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.     

Identification of a debris cloud from the nuclear powered SNAPSHOT satellite with haystack radar measurements

Data from the Massachusetts Institute of Technology Lincoln Laboratory Long Range Imaging Radar (known as the Haystack radar) have been used in the past to examine families of objects from individual satellite breakups or families of orbiting objects that can be isolated in altitude and inclination. This is possible because, for some time after a breakup, the debris cloud of particles can remain grouped together in similar orbit planes. This cloud will be visible to the radar, in fixed staring mode, for a short time twice each day, as the orbit plane moves through the field of view. There should be a unique three-dimensional pattern in observation time, range, and range rate which can identify the cloud. Eventually, through slightly differing precession rates of the right ascension of ascending node of the debris cloud, the observation time becomes distributed so that event identification becomes much more difficult.     

基于相控阵雷达波束篱笆的空间碎片数量与分布估计方法

随着载人航天与空间站等航天活动的增多,不能有效防护、也无法定期跟踪和编目的小尺寸(尤其是1～10 cm)碎片的危害越来越受到关注,这些碎片信息的获取依赖于统计采样技术.针对简化的相控阵雷达波束篱笆空间碎片探测模式,提出了一种采用统计技术估计空间碎片总数量以及高度和倾角分布的方法.将碎片穿越波束篱笆的过程用Poisson分布来建模,根据观测时段内穿越波束篱笆目标的平均到达率及测量的轨道高度和倾角数据来估计给定轨道高度范围或倾角范围内碎片的数量,进而得到碎片的总数量以及碎片数量随轨道高度或倾角的分布.在获取雷达散射截面信息时,该方法还可用于估计碎片数量随尺寸的分布.通过仿真实验验证了该方法的有效性.      

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.     

Modeling of LEO orbital debris populations for ORDEM2008

The NASA Orbital Debris Engineering Model, ORDEM2000, is in the process of being updated to a new version: ORDEM2008. The data-driven ORDEM covers a spectrum of object size from 10 μm to greater than 1 m, and ranging from LEO (low Earth orbit) to GEO (geosynchronous orbit) altitude regimes. ORDEM2008 centimeter-sized populations are statistically derived from Haystack and HAX (the Haystack Auxiliary) radar data, while micron-sized populations are estimated from shuttle impact records. Each of the model populations consists of a large number of orbits with specified orbital elements, the number of objects on each orbit (with corresponding uncertainty), and the size, type, and material assignment for each object. This paper describes the general methodology and procedure commonly used in the statistical inference of the ORDEM2008 LEO debris populations. Major steps in the population derivations include data analysis, reference-population construction, definition of model parameters in terms of reference populations, linking model parameters with data, seeking best estimates for the model parameters, uncertainty analysis, and assessment of the outcomes. To demonstrate the population-derivation process and to validate the Bayesian statistical model applied in the population derivations throughout, this paper uses illustrative examples for the special cases of large-size (>1 m, >32 cm, and >10 cm) populations that are tracked by SSN (the Space Surveillance Network) and also monitored by Haystack and HAX radars operating in a staring mode.     

雷达波束驻留模式下空间碎片数量的置信区间估计

碎片数量估计是空间碎片环境统计特征描述的重要内容之一,对于空间碎片环境模型验证、航天器碰撞风险分析以及碎片数量增长趋势预测有重要意义.针对波束指向正东、正南任意仰角的雷达波束驻留(Beam-park)模式(天顶指向是波束指向仰角为90°时的特例),给出了一种估计碎片数量置信区间的方法.对于给定轨道高度范围内一个具有穿越雷达波束可能性(即雷达散射截面足够大,且轨道倾角相对测站纬度足够大)的碎片,将其是否真正穿越波束这一随机事件用(0-1)分布来建模,根据所采集的轨道高度和倾角数据,计算出该轨道高度范围内碎片穿越波束的平均概率,进而采用中心极限定理来估计碎片数量的置信区间.仿真结果表明了方法的有效性.      

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.     

Size distribution of NaK droplets released during RORSAT reactor core ejection

NaK droplets consist of eutectic sodium–potassium alloy and have been released during RORSAT reactor core ejections mostly on orbits close to 950 km altitude. They contributed to the space debris environment in the centimeter and millimeter regime. NaK droplets have been modeled before in ESAs MASTER Debris and Meteoroid Environment Model. The approach is currently revised for the MASTER 2005 upgrade. The new NaK model gives estimations of the parameters of the size distribution function, which are based on physical relations only. NASA radar observations confirm this physical approach. A bimodal size distribution is derived, which is based on the Rosin–Rammler equation. The Rosin–Rammler equation is an empirical volume distribution function. The number of parameters is limited to two. It is likely that the coolant system contains two types of orifice diameters. This makes it necessary to apply the Rosin–Rammler distribution twice, resulting in a bimodal size distribution with altogether four parameters. The comparison shows that the new NaK model is in good agreement with the NASA model, which is based on radar observations. Results of orbit propagation simulation runs are presented.     

