A novel data association scheme for LEO space debris surveillance based on a double fence radar system

The increasing amount of space debris threatens to seriously deteriorate and damage space-based instruments in Low Earth Orbit (LEO) environments. Therefore, LEO space debris surveillance systems must be developed to provide situational awareness in space and issue warnings of collisions with LEO space debris. In this paper, a double fence radar system is proposed as an emerging paradigm for LEO space debris surveillance. This system exhibits several unique and promising characteristics compared with existing surveillance systems. In this paper, we also investigate the data association scheme for LEO space debris surveillance based on a double fence radar system. We also perform a theoretical analysis of the performance of our proposed scheme. The superiority and the effectiveness of our novel data association scheme is demonstrated by experimental results. The data used in our experiments is the LEO space debris catalog produced by the North American Air Defense Command (NORAD) up to 2009, especially for scenarios with high densities of LEO space debris, which were primarily produced by the collisions between Iridium 33 and Cosmos 2251. We hope that our work will stimulate and benefit future work on LEO space debris surveillance approaches and enable construction of the double fence radar system.     

Instability of the present LEO satellite populations

Several studies conducted during 1991–2001 demonstrated, with some assumed launch rates, the future unintended growth potential of the Earth satellite population, resulting from random, accidental collisions among resident space objects. In some low Earth orbit (LEO) altitude regimes where the number density of satellites is above a critical spatial density, the production rate of new breakup debris due to collisions would exceed the loss of objects due to orbital decay.     

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.     

A novel signal processing approach for LEO space debris based on a fence-type space surveillance radar system

The increase in space debris can seriously threaten regular activities in the Low Earth Orbit (LEO) environment. Therefore, it is necessary to develop robust, efficient and reliable techniques to understand the potential motions of the LEO debris. In this paper, we propose a novel signal processing approach to detect and estimate the motions of LEO space debris that is based on a fence-type space surveillance radar system. Because of the sparse distribution of the orbiting debris through the fence in our observations, we formulate the signal detection and the motion parameter estimation as a sparse signal reconstruction problem with respect to an over-complete dictionary. Moreover, we propose a new scheme to reduce the size of the original over-complete dictionary without the loss of the important information. This new scheme is based on a careful analysis of the relations between the acceleration and the directions of arrival for the corresponding LEO space debris. Our simulation results show that the proposed approach can achieve extremely good performance in terms of the accuracy for detection and estimation. Furthermore, our simulation results demonstrate the robustness of the approach in scenarios with a low Signal-to-Noise Ratio (SNR) and the super-resolution properties. We hope our signal processing approach can stimulate further work on monitoring LEO space debris.     

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.     

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.     

低轨导航增强卫星星座设计

针对目前全球低轨卫星快速发展的现状,对低轨导航增强卫星星座设计方法进行了详细的研究。首先推导了轨道高度与可视球冠的关系,结合太空垃圾分布,从覆盖范围、经济性及碰撞风险几方面联合确定了轨道高度。然后推导了用户仰角与轨道倾角的关系,分析了实现南北极点覆盖的轨道倾角。接着结合铱星星座,推导出单一星座构型无法实现全球范围内均匀的可见星和精度衰减因子（Dilution of Precision,DOP）值分布。最后提出了一种组合低轨卫星星座设计方法。结果表明,该方法设计的组合星座在实现全球覆盖的同时,能够实现可见星数量与DOP值在全球范围内的均匀分布。     

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).     

气动辅助异面变轨在多碎片清除中的应用分析

碎片清除飞行器异面变轨需要消耗大量燃料.从气动辅助异面变轨优化设计及被清除碎片轨道高度差值、倾角差值等参数对变轨性能的影响出发,比较分析了优化气动辅助异面变轨与双脉冲霍曼轨道转移的燃料节约量,研究了不同轨道高度差对于实施气动辅助变轨燃料节约量的影响.当地球静止轨道（GEO）与低地轨道（LEO）间气动辅助变轨优化速度增量约为1.55km·s-1、质量面积比172kg·m-2、比冲310s、轨道倾角变化16°时,燃料节约率约为45%.对比研究了不同轨道高度差LEO轨道间实施气动辅助变轨的燃料节约情况.结果表明:随着轨道高度的增加,气动辅助优化效率逐渐降低;在相同高度轨道间实施异面变轨,随着轨道倾角的增加,气动辅助变轨燃料节约率先增大后减小,倾角改变量约为20°时,燃料节约率最大;当轨道倾角为5°时,采用气动辅助变轨和双脉冲变轨的燃料消耗量相同.      

