基于TLE的弹道系数计算方法及应用分析

针对仅使用两行要素（Two Line Element，TLE）作为数据源的应用需求，研究了基于TLE轨道衰减的弹道系数计算方法。介绍了一种常用的基于两组TLE的直接计算法，分析TLE选取间隔对结果精度的影响；提出了一种基于多组TLE的迭代计算方法，以降低异常TLE对计算结果的影响；从弹道系数计算效果、在再入预报中的应用等方面对这两种方法进行比较分析。结果表明，两种方法各有优劣，基于多组TLE的迭代计算法稳定性更高、受TLE精度的影响更小；由于数据区间更短，基于两组TLE的计算结果对短期轨道衰减特性反应得更准确，用于临近再入时的预报效果更好。     

Track-to-object association algorithm based on TLE filtering

This paper focuses on the track-to-object association problem based on the two-line elements (TLE) set. The TLE’s short-term propagation error characteristics are analyzed to capture its uncertainty. Further, a four-step track-to-object association algorithm is designed for the optical observation data. First, for too-short arc tracklets, a circular orbit determination algorithm is proposed to calculate the inclination and the right ascension of the ascending node. Second, the TLEs are filtered based on these results. Nearly 96% of the TLEs can be filtered, which significantly improves the association efficiency. The last two steps consist of two association processes. A first-order association process is implemented first to get candidate objects, with the angles root mean square error as the metric. Then a precise association process checks the candidate objects and gives the final association result. The proposed approach is tested with simulated and observed data, respectively. With simulated data, the true positive rate is 98.7%. With the observed data, the association results were validated using the precise orbit ephemerides.     

空间碎片环境与碰撞预警仿真系统设计

在轨编目航天器数目已超过了9000,为了保证航天任务的顺利完成,必须对可能威胁到任务轨道的空间目标进行分析,文章首先对两行轨道根数和SGP4／SDP4轨道预报模型进行了分析,在此基础上建立了空间目标数据库及空间碎片环境与碰撞预警仿真和数据可视化系统。     

On prediction of re-entry time of an upper stage from GTO

The evolution of objects in geostationary transfer orbit (GTO) is determined by a complex interplay of atmospheric drag and luni-solar gravity. These orbits are highly eccentric (eccentricity >0.7) and have large variations in velocity and perturbations during a revolution. The periodic changes in the perigee altitudes of these orbits are mainly due to the gravitational perturbations of the Sun and the Moon. The re-entry time of the objects in such orbits is sensitive to the initial conditions. The aim of this paper is to study the re-entry time of the cryogenic stage of the Indian geo-synchronous launch vehicle, GSLV-F04/CS, which has been decaying since 2 September 2007 from initial orbit with eccentricity equal to 0.706. Two parameters, initial eccentricity and ballistic coefficient, are chosen for optimal estimation. It is known that the errors are more in eccentricity for the observations based on two line elements (TLEs). These two parameters are computed with response surface method using a genetic algorithm for the selected eight different zones, based on rough linear variation of the mean apogee altitude during 200 days orbit evolution. The study shows that the GSLV-F04/CS will re-enter between 5 December 2010 and 7 January 2011. The methodology is also applied to study the re-entry of six decayed objects (cryogenic stages of GSLV and Molniya satellites). Good agreement is noticed between the actual and the predicted re-entry times. The absolute percentage error in re-entry prediction time for all the six objects is found to be less than 7%. The present methodology is being adopted at Vikram Sarabhai Space Centre (VSSC) to predict the re-entry time of GSLV-F04/CS.     

Improved orbit predictions using two-line elements

The density of orbital space debris constitutes an increasing environmental challenge. There are two ways to alleviate the problem: debris mitigation and debris removal. This paper addresses collision avoidance, a key aspect of debris mitigation. We describe a method that contributes to achieving a requisite increase in orbit prediction accuracy for objects in the publicly available two-line element (TLE) catalog. Batch least-squares differential correction is applied to the TLEs. Using a high-precision numerical propagator, we fit an orbit to state vectors derived from successive TLEs. We then propagate the fitted orbit further forward in time. These predictions are validated against precision ephemeris data derived from the international laser ranging service (ILRS) for several satellites, including objects in the congested sun-synchronous orbital region. The method leads to a predicted range error that increases at a typical rate of 100 m per day, approximately a 10-fold improvement over individual TLE’s propagated with their associated analytic propagator (SGP4). Corresponding improvements for debris trajectories could potentially provide conjunction analysis sufficiently accurate for an operationally viable collision avoidance system based on TLEs only.     

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.      

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.     

