An empirical solar radiation pressure model for satellites moving in the orbit-normal mode

We present a family of empirical solar radiation pressure (SRP) models suited for satellites orbiting the Earth in the orbit normal (ON) mode. The proposed ECOM-TB model describes the SRP accelerations in the so-called terminator coordinate system. The choice of the coordinate system and the SRP parametrization is based on theoretical assumptions and on simulation results with a QZS-1-like box-wing model, where the SRP accelerations acting on the solar panels and on the box are assessed separately. The new SRP model takes into account that in ON-mode the incident angle of the solar radiation on the solar panels is not constant like in the yaw-steering (YS) attitude mode. It depends on the elevation angle of the Sun above the satellite’s orbital plane. The resulting SRP vector acts, therefore, not only in the Sun-satellite direction, but has also a component normal to it. Both components are changing as a function of the incident angle. ECOM-TB has been used for precise orbit determination (POD) for QZS-1 and BeiDou2 (BDS2) satellites in medium (MEO) and inclined geosynchronous Earth orbits (IGSO) based on IGS MGEX data from 2014 and 2015. The resulting orbits have been validated with SLR, long-arc orbit fits, orbit misclosures, and by the satellite clock corrections based on the orbits. The validation results confirm that—compared to ECOM2—ECOM-TB significantly (factor 3–4) improves the POD of QZS-1 in ON-mode for orbits with different arc lengths (one, three, and five days). Moderate orbit improvements are achieved for BDS2 MEO satellites—especially if ECOM-TB is supported by pseudo-stochastic pulses (the model is then called ECOM-TBP). For BDS2 IGSOs, ECOM-TB with its 9 SRP parameters appears to be over-parameterized. For use with BDS2 IGSO spacecraft we therefore developed a minimized model version called ECOM-TBMP, which is based on the same axis decomposition as ECOM-TB, but has only 2 SRP parameters and is supported by pseudo-stochastic parameters, as well. This model shows a similar performance as ECOM-TB with short arcs, but an improved performance with (3-day) long-arcs. The new SRP models have been activated in CODE’s IGS MGEX solution in Summer 2018. Like the other ECOM models the ECOM-TB derivatives might be used together with an a priori model.     

Influence of the 2:1 resonance in the orbits of GPS satellites

Due to the characteristics of their orbits the GPS satellites are submitted to the following main perturbations: terrestrial gravitational field, luni-solar gravitational attraction and solar radiation pressure (including the effects of the Earth's shadow). An additional perturbation arises due to the 2:1 commensurability of the orbital period of the satellite with the period of the Earth's rotation. An analytical theory is briefly presented to solve the equations of motion including the previously mentioned effects. The analytical solution, based on the Lie-Hori method, is compared with a numerical integration of the equations.     

The adjusted optical properties for Galileo/BeiDou-2/QZS-1 satellites and initial results on BeiDou-3e and QZS-2 satellites

Solar Radiation Pressure (SRP) is the dominant non-gravitational perturbation for GNSS (Global Navigation Satellite System) satellites. In the absence of precise surface models, the Empirical CODE Orbit Models (ECOM, ECOM2) are widely used in GNSS satellite orbit determination. Based on previous studies, the use of an a priori box-wing model enhances the ECOM model, especially if the spacecraft is a stretched body satellite. However, so far not all the GNSS system providers have published their metadata. To ensure a precise use of the a priori box-wing model, we estimate the optical parameters of all the Galileo, BeiDou-2, and QZS-1 (Quasi Zenith Satellite System) satellites based on the physical processes from SRP to acceleration. Validation using orbit prediction proves that the adjusted parameters of Galileo and QZS-1 satellites exhibit almost the same performance as the corresponding published and “best guess” values. Whereas, the estimated parameters of BeiDou-2 satellites demonstrate an improvement of more than 60% over the initial “guess” values. The resulting optical parameters of all the satellites are introduced into an a priori box-wing model, which is jointly used with ECOM and ECOM2 model in the orbit determination. Results show that the pure ECOM2 model exhibits better performance than the pure ECOM model for Galileo, BeiDou-2 GEO and QZS-1 orbits. Combined with the a priori box-wing model the ECOM model (ECOM+BW) results in the best Galileo, BeiDou-2 GEO and QZS-1 orbits. The standard deviation (STD) of satellite laser ranging residuals reduce by about 20% and 5% with respect to the pure ECOM2 model for Galileo and BeiDou-2 GEO orbits, while the reductions are about 40% and 60% for QZS-1 orbits in yaw-steering and orbit-normal mode respectively. BeiDou-2 IGSO and MEO satellite orbits do not benefit much from the a priori box-wing model. In summary, we suggest setting up a unified SRP model of ECOM+BW for Galileo, QZS-1, and BeiDou-2 orbits based on the adjusted metadata. In addition, we estimate the optical parameters of BeiDou-3e and QZS-2 satellites using a limited number of tracking stations. Results regarding the unified SRP model indicate the same advantages, the STD of satellite laser ranging residuals reduces by about 30% and 20% for QZS-2 and BeiDou-3e orbits respectively over orbit products without a priori model. The estimation procedure is effective and easy to apply to the new emerging satellites in the future.     

