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.     

基于稀疏时频分解的空中目标微动特征分析

本文以直升机的RCS 信号为研究对象，利用Gabor 原子构造过完备时频原子库，在该库上实现基于匹配追踪（Matching Pursuit，MP）的信号分解，并结合遗传算法寻找最佳匹配原子。最后将每次分解得到的Gabor 原子进行Wigner-Ville 变换，利用结果叠加得到无交叉干扰项的信号的Wigner-Ville 分布（Wigner-VilleDistribution，WVD）。仿真结果表明，该方法能够提高稀疏分解的效率，并且用少量的Gabor 原子就能表示信号WVD。与直接进行Wigner-Ville 变换相比，本方法可以有效地抑制交叉干扰项，且保持高时频分辨率。     

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.     

Track detection of high-velocity resident space objects in Low Earth Orbit

The world’s economy has become heavily dependent on the services provided by satellites. With the exponential increase in satellite launches, the population of defunct or inactive hardware in space has grown substantially. This is especially true in sensitive orbits such as the Low Earth Orbit (LEO) and Geostationary Earth Orbit (GEO) regimes. These objects, collectively known as orbital debris, can reach speeds of up to 28 000km h^?1 in LEO. At these orbital speeds, even the smallest of objects can pose a considerable threat to operational satellites or astronauts. This makes the monitoring, and detection, of these objects of the utmost importance. This work describes the latest detection strategy used in one of Europe’s largest Space Situational Awareness (SSA) installation; the BIstatic RAdar for LEo Survey (BIRALES) space debris radar. We present a novel bottom-up approach that makes use of single-linkage clustering to identify faint radar streaks in spectrogram data. Tests on synthetic data have shown that the detection strategy presented in this study obtains a higher detection rate when it is compared against existing methods. Unlike other approaches, this detection strategy, using the Multi-beam streak detection strategy (MSDS) algorithm, was still able to recall 90% of the track information at an Signal-to-Noise Ratio (SNR) of 2dB.     

An adaptive threshold method for improving astrometry of space debris CCD images

Optical survey is a main technique for observing space debris, and precisely measuring the positions of space debris is of great importance. Due to several factors, e.g. the angle object normal to the observer, the shape as well as the attitude of the object, the variations of observed characteristics for low earth orbital space debris are distinct. When we look at optical CCD images of observed objects, the size and brightness are varying, hence it’s difficult to decide the threshold during centroid measurement and precise astrometry. Traditionally the threshold is given empirically and constantly in data reduction, and obviously it’s not suitable for data reduction of space debris. Here we offer a solution to provide the threshold. Our method assumes that the PSF (point spread function) is Gaussian and estimates the signal flux by a directly two-dimensional Gaussian fit, then a cubic spline interpolation is performed to divide each initial pixel into several sub-pixels, at last the threshold is determined by the estimation of signal flux and the sub-pixels above threshold are separated to estimate the centroid. A trail observation of the fast spinning satellite Ajisai is made and the CCD frames are obtained to test our algorithm. The calibration precision of various threshold is obtained through the comparison between the observed equatorial position and the reference one, the latter are obtained from the precise ephemeris of the satellite. The results indicate that our method reduces the total errors of measurements, it works effectively in improving the centering precision of space debris images.     

Autonomous space target tracking through state estimation techniques via ground-based passive optical telescope

The presence of operational satellites or small-body space debris is a challenge for autonomous ground-based space object observation. Although most space objects exceeding 10?cm in diameter have been cataloged, the position of each space object (based on six orbital parameters) remains important and should be updated periodically, as the Earth’s orbital perturbations cause disturbances. Modern ground-based passive optical telescopes equipped with complementary metal-oxide semiconductors have become widely used in astrometry engineering, being combined with image processing techniques for target signal enhancement. However, the detection and tracking performance of this equipment when employed with image processing techniques primarily depends on the size and brightness of the space target, which appears on the monitor screen under variable background interference conditions. A small and dim target has a highly sensitive tracking error compared to a bright target. Moreover, most image processing techniques for target signal enhancement require large computational power and memory; therefore, automatic tracking of a space target is difficult. The present work investigates autonomous space target detection and tracking to achieve high-sensitivity detection and improved tracking ability for non-Gaussian and dynamic backgrounds with a simple system mechanism and computational efficiency. We develop an improved particle filter (PF) using the ensemble Kalman filter (KF) for track-before-detect (TBD) frameworks, by modifying and optimizing the computational formula for our non-linear measurement function. We call this extended version the “ensemble Kalman PF-TBD (EnKPF-TBD).” Three sequential astronomical image datasets taken by the Asia-Pacific Ground-Based Optical Space Objects Observation System (APOSOS) telescope under different conditions are used to evaluate three proposed TBD baseline frameworks. Given an optimal random sample size, the EnKPF-TBD exhibits superior performance to PF-TBD and threshold-based unscented KF with two-dimensional peak search (2dPS). The EnKPF-TBD scheme achieves satisfactory performance for all variable background interference conditions, especially for a small and dim space target, in terms of tracking accuracy and computational efficiency.     