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.     

匹配滤波方法在非相干散射雷达测量空间碎片中的应用

利用2010年3月25日欧洲非相干散射雷达的常规电离层探测数据, 分析了实测数据中接收功率突变的现象. 高度发生在500 km以上的功率突变一般不是由于地球物理影响产生的, 而要归因于卫星或空间碎片. 采用匹配滤波方法实现了对空间碎片的探测和提取, 利用相干积累的方法提高了信噪比, 共获得363个碎片, 得到了碎片随高度和时间的分布. 结果表明, 碎片高度分布主要集中在800 km左右, 与欧洲非相干散射组织现有的碎片数据具有一致性.      

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。     

A modelling of the interaction between electromagnetic radiation and West Ford needles clusters: a preliminary study

Radar observations of small space debris made with the Goldstone radar facility have shown that a population of small particles do exist at an altitude larger than 2000 km. This population has been identified with clusters of copper needles created upon the deployment of the West Ford needles project, by MIDAS satellites in 1961 and 1963. This set of particles is either not taken into account in the debris models or only added to other populations. But owing to their specific physical and geometrical properties, the sunlight they scatter could affect, for instance, the spaceborne astronomical experiments. In order to assess this threat it is necessary to model their physical and geometric characteristics. A preliminary modelling using spheres suggests that some improvement is needed. We propose a better approach with long conductive cylinders as a model for the clusters. The interaction of solar light with these particles allows us to estimate the spurious flux scattered inside spaceborne instruments. We conclude that for a given spatial configuration light flashes can affect seriously the operating mode of high sensitivity instruments.     

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.     

空间系绳碎片碰撞生存能力研究

空间系绳结构和几何尺寸对其在复杂空间环境中抵抗碎片碰撞的能力有显著影响.本文根据系绳-碎片碰撞模型和泊松分布,计算了双股系绳和带状系绳被碎片割断的概率,分析了太空碎片对系绳生存能力可能造成的影响.双股系绳是由两条平行系绳每隔一段距离打结连接构成,带状系绳可视为一种横截面为矩形的特殊单股系绳.首先对单股系绳被碎片割断的概率进行建模,然后构建双股系绳和带状系绳生存能力函数,最后根据空间碎片环境模型,对比分析具有不同结构、不同尺寸的系绳的生存能力.仿真结果表明,相较于单股系绳,双股系绳和带状系绳的生存能力有明显提高.      

Using S-band dual polarized radar for convective/stratiform rain indexing and the correspondence with AMSR-E GSFC profiling algorithm

The separation of rain types in convective and stratiform regimes has long been a goal in microwave remote sensing of precipitation research. In this essence, a dual polarized radar based indexing scheme that provides information on convective and stratiform (C/S) rain regimes has been presented in correspondence with advanced microwave scanning radiometer – earth observing system (AMSR-E) GSFC profiling algorithm estimate of convective rain percentage. The dual polarized radar based C/S indexing scheme first retrieves the normalized gamma drop size distribution parameters, median volume drop diameter (D₀) and concentration parameter (N_w), from dual polarized radar measurements Z_H and Z_DR, representing reflectivity and differential reflectivity respectively, by means of the genetic programming approach. Next, the C/S rain index is calculated based on the formulation of an empirical relation in N_w–D₀ domain. The scheme has been inspected and applied on measurements from the S-band Chilbolton dual polarized radar. A considerable number of “coincident” cases from the radar and the AMSR-E observations are investigated. It has been revealed that the dual polarized radar based C/S rain indexing is in a similar pattern with the AMSR-E GSFC profiling algorithm estimate of convective rain percentage. Generally, as C/S rain index value increases, which signifies a stratiform to convective trend, the AMSR-E convective rain percentage also increases.     