An optimal beam alignment method for large-scale distributed space surveillance radar system

Large-scale distributed space surveillance radar is a very important ground-based equipment to maintain a complete catalogue for Low Earth Orbit (LEO) space debris. However, due to the thousands of kilometers distance between each sites of the distributed radar system, how to optimally implement the Transmitting/Receiving (T/R) beams alignment in a great space using the narrow beam, which proposed a special and considerable technical challenge in the space surveillance area. According to the common coordinate transformation model and the radar beam space model, we presented a two dimensional projection algorithm for T/R beam using the direction angles, which could visually describe and assess the beam alignment performance. Subsequently, the optimal mathematical models for the orientation angle of the antenna array, the site location and the T/R beam coverage are constructed, and also the beam alignment parameters are precisely solved. At last, we conducted the optimal beam alignment experiments base on the site parameters of Air Force Space Surveillance System (AFSSS). The simulation results demonstrate the correctness and effectiveness of our novel method, which can significantly stimulate the construction for the LEO space debris surveillance equipment.     

地气光辐射对空间目标成像特性影响分析

为分析地气光辐射对空间目标成像特性的影响,以地球同步轨道(GEO)卫星搭载的可见光成像器为探测平台,利用卫星工具包(STK)设计高椭圆轨道(HEO)及近地轨道(LEO)目标运动场景,根据空间目标、地球、太阳、探测平台之间的位置关系,采用微元法建立空间目标与地气光背景等效星等模型,推导出空间目标信噪比(SNR)计算公式。分析了距离、角度参数变化对不同轨道空间目标、地气光背景等效星等及空间目标信噪比的影响。仿真结果表明:当探测平台距离空间目标较远时,地气光背景等效星等低于空间目标等效星等,地气光辐射比空间目标信号强。当地气光辐射进入和离开空间目标探测视场时,空间目标信噪比最大,该时间段是进行空间目标探测的最佳“观测窗口”。仿真得出的空间目标信噪比值为空间目标探测识别提供了理论计算依据。      

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.      

低轨卫星的北斗反射信号海洋覆盖分析

北斗系统作为我国自行研制的导航系统，具有独特的混合星座特性，其反射事件在海洋上的空间分布和覆盖性能的研究成果较少。针对上述问题，模拟了北斗三号（Beidou System 3，BDS3）以及全球定位系统（Global Positioning System，GPS）空间星座，模拟不同性能参数的低轨接收卫星，在此仿真系统的基础上，计算反射事件在各仿真场景下的海洋覆盖率以及同时发生反射事件的卫星数量。结果表明：BDS3与GPS相比具有更大的反射事件海洋覆盖率，覆盖性能更优；仿真周期7天与1天相比,前者卫星产生的反射事件海洋覆盖率约为后者5倍；低轨道卫星（Low Earth Orbit,LEO）轨道高度越高，天线波束角度越大，反射事件海洋覆盖率越大；3颗LEO卫星下同时发生反射事件卫星数的平均值约为单颗LEO卫星的3倍。可通过设计多星组网来提高反射事件海洋覆盖率。研究结果对星载反射技术海洋遥感应用方面有一定的参考价值。     

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.     

Characterizing space debris longitude-dependent distribution based on RAAN perturbation rate

The space debris environment is one of the major threats against payloads. Space debris orbital distribution is of great importance for space debris environment modeling. Due to perturbation factors, the Right Ascension of Ascending Node (RAAN) of space objects changes consistently, causing regular rotation of the orbit plane around Earth’s axis. Based on the investigation of the RAAN perturbation rate of concerned objects, this paper proposes a RAAN discretization method in order to present the space debris longitude-dependent distribution. Combined with two line element (TLE) data provided by the US Space Surveillance Network, the estimated value from RAAN discretization method is compared with the real case. The results suggest that using only the initial orbital data at the beginning of the time interval of interest, the RAAN discretization method is able to provide reliable longitude distribution of concerned targets in the next following period. Furthermore, spacecraft cumulative flux against space debris is calculated in this paper. The results suggest that the relevance between spacecraft RAAN setup and flux output is much smaller for LEO targets than MEO targets, which corresponds with the theory analysis. Since the nonspherical perturbation is the major factor for RAAN variation, the RAAN perturbation rate has little connection with the size of orbital objects. In other words, the RAAN discretization method introduced in this paper also applies to space debris of different size range, proposing a possible suggestion for the improvement of space debris environment engineering models.     

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.     

Characterization of the cataloged Fengyun-1C fragments and their long-term effect on the LEO environment

The intentional breakup of Fengyun-1C on 11 January 2007 created the most severe orbital debris cloud in history. The altitude where the event occurred was probably the worst location for a major breakup in the low Earth orbit (LEO) region, since it was already highly populated with operational satellites and debris generated from previous breakups. The addition of so many fragments not only poses a realistic threat to operational satellites in the region, but also increases the instability (i.e., collision cascade effect) of the debris population there.