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.     

Simulation of long-term rotational dynamics of large space debris: A TOPEX/Poseidon case study

Accurate knowledge of the rotational dynamics of a large space debris is crucial for space situational awareness (SSA), whether it be for accurate orbital predictions needed for satellite conjunction analyses or for the success of an eventual active debris removal mission charged with stabilization, capture and removal of debris from orbit. In this light, the attitude dynamics of an inoperative satellite of great interest to the space debris community, the joint French and American spacecraft TOPEX/Poseidon, is explored. A comparison of simulation results with observations obtained from high-frequency satellite range measurements is made, showing that the spacecraft is currently spinning about its minor principal axis in a stable manner. Predictions of the evolution of its attitude motion to 2030 are presented, emphasizing the uncertainty on those estimates due to internal energy dissipation, which could cause a change of its spin state in the future. The effect of solar radiation pressure and the eddy-current torque are investigated in detail, and insights into some of the satellite’s missing properties are provided. These results are obtained using a novel, open-source, coupled orbit-attitude propagation software, the Debris SPin/Orbit Simulation Environment (D-SPOSE), whose primary goal is the study of the long-term evolution of the attitude dynamics of large space debris.     

基于线性协方差方法的交会对接误差分析

将线性协方差分析方法和蒙特卡罗仿真相结合,按交会任务和飞行特征把交会过程分为变轨飞行、自由飞行和中途速度修正三种特征段,研究了状态误差的传播规律和交会过程中各种误差对交会对接精度的影响。在变轨飞行段,分析了追踪航天器的姿态误差、控制系统性能状态估计误差,以及目标航天器轨道摄动对状态误差传播的影响。在自由飞行段,分析了追踪航天器估计状态误差的先验值和测轨误差对状态误差传播的影响。在中途速度修正段,分析了追踪航天器姿态误差和控制系统性能误差对状态误差传播的影响。仿真结果表明,误差分析方法设计合理,可以指导交会对接的轨道设计工作,能对已经设计好的交会策略进行误差分析和设计验证。     

Space debris mitigation strategies and practices in geosynchronous transfer orbits

Missions to geosynchronous orbits remain one of the most important elements of space launch traffic, accounting for 40% of all missions to Earth orbit and beyond during the four-year period 2000–2003. The vast majority of these missions leave one or more objects in geosynchronous transfer orbits (GTOs), contributing on a short-term or long-term basis to the space debris population. National and international space debris mitigation guidelines seek to curtail the accumulation of debris in orbits which penetrate the regions of low Earth orbit and of geosynchronous orbit. The orbital lifetime of objects in GTO can be greatly influenced by the initial values of perigee, inclination, and right ascension of the orbital plane, leading to orbital lifetimes of from less than one month to more than 100 years. An examination of the characteristic GTOs employed by launch vehicles from around the world has been conducted. The consequences of using perigees above 300 km and super-synchronous apogees, typically above 40,000 km, have been identified. In addition, the differences in orbital behavior of launch vehicle stages and mission-related debris in GTOs have been investigated. Greater coordination and cooperation between space launch service providers and spacecraft designers and owners could significantly improve overall compliance with guidelines to mitigate the accumulation of debris in Earth orbit.     

Uncertainty-aware Cube algorithm for medium-term collision risk assessment

The number of Earth orbiting objects is constantly growing, and some orbital regions are becoming risky environments for space assets of interest, which are increasingly threatened by accidental collisions with other objects, especially in Low-Earth Orbit (LEO). Collision risk assessment is performed by various methods, both covariance and non-covariance based. The Cube algorithm is a non-covariance-based method used to estimate the collision rates between space objects, whose concept consists in dividing the space in cubes of fixed dimension and, at each time instant, checking if two or more objects share the same cube. Up to now its application has been limited to the long-term scenarios of orbital debris evolutionary models, where considering the uncertainties is not necessary and impractical. Within operative contexts, instead, medium-term collision risk analysis may be an important task, in which the propagation-related uncertainties play a prominent role, but the timescale poses challenges for the application of standard covariance-based conjunction analysis techniques. In this framework, this paper presents an approach for the evaluation of the medium-term collision frequency for objects in LEO, called Uncertainty-aware Cube method. It is a modified version of the Cube, able to take the possible errors in the space objects’ position into account for the detection of the conjunctions. As an object’s orbit is propagated, the along-track position error grows more and more, and each object could potentially be in a different position with respect to the one determined by numerical propagation and, thus, in a different cube. Considering the uncertainties, at each time instant the algorithm associates more than one cube to each object and checks if they share at least one cube. If so, a conjunction is detected and a degree of confidence is evaluated. The performance of the method is assessed in different LEO scenarios and compared to the original Cube method.     

