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.     

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。     

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.     

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.      

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．     

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.     

卫星规避方案量化分析方法研究

空间碎片数量日益增多,为保护在轨卫星的运行安全,需要针对碎片碰撞制定规避方案,用来规避碰撞风险.本文在调研国外卫星规避机动流程的基础上,分别研究了卫星规避相关的轨道机动方式、轨道预报模型以及交会风险计算模型,建立了卫星规避方案量化分析方法,为规避方案的选择提供参考.      

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).     

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。     

基于高斯伪谱法的碰撞规避策略研究

为保证在轨卫星运行安全，对于碰撞概率较高的空间交会情况需要进行规避机动，防止在轨卫星与空间碎片碰撞.选取连续推力策略进行规避机动，将空间碰撞规避过程转化为满足复杂约束的最优控制问题，采用高斯伪谱法对最优控制律进行求解，求解结果满足相应约束.研究结果为航天器有效规避空间碰撞威胁提供了有力支持.      

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.     

Long term and safe relative orbit design for heterogeneous spacecraft clusters

The problem of obtaining long term relative orbit configurations for spacecraft clusters with realistic operational considerations such as safety, station keeping and inter-spacecraft distances is addressed. Two different approaches are developed for station keeping and safety objectives. In the first approach, relative orbit configurations, or relative TLEs, are found minimizing deviations from reference mean orbit which would maximize the station-keeping objective. In second one, relative configurations are found from a reference initial condition by minimizing probability of collision, hence maximizing the safety objective, between the spacecraft in the cluster which are propagated numerically through a high precision orbit propagator. For the design optimization, a derivative free algorithm is proposed. Effectiveness of the approaches is demonstrated through simulations. Using this design framework, several configurations can be found by exploring the limits of the clusters in terms of spacecraft number, distance bounds and probabilities of collision for long time intervals.     

Bayesian linking of geosynchronous orbital debris tracks as seen by the Large Synoptic Survey Telescope

We describe a Bayesian sampling model for linking and constraining orbit models from angular observations of “streaks” in optical telescope images. Our algorithm is particularly suited to situations where the observation times are small fractions of the orbital periods of the observed objects or when there is significant confusion of objects in the observation field. We use Markov Chain Monte Carlo to sample from the joint posterior distribution of the parameters of multiple orbit models (up to the number of observed tracks) and parameters describing which tracks are linked with which orbit models. Using this algorithm, we forecast the constraints on geosynchronous (GEO) debris orbits achievable with the planned Large Synoptic Survey Telescope (LSST). Because of the short 15 s exposure times, preliminary orbit determinations of GEO objects from LSST will have large and degenerate errors on the orbital elements. Combined with the expected crowded fields of GEO debris it will be challenging to reliably link orbital tracks in LSST observations given the currently planned observing cadence.     

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.     

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.     

Spot 1 end of life disposition manoeuvres

The Earth observation satellites of the SPOT family are on a Sun-synchronous orbit at 822 km altitude. The on-orbit lifetime of objects at this altitude is about two centuries, which represents an important risk to the other satellites.The space debris issue has caused the main Agencies to adopt mitigation guidelines with the objective to reduce the population of objects orbiting the Earth. In 1999, CNES published its own standard presenting the management, design and operation rules. This document is fully compliant with the Inter Agency Space Debris Coordination Committee (IADC) mitigation guidelines approved in 2002 by 11 Space Agencies and submitted to United Nations – Committee on Peaceful Uses of Outer Space in February 2003.The space debris mitigation requirements expressed in the CNES standard and in the IADC mitigation guidelines limit the orbital lifetime in LEO to less than 25 years. Although not applicable to Spot 1, launched earlier in 1986, this rule was voluntarily applied and the decision to deorbit Spot 1 was taken.The corresponding operations, performed in November 2003, were complex due to a large number of constraints such as the unusual flight domain, the on-board sensors, the short ground station visibilities or the uncertainties in the estimation of the remaining fuel in the tanks. In the preliminary phase, the orbit was lowered 15 km below the operational orbit to avoid any collision risk with the other Spot satellites. Then, in a second phase, a series of eight apogee boosts lowered progressively the perigee altitude to 619 km. Finally, a large last manoeuvre was performed to empty the tanks and to reduce the perigee altitude the maximum amount. A succession of four ground stations visibilities allowed a real time monitoring of this manoeuvre. In particular the effect of gas bubbles in the propulsion system was observed through telemetry confirming the fuel depletion. The batteries were then disconnected and the telemetry emitter was switched off. According to the obtained perigee altitude, the on-orbit lifetime of Spot 1 should be about 18 years, which meets the space debris mitigation requirements.     

An active debris removal parametric study for LEO environment remediation

Recent analyses on the instability of the orbital debris population in the low Earth orbit (LEO) region and the collision between Iridium 33 and Cosmos 2251 have reignited interest in using active debris removal (ADR) to remediate the environment. There are, however, monumental technical, resource, operational, legal, and political challenges in making economically viable ADR a reality. Before a consensus on the need for ADR can be reached, a careful analysis of its effectiveness must be conducted. The goal is to demonstrate the need and feasibility of using ADR to better preserve the future environment and to explore different operational options to maximize the benefit-to-cost ratio. This paper describes a new sensitivity study on using ADR to stabilize the future LEO debris environment. The NASA long-term orbital debris evolutionary model, LEGEND, is used to quantify the effects of several key parameters, including target selection criteria/constraints and the starting epoch of ADR implementation. Additional analyses on potential ADR targets among the existing satellites and the benefits of collision avoidance maneuvers are also included.     

Removing orbital debris with lasers

Orbital debris in low Earth orbit (LEO) are now sufficiently dense that the use of LEO space is threatened by runaway collision cascading. A problem predicted more than thirty years ago, the threat from debris larger than about 1 cm demands serious attention. A promising proposed solution uses a high power pulsed laser system on the Earth to make plasma jets on the objects, slowing them slightly, and causing them to re-enter and burn up in the atmosphere. In this paper, we reassess this approach in light of recent advances in low-cost, light-weight modular design for large mirrors, calculations of laser-induced orbit changes and in design of repetitive, multi-kilojoules lasers, that build on inertial fusion research. These advances now suggest that laser orbital debris removal (LODR) is the most cost-effective way to mitigate the debris problem. No other solutions have been proposed that address the whole problem of large and small debris. A LODR system will have multiple uses beyond debris removal. International cooperation will be essential for building and operating such a system.     

A simple and valid analysis method for orbit anomaly detection

A simple analysis method for orbit anomaly detection, called semi-major axis change method (SACM) was presented by using a relationship between the change of orbit parameters and velocity increments. In this method, the mean value and standard deviation of the semi-major axis change in different time intervals were first calculated according to historical data. Then, these two parameters, the mean value and standard deviation of the semi-major axis change, are chosen as basis variables and combined as an anomalous criterion. For orbit objects with different characteristic, anomalous thresholds were given in different time intervals for identifying the anomalies of the orbital objects. Finally, this method is used for low earth orbit (LEO) satellites and American–Russian breakup debris. By adopting this method, the characteristics of the orbit change were given. The accuracy rate of anomaly analysis for LEO satellites and American–Russian breakup debris can reach to 100%, which demonstrates that the method was rapid and valid.