相对较小;相对误差随地方时变化,在02:00LT和15:00LT左右较大,10:00LT和20:00LT左右较小.通过模型密度相对误差与太阳F_10.7指数的对比分析发现,在太阳活动低年模型相对误差最大,而在太阳活动高年相对误差较小;将模型结果分别与GRACEA/B双星和CHAMP卫星的密度数据进行比较,发现对于轨道高度更高的GRACE卫星轨道,模型相对误差更大;在地磁平静期,相对误差与地磁ap指数(当前3h)相关性不强,但是在大磁暴发生时,误差急剧增大.      

高精度空间加速度计及其应用

高精度空间加速度计不仅可以用来测量航天器受到的非引力, 例如航天器受到地球的热辐射压力、太阳辐射压力、大气阻力等, 而且还可以作为惯性参考用来改善航天器的微重力水平, 即对航天器进行无拖曳控制. 通过对开环加速度计基本工作原理的研究, 概述了高精度空间加速度计的发展趋势和现状, 介绍了几种不同类型的高精度空间加速度计, 重点讨论了其在地球科学和空间基础物理研究中的应用.      

近圆轨道卫星编队捕获技术研究

基于近圆参考轨道的假设,研究处于同一入轨点多颗卫星的编队捕获方法.首先由高斯型拉格朗日轨道摄动运动方程得到轨道坐标系中控制冲量与轨道根数偏差的关系,基于近圆轨道的条件简化并带入相对运动方程,得到控制冲量与相对运动的关系表达式;通过深入分析各个方向(径向、沿迹向与轨道面法向)的控制冲量对相对运动的影响,给出了分别用径向与轨道面法向控制冲量组合和沿迹向与轨道面法向控制冲量组合实现编队捕获的两种控制策略;最后给出了一个空间圆编队捕获实例,并从燃料消耗、施加冲量次数及捕获时间等角度对比研究了两种控制策略的特点.仿真结果表明,这两种控制策略简单、实用,能够较好地解决近圆轨道卫星编队的捕获问题.      

GLONASS-based precise point positioning and performance analysis

Current precise point positioning (PPP) techniques are mainly based on GPS which has been extensively investigated. With the increase of available GLONASS satellites during its revitalization, GLONASS observations were increasingly integrated into GPS-based PPP. Now that GLONASS has reached its full constellation, there will be a wide interest in PPP systems based on only GLONASS since it provides a PPP implementation independent of GPS. An investigation of GLONASS-based PPP will also help the development of GPS and GLONASS combined PPP techniques for improved precision and reliability. This paper presents an observation model for GLONASS-based PPP in which the GLONASS hardware delay biases are addressed. In view of frequently changed frequency channel number (FCN) for GLONASS satellites, an algorithm has been developed to compute the FCN for GLONASS satellites using code and phase observations, which avoids the need to provide the GLONASS frequency channel information during data processing. The observation residuals from GLONASS-based PPP are analyzed and compared to those from GPS-based PPP. The performance of GLONASS-based PPP is assessed using data from 15 globally distributed stations.     

High-fidelity geometry models for improving the consistency of CHAMP,GRACE, GOCE and Swarm thermospheric density data sets

During the last two decades, accelerometers on board of the CHAMP, GRACE, GOCE and Swarm satellites have provided high-resolution thermosphere density data to improve our knowledge on atmospheric dynamics and coupling processes in the thermosphere-ionosphere region. Most users of the data have focused on relative density variations. Scale differences between datasets and models have been largely neglected or removed using ad hoc scale factors. The origin of these scale differences arises from errors in the aerodynamic modelling, specifically in the modelling of the satellite outer surface geometry and of the gas-surface interactions. Therefore, the first step to remove the scale differences is to enhance the geometry modelling. This work forms the foundation for the future improvement of characterization of satellite aerodynamics and gas-surface interactions models at TU Delft, as well as for extending the use of sideways and angular accelerations in the aerodynamic analysis of accelerations and derivation of thermosphere datasets. Although work to improve geometry and aerodynamic force models by other authors has focused on CHAMP and GRACE, this paper includes the GOCE and Swarm satellites as well. In addition, it uses a density determination algorithm that is valid for arbitrary attitude orientations, enabling a validation making use of attitude manoeuvres. The results show an improvement in the consistency of density data between these four missions, and of data obtained before, during and after attitude manoeuvres of CHAMP and Swarm. The new models result in larger densities, compared to the previously used panel method. The largest average rescaling of density, by switching to the new geometry models is reached for Swarm at 32%, the smallest for GRACE at 5%. For CHAMP and GOCE, mean differences of 11% and 9% are obtained respectively. In this paper, an overview of the improvements and comparisons of data sets is provided together with an introduction to the next research phase on the gas-surface interactions.     