Apparent rotation properties of space debris extracted from photometric measurements

Knowledge about the rotation properties of space debris objects is essential for the active debris removal missions, accurate re-entry predictions and to investigate the long-term effects of the space environment on the attitude motion change. Different orbital regions and object’s physical properties lead to different attitude states and their change over time.Since 2007 the Astronomical Institute of the University of Bern (AIUB) performs photometric measurements of space debris objects. To June 2016 almost 2000 light curves of more than 400 individual objects have been acquired and processed. These objects are situated in all orbital regions, from low Earth orbit (LEO), via global navigation systems orbits and high eccentricity orbit (HEO), to geosynchronous Earth orbit (GEO). All types of objects were observed including the non-functional spacecraft, rocket bodies, fragmentation debris and uncorrelated objects discovered during dedicated surveys. For data acquisition, we used the 1-meter Zimmerwald Laser and Astrometry Telescope (ZIMLAT) at the Swiss Optical Ground Station and Geodynamics Observatory Zimmerwald, Switzerland. We applied our own method of phase-diagram reconstruction to extract the apparent rotation period from the light curve. Presented is the AIUB’s light curve database and the obtained rotation properties of space debris as a function of object type and orbit.     

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。     

LEO空间碎片甚短弧角度数据初轨确定方法对比

光学观测是空间目标观测中最常见的一种观测方式。采用扫描模式工作时光学观测得到的观测弧段弧长通常很短,有时甚至不到被观测空间目标运行周期的1%,这样的角度数据被称为甚短弧角度数据。基于近圆LEO空间碎片地基实测场景,研究比较仅利用角度数据进行初始轨道确定常用方法的性能差异,分析观测弧长对不同初轨确定算法的定轨成功率和误差的影响,为初轨确定工作提供参考。对比分析了常用的几种方法,包括Laplace方法、Gauss方法、Gooding方法和近几年提出的距离搜索算法等。大规模实测数据处理结果显示,距离搜索算法的成功率高于90%,初轨半长轴统计误差仅为25 km。初轨结果表明,距离搜索算法定轨成功率高于其他算法。研究成果可为解决空间碎片初轨确定问题提供参考。      

Analysis of the orbit lifetime of CubeSats in low Earth orbits including periodic variation in drag due to attitude motion

It is estimated that more than 22,300 human-made objects are in orbit around the Earth, with a total mass above 8,400,000 kg. Around 89% of these objects are non-operational and without control, which makes them to be considered orbital debris. These numbers consider only objects with dimensions larger than 10 cm. Besides those numbers, there are also about 2000 operational satellites in orbit nowadays. The space debris represents a hazard to operational satellites and to the space operations. A major concern is that this number is growing, due to new launches and particles generated by collisions. Another important point is that the development of CubeSats has increased exponentially in the last years, increasing the number of objects in space, mainly in the Low Earth Orbits (LEO). Due to the short operational time, CubeSats boost the debris population. One of the requirements for space debris mitigation in LEO is the limitation of the orbital lifetime of the satellites, which needs to be lower than 25 years. However, there are space debris with longer estimated decay time. In LEÓs, the influence of the atmospheric drag is the main orbital perturbation, and is used in maneuvers to increment the losses in the satellite orbital energy, to locate satellites in constellations and to accelerate the decay.The goal of the present research is to study the influence of aerodynamic rotational maneuver in the CubeSat?s orbital lifetime. The rotational axis is orthogonal to the orbital plane of the CubeSat, which generates variations in the ballistic coefficient along the trajectory. The maneuver is proposed to accelerate the decay and to mitigate orbital debris generated by non-operational CubeSats. The panel method is selected to determine the drag coefficient as a function of the flow incident angle and the spinning rate. The pressure distribution is integrated from the satellite faces at hypersonic rarefied flow to calculate the drag coefficient. The mathematical model considers the gravitational potential of the Earth and the deceleration due to drag. To analyze the effects of the rotation during the decay, multiple trajectories were propagated, comparing the results obtained assuming a constant drag coefficient with trajectories where the drag coefficient changes periodically. The initial perigees selected were lower than 400 km of altitude with eccentricities ranging from 0.00 to 0.02. Six values for the angular velocity were applied in the maneuver. The technique of rotating the spacecraft is an interesting solution to increase the orbit decay of a CubeSat without implementing additional de-orbit devices. Significant changes in the decay time are presented due to the increase of the mean drag coefficient calculated by the panel method, when the maneuver is applied, reducing the orbital lifetime, however the results are independent of the angular velocity of the satellite.     