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.     

2006年12月13日太阳射电暴对GPS观测的影响

日地空间环境不仅影响航天器运行和安全, 也是导航、定位和通信等无线 电应用系统主要的误差源. 其中来自太阳L波段的射电暴被认为是全球导航卫星 系统(GNSS)稳定和性能的潜在威胁因素, 当L波段射电爆发达到一定阈值时, 将给用户带来不同程度的射电噪声干扰, 严重时会引起接收机失锁和定位服务 中断. 本文对2006年12月13日太阳射电暴对GPS造成的影响进行了研究, 利用太阳射电 观测数据、L波段闪烁观测数据和向阳面不同区域的GPS观测网数据, 分析 GPS观测对射电暴的响应. 结果表明, 此次事件对GPS观测产生了明显的影响, 射 电暴期间GPS发生幅度闪烁事件和明显失锁现象, 多个台站上空的多颗GPS 卫星 信号完全中断长达6min左右, 且多个台站上空锁定的卫星数目小于4颗, 使 得GPS定位完全失效. 相对而言, 射电暴期间日下点附近的GPS台站受到的影响 比远离日下点的大.      

零偏模式下太阳光压对轨迹保持控制影响分析

从某颗在轨卫星地面轨迹漂移“异常”出发,分析了该现象发生的内在机理,建立了零偏模式下（卫星姿态偏航角保持为零）光压摄动力沿迹方向累积效应解析模型,并基于历史观测数据通过轨道改进估计模型参数。最后,利用该卫星2018年真实地面轨迹对新模型预报精度进行验证。结果表明,采用新模型后,卫星地面轨迹漂移预报误差得到明显改善,为该卫星轨迹保持控制策略制定提供了技术支持。     

Shape optimization of a three-dimensional membrane-structured solar sail using an angular momentum unloading strategy

A shape of the satellite’s solar sail membrane is essential for unloading angular momentum in the three-axis stabilized attitude control system because the three-dimensional solar sail can receive solar radiation pressure from arbitrary directions. In this paper, the objective is the shape optimization of a three-dimensional membrane-structured solar sail using the angular momentum unloading strategy. We modelled and simulated the solar radiation pressure torque, for unloading angular momentum. Using the simulation system, since the unloading angular momentum rate is maximized, the shape of the three-dimensional solar sail was optimized using a Genetic algorithm and Sequential Quadratic Programming. The unloading velocity in the optimized shaped solar sail was greatly improved with respect to a conventional flat or pyramid solar sail.     

Computation of radiation environment during ground level enhancements 65, 69 and 70 at equatorial region and flight altitudes

The radiation environment in the troposphere of the Earth is governed by cosmic rays of galactic and solar origin. During major solar energetic particles events the radiation environment changes dramatically. As a results the risk of biological effects due to exposure to ionizing radiation of aircrew increases. Here we present a numerical model for computation of absorbed dose in air due to cosmic rays of galactic and solar origin. It is applied for computation of radiation environment at flight altitude in the equatorial region during several major ground level enhancements, namely GLE65 on 28 October 2003, GLE69 on 20 January 2005 and GLE70 on 13 December 2006. The model is based on a full Monte Carlo simulation of cosmic ray induced atmospheric cascade. The cascade simulation is carried out with CORSIKA 6.990 code with corresponding hadron generators FLUKA 2011 and QGSJET II. The contribution of different cascade components, namely electromagnetic, hadron and muon is explicitly obtained. The spectra of arriving solar energetic particles are calculated from ground level measurements with neutron monitors and satellite data from GOES. The obtained results are discussed.     

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.      

Impact of orbit modeling on DORIS station position and Earth rotation estimates

The high precision of estimated station coordinates and Earth rotation parameters (ERP) obtained from satellite geodetic techniques is based on the precise determination of the satellite orbit. This paper focuses on the analysis of the impact of different orbit parameterizations on the accuracy of station coordinates and the ERPs derived from DORIS observations. In a series of experiments the DORIS data from the complete year 2011 were processed with different orbit model settings. First, the impact of precise modeling of the non-conservative forces on geodetic parameters was compared with results obtained with an empirical-stochastic modeling approach. Second, the temporal spacing of drag scaling parameters was tested. Third, the impact of estimating once-per-revolution harmonic accelerations in cross-track direction was analyzed. And fourth, two different approaches for solar radiation pressure (SRP) handling were compared, namely adjusting SRP scaling parameter or fixing it on pre-defined values.     

