大气阻力参数修正对低轨空间目标轨道预报精度的改进

对于低轨空间目标, 大气阻力是影响轨道预报精度的主要摄动力. 本文提出了一种 基于空间环境数据和神经网络模型的空间目标大气阻力参数修正方法, 基于目 标的历史两行元根数, 通过模拟得到外推一天轨道预报中预报结果与观测数据 符合最好的阻力调制系数, 分析表明其与太阳F_10.7指数和地磁Ap指数具有很好的相关性. 根据已有数据, 构建神经网络模型, 实现对阻力调制系数 的补偿计算, 从而改进低轨目标外推一天的轨道预报. 结果表明, 神经网络模 型相比两行元根数能够更及时地对空间环境变化进行响应. 将该方案应用于天 宫一号和国际空间站的外推一天轨道预报, 验证了方案的正确性和普适性, 对 地磁扰动引起的较大预报误差改进效果更好, 误差能够降低50%~60%; 平均而言, 预报精度可以提高约30%, 改进成功率达到80%左右.      

利用二维核回归估计的大气密度模式修正

传统经验大气密度模式预测大气密度存在的较大误差会引起低轨卫星轨道预报误差,对卫星的再入轨、控制计划、碰撞规避及精密定轨造成不利影响.利用天宫一号卫星探测数据,针对大气NRLMSISE-00模式计算的误差特点,在地磁相对平静(Ap ≤ 30)的时间段内,对相近地方时和纬度的模式误差分布进行分析发现,相近地方时和纬度的模式误差分布基本相同.利用二维核回归估计方法,对与预测点相近地方时和纬度的样本误差进行加权,估计预测点处的模式误差,进而按距离预测日期天数的长短,采用加权修正法对模式预测结果进行修正,修正后大气模式误差的均方差(RMS)由14.09%降至4.05%.研究结果表明,该修正方法可以显著提高大气密度预报精度.      

High accuracy satellite drag model (HASDM)

The dominant error source in force models used to predict low-perigee satellite trajectories is atmospheric drag. Errors in operational thermospheric density models cause significant errors in predicted satellite positions, since these models do not account for dynamic changes in atmospheric drag for orbit predictions. The Air Force Space Battlelab’s High Accuracy Satellite Drag Model (HASDM) estimates and predicts (out three days) a dynamically varying global density field. HASDM includes the Dynamic Calibration Atmosphere (DCA) algorithm that solves for the phases and amplitudes of the diurnal and semidiurnal variations of thermospheric density near real-time from the observed drag effects on a set of Low Earth Orbit (LEO) calibration satellites. The density correction is expressed as a function of latitude, local solar time and altitude. In HASDM, a time series prediction filter relates the extreme ultraviolet (EUV) energy index E_10.7 and the geomagnetic storm index a_p, to the DCA density correction parameters. The E_10.7 index is generated by the SOLAR2000 model, the first full spectrum model of solar irradiance. The estimated and predicted density fields will be used operationally to significantly improve the accuracy of predicted trajectories for all low-perigee satellites.     

Modeling satellite drag coefficients with response surfaces

Satellite drag coefficients are a major source of uncertainty in predicting the drag force on satellites in low Earth orbit. Among other things, accurately predicting the orbit requires detailed knowledge of the satellite drag coefficient. Computational methods are an important tool in computing the drag coefficient but are too intensive for real-time and predictive applications. Therefore, analytic or empirical models that can accurately predict drag coefficients are desired. This work uses response surfaces to model drag coefficients. The response surface methodology is validated by developing a response surface model for the drag coefficient of a sphere where the closed-form solution is known. The response surface model performs well in predicting the drag coefficient of a sphere with a root mean square percentage error less than 0.3% over the entire parameter space. For more complex geometries, such as the GRACE satellite, the Hubble Space Telescope, and the International Space Station, the model errors are only slightly larger at about 0.9%, 0.6%, and 1.0%, respectively.     

一种基于温度参数的热层密度修正方法

热层大气的阻力效应是影响低轨航天器大量空间操作的重要因素, 尤其是经验密度模式, 其固有的至少15%的内符合误差已严重制约航天器轨道计算精度的提高. 针对广泛应用的经验密度模式, 选择物理背景简明、关联参数较少的JACCHIA71模式, 以地磁平静条件下的全球散逸层顶温度最小值T_c及125 km高度拐点温度T_x为对象, 建立密度相对于上述温度参数的条件方程, 推导密度相对于温度参数的解析偏导数, 并给出其最小二乘解. 同时, 利用CHAMP卫星数据对模式进行修正, 模式平均误差从40%降低至3%左右. 通过TG01飞行器的轨道预报比较, 修正前后轨道预报位置精度从2 km提升至1 km左右. 经过CHAMP卫星和TG01飞行器的实测数据检验, 验证了修正算法的正确性和有效性.      