基于驻留时间比的近地空间碎片环境建模

为分析近地空间碎片的分布规律,提出了一种以碎片在空间网格内驻留时间为基础的碎片环境统计建模方法.该方法利用多项式拟合和求根方法统计碎片在空间网格内的停留时间,获取模型基础数据,并据此采用多项式预测、插值和时间序列分析等技术,综合分析空间碎片的分布与演化规律.给出了一个基于双行根数(TLE,Two Line Elements)数据的建模实例,该实例通过了ORDEM2000模型的对比验证,并获得了一些更精细的近地空间碎片环境特征.所得建模方法和分析结论可为长期运行的近地航天器轨道设计、碰撞风险评估及防护等提供技术支撑.     

Yarkovsky-Schach effect on space debris motion

The Yarkovsky-Schach effect is a small perturbation affecting Earth satellites and space debris illuminated by the Sun. It was first applied to the orbit of LAGEOS satellites as an explanation of the residuals in orbital elements. In this work, we carry out several numerical integration tests taking into consideration various orbit and rotation parameters, in order to analyse this effect in a broader context. The semi-major axis variations remain small and depend on the spin axis attitude with respect to the Sun. We show that the force amplitude is maximised for orbits inclined with $i\approx$?20–30°. We also observe the influence on other orbital elements, notably on the orbit inclination. However, these effects are clearly observed only on long timescales; in our simulations, we propagated the orbits for 200?y. The Yarkovsky-Schach effect is thus confirmed to have a minuscule magnitude. It should be taken into account in studies requiring high-precision orbit determination, or on expanded timescales.     

基于解体事件的空间碎片轨道演化算法研究

针对航天器解体事件所生成的空间碎片的演化过程,进行了数学分析,确定了新生成的空间碎片的速度增量,在该增量作用下碎片轨道会发生变更,本文根据该增量得出了空间碎片在轨道变更后的轨道根数,分析了在大气阻力摄动作用下,空间碎片的数目和轨道分布的演化情况,给出了相关结果,结果表明此算法可行。     

Advanced ensemble modeling method for space object state prediction accounting for uncertainty in atmospheric density

For objects in the low Earth orbit region, uncertainty in atmospheric density estimation is an important source of orbit prediction error, which is critical for space traffic management activities such as the satellite conjunction analysis. This paper investigates the evolution of orbit error distribution in the presence of atmospheric density uncertainties, which are modeled using probabilistic machine learning techniques. The recently proposed “HASDM-ML,” “CHAMP-ML,” and “MSIS-UQ” machine learning models for density estimation (Licata and Mehta, 2022b; Licata et al., 2022b) are used in this work. The investigation is convoluted because of the spatial and temporal correlation of the atmospheric density values. We develop several Monte Carlo methods, each capturing a different spatiotemporal density correlation, to study the effects of density uncertainty on orbit uncertainty propagation. However, Monte Carlo analysis is computationally expensive, so a faster method based on the Kalman filtering technique for orbit uncertainty propagation is also explored. It is difficult to translate the uncertainty in atmospheric density to the uncertainty in orbital states under a standard extended Kalman filter or unscented Kalman filter framework. This work uses the so-called “consider covariance sigma point (CCSP)” filter that can account for the density uncertainties during orbit propagation. As a test-bed for validation purposes, a comparison between CCSP and Monte Carlo methods of orbit uncertainty propagation is carried out. Finally, using the HASDM-ML, CHAMP-ML, and MSIS-UQ density models, we propose an ensemble approach for orbit uncertainty quantification for four different space weather conditions.     

一种基于TLE数据的轨道异常分析方法

空间在轨物体的轨道异常是航天工程及预警领域普遍关注的问题,及时发现轨道异常意义重大,通过分析空间物体的轨道异常,可以及时发现和识别规避事件或碰撞事件,还可以了解监测网的能力.本文提出一种基于TLE数据的简单的轨道异常分析方法——长半轴变化法.该方法快速有效,应用到低轨在用卫星和美俄解体碎片的异常分析中,异常物体正确识别率可达到100%;对美俄解体碎片进行轨道异常分析后得出,美国空间监视网可以稳定探测90%以上的解体碎片.      