Use of two-line element data for thermosphere neutral density model calibration

Traditional empirical thermospheric density models are widely used in orbit determination and prediction of low-Earth satellites. Unfortunately, these models often exhibit large density errors of up to around 30% RMS. Density errors translate into orbit errors, adversely affecting applications such as re-entry operations, manoeuvre planning, collision avoidance and precise orbit determination for geodetic missions. The extensive database of two-line element (TLE) orbit data contains a wealth of information on satellite drag, at a sufficiently high spatial and temporal resolution to allow a calibration of existing neutral density models with a latency of one to two days. In our calibration software, new TLE data for selected objects is converted to satellite drag data on a daily basis. The resulting drag data is then used in a daily adjustment of density model calibration parameters, which modify the output of an existing empirical density model with the aim of increasing its accuracy. Two different calibration schemes have been tested using TLE data for about 50 objects during the year 2000. The schemes involve either height-dependent scale factors to the density or corrections to CIRA-72 model temperatures, which affect the density output based on a physical model. Both schemes have been applied with different spherical harmonic expansions of the parameters in latitude and local solar time. Five TLE objects, varying in perigee altitude between 280 and 530 km, were deliberately not used during calibration, in order to provide independent validation. Even with a single daily parameter, the RMS density model error along their tracks can already be reduced from the 30% to the 15% level. Adding additional parameters results in RMS errors lower than 12%.     

Propagation errors analysis of TLE data

Orbit position uncertainty is an important factor for collision avoidance issues. For a single object with high frequency historical data, we can attain its position uncertainty easily. But sometimes data is not enough for errors analysis, orbits need to be classified. In this paper error analysis is made from two-line element sets data (TLEs). The Simplified General Perturbations-4 (SGP4) propagator was used. Statistical errors of debris and R/B are given for lower-altitude orbits which are classified by perigee altitude and eccentricity. The errors results and analysis for SSO (the Sun synchronous orbit) typical orbits are obtained. At last atmospheric drag as a main cause of downrange errors in lower-altitude orbit is analyzed. BSTAR in TLEs is modified to improve prediction precision.     

TLE预报精度改进及碰撞预警中的应用

双行根数（Two Line Elements,TLE）是目前唯一公开发布且编目最完备的地球轨道空间目标编目数据,由于其根数的特殊性,必须配合SGP4/SDP4 使用导致其预报精度有限. 通过对TLE+SGP4/SDP4预报误差源的分析,利用历史TLE数据生成准观测数据重新进行轨道拟合,针对不同轨道高度和面积质量比情况,确定相应拟合周期,得出了基于弹道系数先验信息有效确定面积质量比的经验方法,对多个独立时段拟合后轨道根数结合数值方法的预报误差进行统计,结果表明,拟合后的TLE根数预报精度与稳定性有很大程度提升. 利用实例对拟合TLE在碰撞预警中的应用进行分析,认为该方法对航天工程中碰撞预警置信度的提高具有重要意义.      

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.      

基于期望最大算法的空间事件及异常值探测

美国ELSET数据库提供的TLE数据是目前使用最广泛的数据,在热层大气密度反演、弹道系数估计、碰撞预警等领域具有重要作用。受空间环境扰动、空间事件以及TLE产生过程等共同影响,ELSET数据库包含大量亟待清理的异常值和识别的空间事件,例如发布错误的TLE、轨道根数异常和Bstar异常。现有方法在清理异常轨道根数时缺乏统一性,需要使用不同的技术,清理流程较为繁杂,并且仅适用于特定轨道区域的少数目标。为克服现有方法的弊端,提出了一种基于期望最大算法的滑动窗口–多项式拟合预报方法,对含有轨道机动的碎片以及受空间环境影响的碎片进行异常值与空间事件探测。研究表明,该方法能够灵活处理不同空间环境下的异常值与空间事件探测,具有普适性,适用于所有轨道碎片。      

Orbital debris–debris collision avoidance

We focus on preventing collisions between debris and debris, for which there is no current, effective mitigation strategy. We investigate the feasibility of using a medium-powered (5 kW) ground-based laser combined with a ground-based telescope to prevent collisions between debris objects in low-Earth orbit (LEO). The scheme utilizes photon pressure alone as a means to perturb the orbit of a debris object. Applied over multiple engagements, this alters the debris orbit sufficiently to reduce the risk of an upcoming conjunction. We employ standard assumptions for atmospheric conditions and the resulting beam propagation. Using case studies designed to represent the properties (e.g. area and mass) of the current debris population, we show that one could significantly reduce the risk of nearly half of all catastrophic collisions involving debris using only one such laser/telescope facility. We speculate on whether this could mitigate the debris fragmentation rate such that it falls below the natural debris re-entry rate due to atmospheric drag, and thus whether continuous long-term operation could entirely mitigate the Kessler syndrome in LEO, without need for relatively expensive active debris removal.     