基于实时观测数据的大气密度模式修正

针对国际大气密度模式NRLMSISE-00, 以中国神舟飞船探测数据为基础, 提出一种基于实时大气密度观测数据的模式修正方法. 通过计算分析模式计算结果与探测数据的误差分布特征, 针对地磁相对平静期(Ap≤ 30)模式计算的误差特点, 建立了一种平均误差修正方法, 即认为在相对平静期, 在相同纬度和地方时, 模式误差基本相同, 某一时刻模式预测误差可以近似用与其相同纬度和地方时的平均误差来替代, 从而对模式预测结果进行修正. 以神舟4号探测数据为基础, 通过对模式预测结果采用两种方式进行修正, 可以看到模式误差得到了一定的改善. 采用误差库累积准实时修正, 修正后的误差由原来的20 %降至6 %; 采用误差库5天滑动预报修正后, 模式提前1, 2, 3天的预测误差由原来的20 %分别降至7.8 %, 9.4 %和10.5%.      

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.      

同步轨道通信卫星占频保轨现象分析与实测

为了应对国际电信联盟对卫星频轨资源的相关规定，卫星运营商可能会选择将卫星送至另一个不同的轨位并连续保持 90 天来启用该位置的频率指配.这种变轨行为称作“占频保轨”，是一些同步通信卫星的常规操作.本文以国际通信组织的 INTELSAT 系列卫星为研究对象，基于双行根数 (TLE) 和SGP4/SDP4模型计算了67个INTELSAT (国际通信卫星) 的自发射以来的轨道数据，提出了基于密度和k 最近邻的离群点检测来筛选数据野值的方法，提高了数据准确性；对这些卫星的占频保轨行为进行统计和分析，提出我国卫星运营商应充分利用国际规则，维护自身太空权益的建议.     

Towards accurate atmospheric mass density determination Using precise positional information of space objects

This paper presents a new method of deriving atmospheric mass densities with a high temporal resolution from precise orbit data of low earth orbiting (LEO) space objects. This method is based on the drag perturbation equation of the semi-major axis of the orbit of LEO space objects which relates the change rate of the semi-major axis to the atmospheric mass density. The effectiveness of the new method is evaluated using the GFZ-ISDC GPS rapid science orbit (RSO) products of the CHAMP satellite over a time period of 3 months. The densities derived using this new method and obtained from accelerometer data are compared and good agreements are achieved. An example of using the derived density to generate good orbit prediction for CHAMP is presented.     

空间TDICCD相机动态信噪比计算方法研究

信噪比是空间光学相机系统的主要设计指标之一,可用于表征相机的辐射性能。文章通过建立遥感卫星轨道模型,分析计算一年中任意时刻用太阳高度角和卫星观测角描述太阳、卫星、地面目标点之间的相对位置关系,并将计算得到的卫星观测角和太阳高度角等参数导入大气传输软件MODTRAN,输出在相机入瞳处的地面目标光谱辐亮度,再根据信噪比的计算方法,最后完成TDICCD相机动态的信噪比计算值。通过该方法,可以计算任一时刻任一观测目标的信噪比,这将有利于判断在某一时刻的能量是否满足观测要求,以随时改变TDICCD的探测器级数,使得成像像质达到最佳。     

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.     

空间目标碰撞预警的协方差计算与应用

碰撞概率是碰撞预警工程中空间目标危险交会的重要判据之一,其计算精度会受到预报协方差计算精度的影响. 本文统计计算了两种形式的预报协方差. 一是利用精密数值预报模型对卫星精密根数进行预报,将预报根数与精密根数的差作为样本,统计得出1～7天不同预报期的预报协方差;二是采用 SGP4/SDP4预报模型对TLE数据进行预报,将预报根数与TLE根数的差作为样本,统计得出1～7d不同预报期的预报协方差. 分别分析两种方法中包含变轨过程和无变轨情况下的轨道预报精度. 结合2012年某低轨道卫星的危险交会,分析了采用不同协方差时,协方差精度对碰撞预警精度的影响. 协方差计算可为实际碰撞预警工程提供参考.      