Numerical modeling of a Global Navigation Satellite System in a general relativistic framework

In this article we model a Global Navigation Satellite System (GNSS) in a Schwarzschild space–time, as a first approximation of the relativistic geometry around the Earth. The closed time-like and scattering light-like geodesics are obtained analytically, describing respectively trajectories of satellites and electromagnetic signals. We implement an algorithm to calculate Schwarzschild coordinates of a GNSS user who receives proper times sent by four satellites, knowing their orbital parameters; the inverse procedure is implemented to check for consistency. The constellation of satellites therefore realizes a geocentric inertial reference system with no a priori realization of a terrestrial reference frame. We perform a simulation of position determination and show that the determination of the four coordinates with a 25–32 digit accuracy takes only around 60 ms. Effects of non-gravitational perturbations on positioning errors are assessed, and methods to reduce them are sketched. In particular, inter-links between satellites could greatly enhance stability and accuracy of the positioning system. Effects of gravitational perturbations are omitted in this paper in order to make a clearer comparison between the relativistic and non-relativistic scheme, but they will be included in subsequent work. We believe that the final algorithm will be a serious alternative to the usual post-Newtonian scheme.     

Geostationary orbit determination using SATRE

A new strategy of precise orbit determination (POD) for GEO (Geostationary Earth Orbit) satellite using SATRE (SAtellite Time and Ranging Equipment) is presented. Two observation modes are proposed and different channels of the same instruments are used to construct different observation modes, one mode receiving time signals from their own station and the other mode receiving time signals from each other for two stations called pairs of combined observations. Using data from such a tracking network in China, the results for both modes are compared. The precise orbit determination for the Sino-1 satellite using the data from 6 June 2005 to 13 June 2005 has been carried out in this work. The RMS (Root-Mean-Square) of observing residuals for 3-day solutions with the former mode is better than 9.1 cm. The RMS of observing residuals for 3-day solutions with the latter mode is better than 4.8 cm, much better than the former mode. Orbital overlapping (3-day orbit solution with 1-day orbit overlap) tests show that the RMS of the orbit difference for the former mode is 0.16 m in the radial direction, 0.53 m in the along-track direction, 0.97 m in the cross-track direction and 1.12 m in the 3-dimension position and the RMS of the orbit difference for the latter mode is 0.36 m in the radial direction, 0.89 m in the along-track direction, 1.18 m in the cross-track direction and 1.52 m in the 3-dimension position, almost the same as the former mode. All the experiments indicate that a meter-level accuracy of orbit determination for geostationary satellite is achievable.     

DORIS processing at the European Space Operations Centre

This paper gives an overview of the DORIS related activities at the Navigation Support Office of the European Space Operations Centre. The DORIS activities were started in 2002 because of the launch of the Envisat satellite where ESOC is responsible for the validation of the Envisat Precise Orbits and a brief overview of the key Envisat activities at ESOC is given. Typical orbit comparison RMS values between the CNES POE (GDR-C) and the ESOC POD solution is 6.5, 18.8 and 23.1 mm in radial-, along- and cross-track direction. In the framework of the generation of the ITRF2008 ESOC participated in the reprocessing of all three space geodetic techniques; DORIS, SLR, and GPS. Here the main results of our DORIS reprocessing, in the framework of the International DORIS Service (IDS), are given. The WRMS of the weekly ESOC solution (esawd03) for the 2004–2009 period compared to the IDS-1 combined solution is of the order of 12 mm. Based on the long time series of homogeneously processed data a closer look is taken at the estimated solar radiation pressure parameters of the different satellites used in this DORIS analysis. The main aim being the stabilization of the Z-component of the geocentre estimates. We conclude that the ESOC participation to the IDS ITRF2008 contribution has been beneficial for both ESOC and the IDS. ESOC has profited significantly from the very open and direct communications and comparisons that took place within the IDS during the reprocessing campaign.     

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。