TLE数据误差与基于TLE数据的交会预报分析

目前普遍使用TLE数据进行在轨物体的危险交会预报. TLE数据误差不仅会影响交会预报的准确性, 还是计算碰撞概率的必要参数, 因此, 只有准确估计TLE数据误差, 才能得到可信的碰撞概率数值. 本文采用两种方法, 即TLE数据自比和与高精度轨道预报数据相比较的方法, 计算TLE数据误差, 并分别利用TLE数据和高精度数据计算同一交会, 比较两种数据预报的交会结果差异. 结果表明, 采用TLE根数自比方法的计算误差偏小, 而使用精轨数据作为校准数据所得到的TLE误差更接近真实误差, 计算碰撞概率更为合理, 有利于减少虚警.      

行星际南向磁场事件与强磁暴

利用１９７８－１９８８年期间的太阳风和地磁资料对行星际磁场（ＩＭＦ）南向分量Ｂｓ事件（即Ｂｓ〉１０ｎＴ及其所驱动的错向电场ＶＢｓ〉５ｍＶ／ｍ、持续时间△Ｔ〉３ｈ的事件）与弱磁暴（Ｄｓｔ≤－１００ｎＴ）关系进行了分析。结果表明,１００％的Ｂｓ事件能能引起磁暴的发生,但其中只有８４％为强磁暴;强磁暴的发生都与较强的ＩＭＦ Ｂｓ活动密切相关,但只有６８％的强磁共伴随Ｂｓ事件而发生;Ｂｓ事件与强磁暴并不是     

空间非合作目标双行轨道根数快速生成算法

针对空间目标TLE拟合过程中可能出现的奇点问题,提出了基于无奇异变换的空间目标双行轨道根数（TLE）生成算法. 为提高观测平台对空间目标状态估计效率,提出带有自适应遗忘因子的非线性最小二乘递推算法,利用最速下降法在线修正遗忘因子,使得估计值有较快的跟踪速度和较小的稳态误差. 仿真结果表明,该TLE生成算法的数据处理速度和轨道预报误差满足要求,可用于低轨目标的天基监视.      

CHAMP和GRACE-A/B反演大气密度数据评估分析

利用Colorado大学公开发布的2001-2008年CHAMP和GRACE-A/B三颗卫星加速度计反演的400km高度上的大气密度数据,以大气模式NLRMSISE-00为参考,分析反演数据与模式值的误差特点、产生误差的原因、密度的变化及合理性,并通过卫星轨道两行根数（TLE）的反演结果进行验证,主要结论如下.CHAMP密度值整体稍高于GRACE-A/B,CHAMP密度与模式值之间的误差整体小于GRACE-A/B,2007-2008年 GRACE-A/B与模式的相对误差变化起伏较大.2001年CHAMP与模式存在整体偏差,通过相似空间环境条件下的密度变化比对以及利用TLE的反演结果验证,确定2001年的CHAMP反演密度整体偏低.CHAMP及GRACE-A/B密度变化个例显示,卫星密度值会出现一些个性化特征,使用时应根据需求进行分析处理.研究结果可为合理应用该数据提供参考.      

A Partially Orthogonal EnKF approach to atmospheric density estimation using orbital debris

A key requirement for accurate trajectory prediction and space situational awareness is knowledge of how non-conservative forces affect space object motion. These forces vary temporally and spatially, and are driven by the underlying behavior of space weather particularly in Low Earth Orbit (LEO). Existing trajectory prediction algorithms adjust space weather models based on calibration satellite observations. However, lack of sufficient data and mismodeling of non-conservative forces cause inaccuracies in space object motion prediction, especially for uncontrolled debris objects. The uncontrolled nature of debris objects makes them particularly sensitive to the variations in space weather. Our research takes advantage of this behavior by utilizing observations of debris objects to infer the space environment parameters influencing their motion.The hypothesis of this research is that it is possible to utilize debris objects as passive, indirect sensors of the space environment. We focus on estimating atmospheric density and its spatial variability to allow for more precise prediction of LEO object motion. The estimated density is parameterized as a grid of values, distributed by latitude and local sidereal time over a spherical shell encompassing Earth at a fixed altitude of 400 km. The position and velocity of each debris object are also estimated. A Partially Orthogonal Ensemble Kalman Filter (POEnKF) is used for assimilation of space object measurements to estimate density.For performance comparison, the scenario characteristics (number of objects, measurement cadence, etc.) are based on a sensor tasking campaign executed for the High Accuracy Satellite Drag Model project. The POEnKF analysis details spatial comparisons between the true and estimated density fields, and quantifies the improved accuracy in debris object motion predictions due to more accurate drag force models from density estimates. It is shown that there is an advantage to utilizing multiple debris objects instead of just one object. Although the work presented here explores the POEnKF performance when using information from only 16 debris objects, the research vision is to utilize information from all routinely observed debris objects. Overall, the filter demonstrates the ability to estimate density to within a threshold of accuracy dependent on measurement/sensor error. In the case of a geomagnetic storm, the filter is able to track the storm and provide more accurate density estimates than would be achieved using a simple exponential atmospheric density model or MSIS Atmospheric Model (when calm conditions are assumed).