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.     

Comparison of standard TEC models with a Neural Network based TEC model using multistation GPS TEC around the northern crest of Equatorial Ionization Anomaly in the Indian longitude sector during the low and moderate solar activity levels of the 24th solar cycle

The highest Total Electron Content (TEC) values in the world normally occur at Equatorial Ionization Anomaly (EIA) region resulting in largest ionospheric range delay values observed for any potential Space Based Augmentation System (SBAS). Reliable forecasting of TEC is crucial for satellite based navigation systems. The day to day variability of the location of the anomaly peak and its intensity is very large. This imposes severe limitations on the applicability of commonly used ionospheric models to the low latitude regions. It is necessary to generate a mathematical ionospheric forecasting and mapping model for TEC based on physical ionospheric influencing parameters. A model, IRPE-TEC, has been developed based on real time low latitude total electron content data using GPS measurements from a number of stations situated around the northern crest of the EIA during 2007 through 2011 to predict the vertical TEC values during the low and moderate solar activity levels of the 24th solar cycle. This model is compared with standard ionospheric models like International Reference Ionosphere (IRI) and Parameterized Ionospheric Model (PIM) to establish its applicability in the equatorial region for accurate predictions.     

Drag and energy accommodation coefficients during sunspot maximum

Conditions appropriate to gas-surface interactions on satellite surfaces in orbit have not been successfully duplicated in the laboratory. However, measurements by pressure gauges and mass spectrometers in orbit have revealed enough of the basic physical chemistry that realistic theoretical models of the gas-surface interaction can now be used to calculate physical drag coefficients. The dependence of these drag coefficients on conditions in space can be inferred by comparing the physical drag coefficient of a satellite with a drag coefficient fitted to its observed orbital decay. This study takes advantage of recent data on spheres and attitude stabilized satellites to compare physical drag coefficients with the histories of the orbital decay of several satellites during the recent sunspot maximum. The orbital decay was obtained by fitting, in a least squares sense, the semi-major axis decay inferred from the historical two-line elements acquired by the US Space Surveillance Network. All the principal orbital perturbations were included, namely geopotential harmonics up to the 16th degree and order, third body attraction of the Moon and the Sun, direct solar radiation pressure (with eclipses), and aerodynamic drag, using the Jacchia-Bowman 2006 (JB2006) model to describe the atmospheric density. After adjusting for density model bias, a comparison of the fitted drag coefficient with the physical drag coefficient has yielded values for the energy accommodation coefficient as well as for the physical drag coefficient as a function of altitude during solar maximum conditions. The results are consistent with the altitude and solar cycle variation of atomic oxygen, which is known to be adsorbed on satellite surfaces, affecting both the energy accommodation and angular distribution of the reemitted molecules.     

一种NRLMSISE-00模型太阳辐射校正方法

根据空间天气的状态,调整大气模型的相关输入参数能够减小模型的计算误差.通过对比CHAMP卫星在轨大气密度探测数据与NRLMSISE-00模式的计算结果发现,通过调整F_10.7的输入,使轨道大气密度积分的模式计算结果与探测结果之间的误差达到最小,此时的F_10.7被称为理想F_10.7输入（F*）.进一步的分析发现,F*与太阳紫外辐射MgII指数存在很好的相关性,因此可以选择其他的太阳紫外辐射代理参数取代F_10.7,从而减小模型计算误差.本文采用神经网络技术,建立新的太阳紫外辐射代理参量F_euv与MgII,F_10.7等的对应模型,能够根据当日参数值计算F_euv.研究结果表明,新的代理参数能够有效减小NRLMSISE-00的计算误差.      

Mixed surface reflection functions determined from a priori knowledge and satellite radiance

A method to derive mesoscale area means of surface solar flux densities from a priori knowledge and actual cloudfree satellite radiances is presented. It is based on the concept of the mixed reflection function which can be derived from existing data. Herewith and with actual atmospheric data derived from the operational meteorological network the cloudfree radiation field is computed. By comparison of computed and measured satellite radiance the surface albedo of the model is tuned. In a case study this method is applied to an agricultural region called La Mancha, Spain, and comprehensively checked against airborne radiance measurements. The surface albedo can be determined to about ± 0.01.     

X射线脉冲星自主导航的卫星运动方程

基于X射线脉冲星的卫星自主导航模型中, 无论从理论上还是从测量精度方面考虑, 光子到达时间测量方程(观测方程)和卫星运动方程(状态方程)应在同一参考系中讨论. 在DSX体系中太阳系质心系是惯性系, 可以使用现行时间测量方程, 但卫星摄动加速度中除了地球多极矩、日月引力摄动和太阳光压三项外, 还应考虑相对论修正项, 计算表明该修正项导致卫星位置误差在10m量级. 而地心系是非惯性系, 在此系中卫星运动方程中的相对论效应导致卫星误差在10 cm量级, 因而可以忽略, 但要将BCRS的时间测量方程转换到GCRS中. 在此基础上建立的导航模型较为精确和完整.      