Drag coefficient modeling for grace using Direct Simulation Monte Carlo

Drag coefficient is a major source of uncertainty in predicting the orbit of a satellite in low Earth orbit (LEO). Computational methods like the Test Particle Monte Carlo (TPMC) and Direct Simulation Monte Carlo (DSMC) are important tools in accurately computing physical drag coefficients. However, the methods are computationally expensive and cannot be employed real time. Therefore, modeling of the physical drag coefficient is required. This work presents a technique of developing parameterized drag coefficients models using the DSMC method. The technique is validated by developing a model for the Gravity Recovery and Climate Experiment (GRACE) satellite. Results show that drag coefficients computed using the developed model for GRACE agree to within 1% with those computed using DSMC.     

基于单纯形法的TLE轨道确定

TLE数据库是目前公开获得轨道信息的唯一来源，其包含的空间目标将持续增加.利用TLE数据库获得精确的定轨结果已成为研究重点.由于TLE数据本身精度未知且存在波动，需要利用历史TLE数据对参考时刻的TLE状态进行轨道确定.常用方法为最小二乘法，但是该方法具有局限性，需要较为精确的初始值，且误差评估不可靠，解易产生发散.为克服现有方法的局限性，本文提出了一种局部搜索算法——单纯形调优法来实现TLE轨道确定.为避免构建的初始单纯形搜索得到的最优解属于局部最优，引入蒙特卡罗方法对初始单纯形进行采样，获得一系列解的统计分布，通过求该分布的期望和方差获得最终结果.研究结果表明，将单纯形调优法获得的结果用于传播预报可显著降低位置和速度误差.      

利用卫星两行轨道根数反演热层密度

两行轨道根数（TLEs）是基于一般摄动理论产生的用于预报地球轨道飞行器位置和速度的一组轨道参数,通过求解大气阻力微分方程,可反演出热层大气密度. 本文选取近圆轨道CHAMP卫星和椭圆轨道Explorer8卫星,以两行轨道根数数据为基础,计算反弹道系数,并根据不同轨道特征采用两种不同反演方法对热层大气密度进行研究. 结果表明,这两种方法反演得到的大气密度与实测值均符合较好,其中CHAMP卫星的反演结果和经验模式值相对于实测值的误差分别为7.94%和13.94%,Explorer8卫星的误差分别为9.04%和14.32%. 相比模式值,利用两行轨道根数数据反演的热层大气密度更接近于实测值,说明该方法可以作为获取大量可靠大气密度数据的一种有效途径.      

Estimation of ballistic coefficients of low altitude debris objects from historical two line elements

This paper presents a new method for estimating ballistic coefficients (BCs) of low perigee debris objects from their historical two line elements (TLEs). The method uses the drag perturbation equation of the semi-major axis of the orbit. For an object with perigee altitude below 700 km, the variation in the mean semi-major axis derived from the TLE is mainly caused by the atmospheric drag effect, and therefore is used as the source in the estimation of the ballistic coefficient. The method is tested using the GRACE satellites, and a number of debris objects with external ballistic coefficient values, and agreements of about 10% are achieved.     

Thermospheric neutral density response to solar forcing

Recent measurements by the Solar EUV (Extreme Ultra Violet) Experiment (SEE) aboard the Thermosphere–Ionosphere–Mesosphere Energetics and Dynamics satellite (TIMED) provide solar EUV spectral irradiance with adequate spectral and temporal resolution, and thus the opportunity to use solar measurements directly in upper atmospheric general circulation models. Thermospheric neutral density is simulated with the NCAR Thermosphere–Ionosphere–Electrodynamic General Circulation Model (TIEGCM) using TIMED/SEE measurements and using the EUVAC solar proxy model. Neutral density is also calculated using the NRLMSISE-00 empirical model. These modeled densities are then compared to density measurements derived from satellite drag data. It is found that using measured solar irradiance in the general circulation model can improve density calculations compared to using the solar proxy model. It is also found that the general circulation model can improve upon the empirical model in simulating geomagnetic storm effects and the solar cycle variation of neutral density.     

