基于历史TLE的空间目标轨道预报误差演化规律研究

北美防空司令部(North American Aerospace Defense Command, NORAD)发布的双行根数(Two Line Element, TLE)是广大航天工作者最常用的轨道根数,与其对应的轨道模型是SGP4/SDP4 (Simplified General Perturbation Version 4/Simplified Deep-space Perturbation Version 4)解析模型.由于TLE中并没有包含相应的轨道精度信息,编目轨道的应用范围受到很大的限制.基于Space-Track网站发布的历史TLE数据和配套的SGP4/SDP4动力学模型,采用定轨标预报的方法统计并生成了大量目标轨道的预报误差,通过对预报轨道的时间区间划分给出了每个目标的预报误差随预报时间变化的拟合系数,并进一步对不同类型轨道预报误差的演化规律和特征进行了分类讨论,给出了4种轨道类型目标的轨道预报误差随时间演化的平均解析模型,为拓展双行根数的应用提供有价值的参考.     

An Accuracy Analysis of the SGP4/SDP4 Model

Based on the latest release of the SGP4/SDP4 (Simplified General Perturbation Version 4/ Simplified Deep-space Perturbation Version 4) model, in this paper we have designed an orbit determination program. Through calculations for the 1120 objects with various types and orbital elements selected from the space objects database, we have obtained the accuracies of the orbit determination prediction dealt with various types of space objects by the SGP4/SDP4 model. The results show that the accuracies of the near-earth objects are in the order of magnitude of 100 meters; the averages of the orbit determination accuracies of the semi-synchronous and geosynchronous orbits are, respectively, 0.7 and 1.9 km. The orbit determination accuracies of the elliptical orbit objects are related to their eccentricities. Except for few elliptical orbit objects with e > 0.8, the orbit determination errors of the vast majority of the elliptical orbit objects are all less than 10 km. By using the SGP4/SDP4 model to make 3 days predictions for near-earth objects, 30 days for semi-synchronous orbit objects, 15 days for geosynchronous orbit objects and 1 day for elliptical orbit objects, the errors of prediction generally don’t exceed 40 km.     

日月轨道计算对TLE深空编目目标预报精度的影响

双行根数(Two Line Element, TLE)作为一类广泛使用的空间物体编目数据, 其预报精度和误差特性是TLE编目 在空间碎片研究中所要关注的问题之一. TLE编目需要配合SGP4/SDP4 (Simplified General Perturbations 4/Simplified Deep Space 4)模型进行轨道预报, 对深空物体来说, 主要考虑带谐项$J_2$、$J_3$、$J_4$摄动、 第三体日月摄动和特殊轨道共振问题修正等. 其中, SGP4/SDP4模型第三体摄动计算时, 对日月轨道近似采用了长期进动根数和 简单平运动的方式, 在外推10d时存在约2$^\circ$--3${^\circ     

SGP4/SDP4模型精度分析

本文基于最新发布的SGP4/SDP4(Simplified General Perturbation Version 4/Simplified Deep-space Perturbation Version 4)模型设计了一套定轨方案,从空间目标库中挑选出不同类型和轨道参数的1120个目标进行计算,定量给出了SGP4/SDP4模型处理不同类型空间目标的定轨预报精度.结果表明:近地目标定轨精度为百米量级;半同步和同步轨道定轨精度平均为0.7和1.9km.椭圆轨道目标的定轨精度与偏心率有关,除少数e>0.8的椭圆轨道目标,绝大多数椭圆轨道目标定轨误差均小于10km.用SGP4/SDP4模型对近地目标预报3天,半同步轨道预报30天,同步轨道预报15天,椭圆轨道预报1天,预报误差一般不超过40km.     

两行根数辅助的SLR单站定轨

单站测距资料定轨的困难限制了漫反射SLR(Satellite Laser Ranging)测距资料的应用.为此,提出利用两行根数模拟多站SLR测距资料作为辅助,实现单站SLR测距资料定轨的方法.该方法对卫星Ajisai单站SLR测距资料定轨并生成5 d预报轨道,误差小于40 m,实现利用单站测距资料的轨道改进,验证了方法的可行性.     

Orbit error characteristic and distribution of TLE using CHAMP orbit data

Space object orbital covariance data is required for collision risk assessments, but publicly accessible two line element (TLE) data does not provide orbital error information. This paper compared historical TLE data and GPS precision ephemerides of CHAMP to assess TLE orbit accuracy from 2002 to 2008, inclusive. TLE error spatial variations with longitude and latitude were calculated to analyze error characteristics and distribution. The results indicate that TLE orbit data are systematically biased from the limited SGP4 model. The biases can reach the level of kilometers, and the sign and magnitude are correlate significantly with longitude.     