Hypervelocity impacts on HST solar arrays and the debris and meteoroids population

Accurate debris and meteoroid flux models are crucial for the design of manned and unmanned space missions. For the most abundant particle sizes smaller than a few millimetres, knowledge of the populations can only be gained from in situ detectors or the analysis of retrieved space hardware. The measurement of impact flux from exposed surfaces improves with increased surface area and exposure time.A post-flight impact investigation was initiated by the European Space Agency to record and analyse the impact fluxes and any potential resulting damage on the two flexible solar arrays of the Hubble Space Telescope. The arrays were deployed during the first Hubble Space Telescope servicing mission in December 1993 and retrieved in March 2002. They have a total exposed surface area of roughly 120 m², including 42 m² covered with solar cells. This new Hubble post-flight impact study follows a similar activity undertaken after the retrieval of one of the first solar arrays, in 1993. The earlier study provided the first opportunity for a numerical survey of damage to exposed surfaces from more than 600 km altitude, and of impacts from particles larger than 1 mm. The results have proven very valuable in validation of important flux model regimes. The second set of Hubble solar arrays has again provided an unrivalled opportunity to measure the meteoroid and debris environment, now sampled during a long interval in low Earth orbit, and to identify changes in the space debris environment since the previous survey. The retrieved solar array wings exhibit thousands of craters, many of which are visible to the naked eye. A few hundred impacts have completely penetrated the 0.7 mm thick array. The largest impact features are about 7–8 mm in diameter. The cover glass of the solar cells is particularly well suited to the recognition of small impact features by optical and electron microscopy. In this paper, we present the first results of the impact survey. Data upon the abundance of craters of specific measured size ranges are plotted as cumulative flux curves, and compared to the results of model predictions. The most significant change to the particle flux since 1993 is a decrease in the small debris population.     

流星参数的数值分析和流星高度分布模型

流星余迹能够被后向散射雷达观测到, 利用观测结果, 可以分析和研究流星的空间分布和时间变化规律. 同时, 利用流星空间分布还可以进行空间碎片的研究. 基于标准理论, 对影响雷达回波功率的主要因素, 例如如双极扩散、余迹的初始半径、流星的有限速度, 以及雷达的脉冲重复频率在不同频率和速度下进行了数值分析和计算, 得到的流星衰减时间及双极扩散系数的观测结果与理论结果一致. 通过对昆明流星雷 达观测到的571632个流星进行统计分析, 得到了流星高度分布统计模型, 并利用该模型的分析结果与不同月份流星的观测数据进行对比, 结果比较一致.      

Space debris cumulative flux considering the Interval Distance-based method

The availability of engineering models to estimate the risk from space debris is essential for space missions. According to current research, cumulative flux calculation is mostly carried out based on the equal-width interval discretization. The method discretizes the volume around the Earth into cells defined in earth centered inertial coordinates. The resulting debris flux onto a target object is shown to depend on the chosen size of the cells. To avoid a discretization error, this must be accounted for. In order to present reliable flux predictions for space mission, the algorithm improvement is an ongoing topic for the related research field. The aim of this study was to examine the discretization error during the cumulative flux determination process. Both the effect of interval step length and the orbital boundary are under investigation. Several typical orbits are selected as examples here and the 2018/01/03 TLE (Two Line Element) data published by the US Space Surveillance Network is used as the debris background in this paper. Furthermore, the Interval Distance-Based method for Discretization (IDD) is adopted in this paper. A position-centered flux determination method is introduced based on the IDD method. According to the example analysis, the IDD used in the flux calculation process provides results which are less affected by the interval step-size setup; and the orbital boundary has no effect on the calculation process. In other words, the discretization error is significantly reduced. The position-centered method provided a possible suggestion for the improvement of space debris environment models.     

Finite element reconstruction approach for on-orbit spacecraft breakup dynamics simulation and fragment analysis

Breakup model is the key area of space debris environment modeling. NASA standard breakup model is currently the most widely used for general-purpose. It is a statistical model found based on space surveillance data and a few ground-based test data. NASA model takes the mass, impact velocity magnitude for input and provides the fragment size, area-to-mass ratio, velocity magnitude distributions for output. A more precise approach for spacecraft disintegration fragment analysis is presented in this paper. This approach is based on hypervelocity impact dynamics and takes the shape, material, internal structure and impact location etc. of spacecraft and impactor, which might greatly affect the fragment distribution, into consideration. The approach is a combination of finite element and particle methods, entitled finite element reconstruction (FER). By reconstructing elements from the particle debris cloud, reliable individual fragments are identified. Fragment distribution is generated with undirected graph conversion and connected component analysis. Ground-based test from literature is introduced for verification. In the simulation satellite targets and impactors are modeled in detail including the shape, material, internal structure and so on. FER output includes the total number of fragments and the mass, size and velocity vector of each fragment. The reported fragment distribution of FER shows good agreement with the test, and has good accuracy for small fragments.     

SPACE DEBRIS RESEARCH IN CHINA(2000-2002)

Space debris is is referred to as the human made pollution in the space environment.Ever since the first launch of man made satellite in 1957, millions of kilograms of objects have been sent into the space. Large space objects that are traceable and cataloged by ground base telescope and radar reach around 9 000, becoming grave threat to the social development of human beings as well as astronautics.