空间碎片碰撞预警研究

介绍了空间碎片的分布和危害，阐明了航天器进行碎片预警规避的必要性，讨论了碎片碰撞预警技术中的关键问题，用已有的碰撞和规避实例对自行研制的软件进行了计算检验，结果证明了软件的正确性，也说明了国内进行碎片预警工作的可行性．     

Analysis of laser ranges and angular measurements data fusion for space debris orbit determination

In the framework of space debris, the orbit determination process is a fundamental step, both, for researchers and for satellite operators. The accurate knowledge of the orbit of space debris objects is needed to allow space debris characterization studies and to avoid unnecessary collision avoidance maneuvers.The accuracy of the results of an orbit determination process depends on several factors as the number, the accuracy, the kind of processed measurements, their distribution along the orbit, and the object-observer relative geometry. When the observation coverage of the target orbit is not homogeneous, the accuracy of the orbit determination can be improved processing different kind of observables. Recent studies showed that the satellite laser ranging technique can be successfully applied to space debris.In this paper, we will investigate the benefits of using laser ranges and angular measurements for the orbit determination process. We will analyze the influence of the number of used observations, of the covered arc of orbit, of each observable, and of the observation geometry on the estimated parameters. Finally, using data acquired on short observation arcs, we analyze the achievable accuracies for the orbital regimes with the highest space debris density, and to the consequences of the data fusion on catalog maintenance operations. The results shown are obtained using only real data (both angular and laser measurements) provided by sensors of the Swiss Optical Ground Station and Geodynamics Observatory Zimmerwald owned by the Astronomical Institute of the University of Bern (AIUB) and for some studies also using ranges provided from other stations of the International Laser Ranging Service (ILRS).     

Debris flux comparisons from the Goldstone Radar,Haystack Radar,and Hax Radar prior,during, and after the last solar maximum

The continual monitoring of the low Earth orbit (LEO) debris environment using highly sensitive radars is essential for an accurate characterization of these dynamic populations. Debris populations are continually evolving since there are new debris sources, previously unrecognized debris sources, and debris loss mechanisms that are dependent on the dynamic space environment. Such radar data are used to supplement, update, and validate existing orbital debris models. NASA has been utilizing radar observations of the debris environment for over a decade from three complementary radars: the NASA JPL Goldstone radar, the MIT Lincoln Laboratory (MIT/LL) Long Range Imaging Radar (known as the Haystack radar), and the MIT/LL Haystack Auxiliary radar (HAX). All of these systems are highly sensitive radars that operate in a fixed staring mode to statistically sample orbital debris in the LEO environment. Each of these radars is ideally suited to measure debris within a specific size region. The Goldstone radar generally observes objects with sizes from 2 mm to 1 cm. The Haystack radar generally measures from 5 mm to several meters. The HAX radar generally measures from 2 cm to several meters. These overlapping size regions allow a continuous measurement of cumulative debris flux versus diameter from 2 mm to several meters for a given altitude window. This is demonstrated for all three radars by comparing the debris flux versus diameter over 200 km altitude windows for 3 nonconsecutive years from 1998 to 2003. These years correspond to periods before, during, and after the peak of the last solar cycle. Comparing the year to year flux from Haystack for each of these altitude regions indicate statistically significant changes in subsets of the debris populations. Potential causes of these changes are discussed. These analysis results include error bars that represent statistical sampling errors.     

The impact of alternative mission models on the future orbital debris environment

In reviewing discussions of future directions for space activity, it becomes obvious that there are a large number of groups formulating a wide diversity of plans for the future use of space. These plan alternatives are being made to account for user needs, technology development constraints, economic constraints, and launch support, and each of the plans will have direct or indirect effects on the orbital debris environment in terms of mass to orbit, deposition of operational debris, and control of accidental breakups. Thus it is important to develop the ability to project future debris states for a range of possible space traffic scenarios. The impact that these possible traffic environments would have on space operations forms the basis for studies of alternative options for the usage of space. In this paper, the effects on the orbital debris environment of a base-line mission model and two alternatives are investigated, using a numerical debris environment simulation code under development at JSC.     

利用TLE数据分析LEO卫星轨道异常的新方法——————综合判据法

及时准确地发现在轨卫星的轨道异常意义重大. 通过有效的异常算法, 能够找出发生轨道异常的碎片或航天器, 为空间碎片碰撞预警系统分析和验证碰撞事件提供数据支持. 通过对利用TLE (Two Line Elements)数据分析LEO在轨卫星轨道异常的方法研究, 提出了一个利用单个卫星相邻根数时间差控制加综合判据的判别方法. 分析表明, 相对于取单一因素阈值的判别方法, 综合判据法能够最大限度地减少漏判, 并且保持相对较高的判断准确率.