空间碎片轨道预报中动力学模型基准的选取

在不同的轨道预报场景中, 使用的动力学模型也不同. 例如, 在低轨空间碎片的预报中大气阻力是十分重要的摄动力, 而到了中高轨, 大气阻力就可以忽略不计. 如何为不同轨道类型的空间碎片选择最优(满足精度要求下的最简)动力学模型还没有系统、详尽的研究. 将对不同精度需求、不同轨道类型下的大批量轨道进行预报, 通过比较不同动力学模型下的预报结果, 给出各种预报场景的最优动力学模型建议. 可以为不同轨道类型的空间碎片在轨道预报时选择基准动力学模型提供参考或标准.     

The assessment of the semi-analytical method in the long-term orbit prediction of Earth satellites

To understand the long-term evolution and distribution of the space objects, it is necessary to predict their orbits. Compared with the short-term prediction of a few days, the priority concerns of the long-term orbit prediction are the calculation speed, and the accuracies of major orbital elements, including the semi-major axis and eccentricity which define the shape of the orbit, as well as the orbital inclination and the right ascension of ascending node which define the orientation of the orbit. Given these requirements, it is preferable to adopt the semi-analytical method, which averages the system over the orbital period, and integrates the averaged system using the numerical method. It is not new, however, in the available literature, we can hardly find a quantitative assessment regarding its accuracy and speed when it is applied to various types of orbits. In this paper, we would like to report our implementation and assessment of the semi-analytical method, expecting that it would help to estimate its feasibility in the long-term orbit prediction. The quantitative assessment covers the commonly used orbits for the Earth satellites. In some rare and special cases where the performance of our method appears abnormal, we discuss the reasons and possible solutions. We hope our results can provide some useful reference for the similar applications of the semi-analytical method since our method is a relatively common approach in terms of both accuracy and implementation.     

任务轨道设计

本文首先说明太空任务与轨道设计的关系 ,接着介绍轨道的基本性质。从地球重力势的观点看各种常用的绕地轨道 ,包括地球和太阳同步轨道及Molniya轨道。从扰动的观点看常用的星际轨道 ,包括LISA、ASTROD、SOHO轨道。最后对星际轨道设计 ,说明二点边界值问题的数值解法、飞掠星体的应用、最佳化的考虑 ,并用以设计 2 0 1 5年发射的ASTROD初步任务轨道。     

基于深度学习的太阳F_10.7辐射通量的短期预报研究

F_10.7太阳辐射通量作为输入参数被广泛运用于大气经验模型、电离层模型等空间环境模型,其预报精度直接影响航天器轨道预报精度.采用时间序列法统计了太阳辐射通量F10.7指数和太阳黑子数(SSN)的关系,给出了两者之间的线性关系,在此基础上提出了一种基于长短时记忆神经网络(Long and Short Term Memory,LSTM)的预报方法,方法结合了54 d太阳辐射通量指数和SSN历史数据来对F_10.7进行未来7 d短期预报,并与其他预报方法的预报结果进行了比较,结果表明:(1)所建短期预报7 d方法模型的性能优于美国空间天气预报中心(Space Weather Prediction Center, SWPC)的方法,预测值和观测值的相关系数(CC)达到0.96,同时其均方根误差约为11.62个太阳辐射通量单位(sfu),预报结果的均方根误差(RMSE)低于SWPC,下降约11%;(2)对预测的23、24周太阳活动年结果统计表明,太阳活动高年的第7 d F10.7指数预报平均绝对百分比误差(MAPE)最优可达12.9%以内,低年最优可达2...     

The Application of GIM in Precise Orbit Determination for LEO Satellites with Single-Frequency GPS Measurements