Differential code bias estimation based on uncombined PPP with LEO onboard GPS observations

Differential Code Bias (DCB) is an essential correction that must be provided to the Global Navigation Satellite System (GNSS) users for precise position determination. With the continuous deployment of Low Earth Orbit (LEO) satellites, DCB estimation using observations from GNSS receivers onboard the LEO satellites is drawing increasing interests in order to meet the growing demands on high-quality DCB products from LEO-based applications, such as LEO-based GNSS signal augmentation and space weather research. Previous studies on LEO-based DCB estimation are usually using the geometry-free combination of GNSS observations, and it may suffer from significant leveling errors due to non-zero mean of multipath errors and short-term variations of receiver code and phase biases. In this study, we utilize the uncombined Precise Point Positioning (PPP) model for LEO DCB estimation. The models for uncombined PPP-based LEO DCB estimation are presented and GPS observations acquired from receivers onboard three identical Swarm satellites from February 1 to 28, 2019 are used for the validation. The results show that the average Root Mean Square errors (RMS) of the GPS satellite DCBs estimated with onboard data from each of the three Swarm satellites using the uncombined PPP model are less than 0.18 ns when compared to the GPS satellite DCBs obtained from IGS final daily Global Ionospheric Map (GIM) products. Meanwhile, the corresponding average RMS of GPS satellite DCBs estimated with the conventional geometry-free model are 0.290, 0.210, 0.281 ns, respectively, which are significantly larger than those obtained with the uncombined PPP model. It is also noted that the estimated GPS satellite DCBs by Swarm A and C satellites are highly correlated, likely attributed to their similar orbit type and space environment. On the other hand, the Swarm receiver DCBs estimated with uncombined PPP model, with Standard Deviation (STD) of 0.065, 0.037 and 0.071 ns, are more stable than those obtained from the official Swarm Level 2 products with corresponding STD values of 0.115, 0.101, and 0.109 ns, respectively. The above indicates that high-quality DCB products can be estimated based on uncombined PPP with LEO onboard observations.     

Validation of GOCE densities and evaluation of thermosphere models

Atmospheric densities from ESA’s GOCE satellite at a mean altitude of 270 km are validated by comparison with predictions from the near real time model HASDM along the GOCE orbit in the time frame 1 November 2009 through 31 May 2012. Except for a scale factor of 1.29, which is due to different aerodynamic models being used in HASDM and GOCE, the agreement is at the 3% (standard deviation) level when comparing daily averages. The models NRLMSISE-00, JB2008 and DTM2012 are compared with the GOCE data. They match at the 10% level, but significant latitude-dependent errors as well as errors with semiannual periodicity are detected. Using the 0.1 Hz sampled data leads to much larger differences locally, and this dataset can be used presently to analyze variations down to scales as small as 150 km.     

Time synchronization of new-generation BDS satellites using inter-satellite link measurements

Autonomous satellite navigation is based on the ability of a Global Navigation Satellite System (GNSS), such as Beidou, to estimate orbits and clock parameters onboard satellites using Inter-Satellite Link (ISL) measurements instead of tracking data from a ground monitoring network. This paper focuses on the time synchronization of new-generation Beidou Navigation Satellite System (BDS) satellites equipped with an ISL payload. Two modes of Ka-band ISL measurements, Time Division Multiple Access (TDMA) mode and the continuous link mode, were used onboard these BDS satellites. Using a mathematical formulation for each measurement mode along with a derivation of the satellite clock offsets, geometric ranges from the dual one-way measurements were introduced. Then, pseudoranges and clock offsets were evaluated for the new-generation BDS satellites. The evaluation shows that the ranging accuracies of TDMA ISL and the continuous link are approximately 4?cm and 1?cm (root mean square, RMS), respectively. Both lead to ISL clock offset residuals of less than 0.3?ns (RMS). For further validation, time synchronization between these satellites to a ground control station keeping the systematic time in BDT was conducted using L-band Two-way Satellite Time Frequency Transfer (TWSTFT). System errors in the ISL measurements were calibrated by comparing the derived clock offsets with the TWSTFT. The standard deviations of the estimated ISL system errors are less than 0.3?ns, and the calibrated ISL clock parameters are consistent with that of the L-band TWSTFT. For the regional BDS network, the addition of ISL measurements for medium orbit (MEO) BDS satellites increased the clock tracking coverage by more than 40% for each orbital revolution. As a result, the clock predicting error for the satellite M1S was improved from 3.59 to 0.86?ns (RMS), and the predicting error of the satellite M2S was improved from 1.94 to 0.57?ns (RMS), which is a significant improvement by a factor of 3–4.