Estimation of differential code biases with Jason-2/3 onboard GPS observations

With the continuous deployment of Low Earth Orbit (LEO) satellites, the estimation of differential code biases (DCBs) based on GNSS observations from LEO has gained increasing attention. Previous studies on LEO-based DCB estimation are usually using the spherical symmetry ionosphere assumption (SSIA), in which a uniform electron density is assumed in a thick shell. In this study, we propose an approach (named the SHLEO method) to simultaneously estimate the satellite and LEO onboard receiver DCBs by modeling the distribution of the global plasmaspheric total electron content (PTEC) above the satellite orbit with a spherical harmonic (SH) function. Compared to the commonly used SSIA method, the SHLEO model improves the GPS satellite DCB estimation accuracy by 13.46% and the stability by 22.34%, respectively. Compared to the GPS satellite DCBs estimated based on the Jason-3-only observations, the accuracy and monthly stability of the satellite DCBs can be improved by 14.42% and 26.8% when both Jason-2 and Jason-3 onboard observations are jointly processed. Compared with the Jason-2 solutions, the GPS satellite DCB estimates based on the fusion of Jason-2 and Jason-3 observations have an improved consistency of better than 18.26% and 9.71% with the products provided by the Center for Orbit Determination in Europe (CODE) and Chinese Academy of Sciences (CAS). Taking the DCB products provided by the German Aerospace Center (DLR) as references, there is no improvement in accuracy of the GPS satellite DCB estimates based on the fusion of Jason-2 and Jason-3 observations than the Jason-2 solutions alone. A periodic variation is found in the time series of both the Jason-3 and Jason-2 onboard receiver DCB estimates. Preliminary analysis of the PTEC distribution based on the estimated SH coefficients are also presented.     

临近空间太阳紫外辐射环境模拟与地区差异

太阳紫外辐射是临近空间能量输入的主要来源之一,对其在中层大气的辐射特性进行研究,是研究临近空间大气成分与密度变化、光化学反应以及动力学过程的重要基础。依托“鸿鹄”临近空间探测专项计划,利用MODTRAN5辐射传输模型及卫星实测数据,模拟并对比中国11个主要地形区上空临近空间（20~50 km）紫外辐射（200~400 nm）垂直分布和季节演变的异同,计算了臭氧含量、太阳天顶角和日地距离等关键因素对辐射强度的影响。结果表明,各地形区的辐射流量垂直分布廓线和年较差垂直分布廓线较为一致,在地理位置上毗邻的地区辐射特性及季节演变较为接近,但在太阳紫外的不同波段之间区别较大。研究成果为临近空间探测实验提供了数据支撑,为大气反演等相关领域提供参考。      

GPS derived TEC and foF2 variability at an equatorial station and the performance of IRI-model

The ionosphere induces a time delay in transionospheric radio signals such as the Global Positioning System (GPS) signal. The Total Electron Content (TEC) is a key parameter in the mitigation of ionospheric effects on transionospheric signals. The delay in GPS signal induced by the ionosphere is proportional to TEC along the path from the GPS satellite to a receiver. The diurnal monthly and seasonal variations of ionospheric electron content were studied during the year 2010, a year of extreme solar minimum (F10.7 = 81 solar flux unit), with data from the GPS receiver and the Digisonde Portable Sounder (DPS) collocated at Ilorin (Geog. Lat. 8.50°N, Long. 4.50°E, dip −7.9°). The diurnal monthly variation shows steady increases in TEC and F2-layer critical frequency (foF2) from pre-dawn minimum to afternoon maximum and then decreases after sunset. TEC show significant seasonal variation during the daytime between 0900 and 1900 UT (LT = UT + 1 h) with a maximum during the March equinox (about 35 TECU) and minimum during the June solstice (about 24 TECU). The GPS-TEC and foF2 values reveal a weak seasonal anomaly and equinoctial asymmetry during the daytime. The variations observed find their explanations in the amount of solar radiation and neutral gas composition. The measured TEC and foF2 values were compared with last two versions of the International Reference Ionosphere (IRI-2007 and IRI-2012) model predictions using the NeQuick and CCIR (International Radio Consultative Committee) options respectively in the model. In general, the two models give foF2 close to the experimental values, whereas significant discrepancies are found in the predictions of TEC from the models especially during the daytime. The error in height dependent thickness parameter, daytime underestimation of equatorial drift and contributions of electrons from altitudes above 2000 km have been suggested as the possible causes.