With the precise GPS ephemeris and clock error available, the iono- spheric delay is left as the dominant error source in the single-frequency GPS data. Thus, the removal of ionospheric effects is a ma jor prerequisite for an improved orbit reconstruction of LEO satellites based on the single-frequency GPS data. In this paper, the use of Global Ionospheric Maps (GIM) in kine- matic and dynamic orbit determinations for LEO satellites with single-frequency GPS pseudorange measurements is discussed first, and then, estimating the iono- spheric scale factor to remove the ionospheric effects from the C/A-code pseu- dorange measurements for both kinematic and dynamic orbit determinations is addressed. As it is known that the ionospheric delay of space-borne GPS sig- nals is strongly dependent on the orbit altitudes of LEO satellites, we select the real C/A-code pseudorange measurement data of the CHAMP, GRACE, TerraSAR-X and SAC-C satellites with altitudes between 300 km and 800 km as sample data in this paper. It is demonstrated that the approach to eliminating ionospheric effects in C/A-code pseudorange measurements by estimating the ionospheric scale factor is highly effective. Employing this approach, the accu- racy of both kinematic and dynamic orbits can be improved notably. Among those five LEO satellites, CHAMP with the lowest orbit altitude has the most remarkable improvements in orbit accuracy, which are 55.6% and 47.6% for kine- matic and dynamic orbits, respectively. SAC-C with the highest orbit altitude has the least improvements in orbit accuracy accordingly, which are 47.8% and 38.2%, respectively.     

The pendulum dilemma of fish orbits

The shape of a galaxy is constrained both by mechanisms of formation (dissipational versus dissipationless) and by the available orbit families (the shape and amount of regular and stochastic orbits). It is shown that, despite the often very flattened shapes of banana and fish orbits, these boxlet orbits generally do not fit a triaxial galaxy in detail because, similar to loop orbits, they spend too little time at the major axis of the model density distribution. This constraint from the shape of fish orbits is relaxed at (large) radii where the density profile of a galaxy is steep.     

A new search method for streams in meteor data bases and its application

A new search method for locating meteoroid streams within an orbit data base and obtaining their central core orbits is introduced. The method is based on the transformation of a data base of discrete orbits into a continuous density map. Artificial data bases are used to determine if a density is statistically unlikely to occur by random chance. A search is then run to identify all density peaks within the map that correspond to the central core of a meteoroid stream. Drummond D' criterion is used as a metric within the transformation and a D' acceptability limit, D _l, defines the length scale over which a discrete meteor orbit can have an influence on the density map. Examination of the search dependence on D _l for both real and artificial data sets indicates an appropriate standard value. A full search is run on 5280 meteor orbits from the IAU data base, detecting 16 known major and minor meteoroid streams. New central core orbits are presented for these. No major differences from the published orbits are detected, apart from possible multi-branched structure in the southern δ Aquarids.     

TLE-Aided Orbit Determination Using Single-Station SLR Data

It is difficult to use the single-station satellite laser ranging (SLR) data for orbit determination, due to the singular geometrical distribution of the observations. The single-station data produced by performing the diffuse- reflection SLR on the earth-orbiting space debris are therefore ineffective for orbit improvement. To solve this problem, we propose an orbit determination method by using single-station SLR data in aid of the two-line element set (TLE). For verifying its feasibility, this method is implemented and applied to the orbit determination of the satellite Ajisai, using the single-station SLR data of five passes in one day and the corresponding TLE. And on this basis, the five-day orbit prediction is generated, the result indicates that the errors of predicted positions are less than 40 m. In addition, the potential application of this method in the orbit improvement of space debris is discussed.     

Research on the Method of Orbit Determination Based on the Self-adaptive Stable Least p-norm Estimate

The traditional least square estimation (LSE) method for orbit determination will not be optimal if the error of observational data does not obey the Gaussian distribution. In order to solve this problem, the least p-norm (Lp) estimation method is presented in this paper to deal with the non-Gaussian distribution cases. We show that a suitable selection of parameter p may guarantee a reasonable orbit determination result. The character of Lp estimation is analyzed. It is shown that the traditional Lp estimation method is not a robust method. And a stable Lp estimating based on data depth weighting is put forward to deal with the model error and outlier. In the orbit determination process, the outlier of observational data and coarse model error can be quantitatively described by their weights. The farther is the data from the data center, the smaller is the value of data depth and the smaller is the weighted value accordingly. The result of the new Lp method is stabler than that of the traditional Lp estimation and the breakdown point could be up to 1/2. In addition, the orbit parameter is adaptively estimated by residual analysis and matrix estimation method, and the estimation efficiency is enhanced. Finally, by taking the Space-based Space Surveillance System as an example and performing simulation experiments, we show that if there are system error or abnormal value in the observational data or system error in satellite dynamical model and space-based observation platform, LSE will not be optimal even though the observational data obeys the Gaussian distribution, and the orbit determination precision by the self-adaptive robust Lp estimation method is much better than that by the traditional LSE method.     

