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.      

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.      

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.      

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.      

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.      

基于预报偏差的LEO航天器轨道异常检测

针对由轨道控制、大气环境、碰撞等因素造成的低轨(LEO)航天器轨道突变问题,提出了一种基于预报偏差的轨道异常检测方法。选择LEO轨道的半长轴和倾角作为特征轨道参数,利用SGP4模型长期项对目标的两行轨道要素(TLE)进行预报得到特征轨道参数的预报值,通过对特征轨道参数的编目数据和预报数据进行平滑后求差得到预报偏差序列,基于马氏距离对预报偏差数据的两个分量进行联合异常检测。对Terra卫星2010年的机动事件分析结果同NASA发布的其机动历史相吻合,表明该方法可以有效地检测航天器轨道异常的次数、时间和类型,可应用于空间目标的监视与空间态势的感知。     

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.      

基于雷达测距和测速的GEO目标实时关联算法

针对航迹密集情况下地球同步轨道（GEO）目标容易关联错误的问题，提出了一种基于雷达测距和测速二维判决的GEO目标实时关联算法。利用空间目标两行轨道根数（TLE）建立待关联初始库属目标集；根据空间目标轨道预报误差扩散规律设置粗关联门限，得到二次关联库属目标集；利用雷达测距和测速精度高的特点构建二次关联代价函数，根据归一化加权均方根误差最小原则得到关联结果。仿真结果表明：该算法在目标航迹密集的情况下取得了较好的关联效果，具有较高的关联正确率。     

基于多项式近似的空间碎片群体轨道预报算法

快速准确地分析空间碎片群轨道演化行为对于其他在轨航天器碰撞规避至关重要。在各摄动力的作用下,空间碎片群演化运动呈现出复杂的非线性特征。空间碎片群体个体数量巨大,如果通过对空间碎片群中每个空间碎片进行轨道积分来分析群体预报的方法会导致计算量过大。针对该问题,提出一种基于多项式近似的轨道快速预报分析方法。该方法将空间碎片群分为少量的标称碎片和其他大量关联碎片。针对标称碎片的轨道预报采用数值积分求解保证预报精度;而针对其他大量的关联碎片轨道预报问题,采用多项式泰勒展开半解析方法求解,从而在保证预报精度的前提下有效减少空间碎片群轨道预报的计算量。为了验证方法的有效性,对不同空间碎片群进行了轨道预报仿真。仿真结果表明,当轨道预报精度设定在1m范围内时,多项式近似算法的计算量较蒙特卡洛方法计算效率提高了2.2~17.2倍,验证了所提出方法的有效性。     

基于多冲量能耗估算的小推力任务窗口搜索

针对小推力轨道设计中任务窗口参数具有范围跨度大、非连续性强、对设计结果影响显著等特点,提出了一种基于多冲量能耗估算的任务窗口搜索方法.该方法基于多冲量轨道和小推力轨道的能耗一致性,先由朗伯特两冲量轨道经过数次迭代扩展快速获得多冲量轨道,再通过多冲量轨道能耗估算对任务区间进行全局栅格搜索,最终得到任务窗口的可行区域.仿真结果表明:1)该方法同时适用于交会和飞越任务;2)同朗伯特两冲量相比,它与小推力轨道能耗的一致性更强;3)同Sims和Flanagan最优多冲量相比,计算时间缩短了1～2个量级,计算效率显著提高.地球—火星交会任务的仿真应用表明,该方法只需8.59s即可获得任务窗口的可行区域,进而快速给出小推力最优转移轨道,验证了该方法的有效性.     

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.     

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。      

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.     

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.     

Optimising filtering of two-line element sets to increase re-entry prediction accuracy for GTO objects

Predicting re-entry epoch of space objects enables managing the risk to ground population. Predictions are particularly difficult for objects in highly-elliptical orbits, and important for objects with components that can survive re-entry, e.g. rocket bodies (R/Bs). This paper presents a methodology to filter two-line element sets (TLEs) to facilitate accurate re-entry prediction of such objects. Difficulties in using TLEs for precise analyses are highlighted and a set of filters that identifies erroneous element sets is developed. The filter settings are optimised using an artificially generated TLE time series. Optimisation results are verified on real TLEs by analysing the automatically found outliers for exemplar R/Bs. Based on a study of 96 historical re-entries, it is shown that TLE filtering is necessary on all orbital elements that are being used in a given analysis in order to avoid considerably inaccurate results.     

Accurate orbit predictions for debris orbit manoeuvre using ground-based lasers

Orbit manoeuvre of low Earth orbiting (LEO) debris using ground-based lasers has been proposed as a cost-effective means to avoid debris collisions. This requires the orbit of the debris object to be determined and predicted accurately so that the laser beam can be locked on the debris without the loss of valuable laser operation time. This paper presents the method and results of a short-term accurate LEO (<900 km in altitude) debris orbit prediction study using sparse laser ranging data collected by the EOS Space Debris Tracking System (SDTS). A main development is the estimation of the ballistic coefficients of the LEO objects from their archived long-term two line elements (TLE). When an object is laser tracked for two passes over about 24 h, orbit prediction (OP) accuracy of 10–20 arc seconds for the next 24–48 h can be achieved – the accuracy required for laser debris manoeuvre. The improvements in debris OP accuracy are significant in other applications such as debris conjunction analyses and the realisation of daytime debris laser tracking.     

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.