同步卫星短弧定轨

同步卫星受到摄动力的影响,它的实际轨道有一点漂移．卫星需要不断的调轨调姿,以保证其正常运行．为了研究卫星在几小时,甚至更短的时间内的轨迹情况,采用短弧段定轨法．用动力学方法进行短弧定轨,分别研究1小时和15分钟定轨并进行比较,目的是为了在同步轨道卫星变轨后,能尽快地为卫星提供精密的预报轨道．此外,在系列短弧定轨后,得到精密轨道系列,为研究轨道变化的力学因素及研究短弧中卫星转发器时延变化规律等提供依据．     

Tidal tails of star clusters

Based on recent findings of a formation mechanism of substructure in tidal tails by Küpper et al., we investigate a more comprehensive set of N -body models of star clusters on orbits about a Milky Way like potential. We find that the predicted epicyclic overdensities arise in any tidal tail no matter which orbit the cluster follows as long as the cluster lives long enough for the overdensities to build up.
The distance of the overdensities along the tidal tail from the cluster centre depends for circular orbits only on the mass of the cluster and the strength of the tidal field, and therefore decreases monotonically with time, while for eccentric orbits the orbital motion influences the distance, causing a periodic compression and stretching of the tails and making the distance oscillate with time. We provide an approximation for estimating the distance of the overdensities in this case.
We describe an additional type of overdensity which arises in extended tidal tails of clusters on eccentric orbits, when the acceleration of the tidal field on the stellar stream is no longer homogeneous. Moreover, we conclude that a pericentre passage or a disc shock is not the direct origin of an overdensity within a tidal tail. Escape due to such tidal perturbations does not take place immediately after the perturbation but is rather delayed and spread over the orbit of the cluster. All observable overdensities are therefore of the mentioned two types. In particular, we note that substructured tidal tails do not imply the existence of dark matter substructures in the haloes of galaxies.     

Error Analysis and Trajectory Correction Maneuvers of Lunar Transfer Orbit

For a returnable lunar probe, this paper studies the characteristics of both the Earth-Moon transfer orbit and the return orbit. On the basis of the error propagation matrix, the linear equation to estimate the ?rst midcourse trajectory correction maneuver (TCM) is ?gured out. Numerical simulations are performed, and the features of error propagation in lunar transfer orbit are given. The advantages, disadvantages, and applications of two TCM strategies are discussed, and the computation of the second TCM of the return orbit is also simulated under the conditions at the reentry time.     

Orbital structure in N-body models of barred-spiral galaxies

We study the orbital structure in a series of self-consistent N -body configurations simulating rotating barred galaxies with spiral and ring structures. We perform frequency analysis in order to measure the angular and the radial frequencies of the orbits at two different time snapshots during the evolution of each N -body system. The analysis is done separately for the regular and the chaotic orbits. We thereby identify the various types of orbits, determine the shape and percentages of the orbits supporting the bar and the ring/spiral structures, and study how the latter quantities change during the secular evolution of each system. Although the frequency maps of the chaotic orbits are scattered, we can still identify concentrations around resonances. We give the distributions of frequencies of the most important populations of orbits. We explore the phase-space structure of each system using projections of the 4D surfaces of section. These are obtained via the numerical integration not only of the orbits of test particles, but also of the real N -body particles. We thus identify which domains of the phase space are preferred and which are avoided by the real particles. The chaotic orbits are found to play a major role in supporting the shape of the outer envelope of the bar as well as the rings and the spiral arms formed outside corotation.     

天体轨道长期数值积分的误差估计方法

数值积分方法是进行天体力学研究的重要工具, 尤其对于行星历表的研究工作而言. 由于在使用数值方法计算天体轨道时, 最终误差通常是难以预知的, 所以在面对精度要求较高或者积分时间较长的工作时具体积分方案的设计---尤其是当使用定步长方法时的步长选择---需要十分谨慎, 因为这将意味着是否能在时间成本可以被接受的范围内使解的精度达到要求. 因此, 在使用数值方法解决实际问题时如何快速寻找效率与精度之间的最佳平衡点是每一个数值积分方法的设计者与使用者都会面临的难题. 为解决这一问题, 在定步长条件下对数值积分方法的舍入误差概率分布函数以及截断误差积累量对步长的依赖关系和随时间的增长关系进行了深入研究. 基于所得结论, 提出了一种仅需较少的数值实验资料即可对选择任意时间步长积分至任意积分时刻时的舍入误差概率分布函数与截断误差积累量进行准确估计的方法, 并使用Adams-Cowell方法对该误差估计方法在圆周期轨道条件下进行了验证. 该误差估计方法在未来有望用于不同数值算法的性能对比研究, 同时也可以对数值积分方法求解实际轨道问题时的决策工作带来重要帮助.