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.     

天基空间碎片光学探测影响因素分析及仿真

光学手段在天基空间碎片探测中被广泛应用,但容易受到杂光等因素影响。结合在轨试验数据,从探测器和碎片两方面分析了影响天基空间碎片光学探测的因素。影响探测器探测效果的因素包括太阳光、月光、地气光、大气辉光等杂光及南大西洋异常区辐射等;影响碎片可见性的因素包括地球遮挡、地影及反射的太阳光等。分别给出了上述影响因素涉及的特征量及规避影响的计算方法。基于某天基探测设备的仿真结果表明,上述影响在自然交会及姿态机动模式下均可能发生,在试验设计时需被充分考虑。最后,针对某天基空间碎片探测任务进行了规划。文章对天基光学探测试验设计具有一定的指导意义。     

First laser measurements to space debris in Poland

The Borowiec Satellite Laser Ranging station (BORL 7811, Borowiec) being a part of the Space Research Centre of the Polish Academy of Sciences (SRC PAS) went through modernization in 2014–2015. One of the main tasks of the modernization was the installation of a high-energy laser module dedicated to space debris tracking. Surelite III by Continuum is a Nd:YAG pulse laser with 10?Hz repetition rate, a pulse width of 3–5?ns and a pulse energy of 450?mJ for green (532?nm). This new laser unit was integrated with the SLR system at Borowiec performing standard satellite tracking. In 2016 BORL 7811 participated actively to the observational campaigns related to the space debris targets from LEO region managed by the Space Debris Study Group (SDSG) of the International Laser Ranging Service (ILRS).Currently, Borowiec station regularly tracks 36 space debris from the LEO regime, including typical rocket bodies (Russian/Chinese) and cooperative targets like the inactive TOPEX/Poseidon, ENVISAT, OICETS and others. In this paper the first results of space debris laser measurements obtained by the Borowiec station in period August 2016 – January 2017 are presented. The results gained by the SRC PAS Borowiec station confirm the rotation of the defunct TOPEX/Poseidon satellite which spins with a period of approximately 10?s. The novelty of this work is the presentation of the sample results of the Chinese CZ-2C R/B target (NORAD catalogue number 31114) which is equipped (probably) with retroreflectors. Laser measurements to space debris is a very desirable topic for the next years, especially in the context of the Space Surveillance and Tracking (SST) activity. Some targets are very easy to track like defunct ENVISAT or TOPEX/Poseidon. On the other hand, there is a big population of different LEO targets with different orbital and physical parameters, which are challenging for laser ranging like small irregular debris and rocket boosters.     

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.     

MCMC-Particle-based group tracking of space objects within Bayesian framework

With the intense increase in space objects, especially space debris, it is necessary to efficiently track and catalog the extensive dense clusters of space objects. As the main instrument for low earth orbit (LEO) space surveillance, ground-based radar system is usually limited by its resolution while tracking small space debris with high density. Thus, the obtained measurement information could have been seriously missed, which makes the traditional tracking method inefficient. To address this issue, we conceived the concept of group tracking. For group tracking, the overall tendency of the group objects is expected to be revealed, and the trajectories of individual objects are simultaneously reconstructed explicitly. According to model the interaction between the group center and individual trajectories using the Markov random field (MRF) within Bayesian framework, the objects’ number and individual trajectory can be estimated more accurately in the condition of high miss alarm probability. The Markov chain Monte Carlo (MCMC)-Particle algorithm was utilized for solving the Bayesian integral problem. Furthermore, we introduced the mechanism for describing the behaviors of groups merging and splitting, which can expand the single group tracking algorithm to track variable multiple groups. Finally, simulation of the group tracking of space objects was carried out to validate the efficiency of the proposed method.     

Real-time space debris monitoring with EISCAT

Following a feasibility study in 2000–2001 on using the EISCAT ionospheric research radars to detect centimetre-sized space debris in the frame of an ESA contract, we are now finishing a continuation study, aimed at achieving debris detection and parameter estimation in real-time. A requirement is to “piggy-back” space debris measurements on top of EISCAT’s normal ionospheric work, without interfering with that work, and to be able to handle about 500 h of measurements per year. We use a special digital receiver back-end in parallel with EISCAT’s standard receiver. We sample fast enough to correctly band-pass sample the EISCAT analog frequency band. To increase detection sensitivity, we use coherent pulse-to-pulse integration. The coherent integration is built-in in our method of parameter estimation, which we call the match function (MF) method. The method is derived from Bayesian statistical inversion, but reduces, with standard assumptions about noise and prior, to minimizing the least squares norm ∥z(t) − bχ(R,v,a;t)∥, where z is the measured signal and {bχ} is a set of model signals. Because the model signals depend linearly on the amplitude b, it is sufficient to maximize the magnitude of the inner product (cross correlation) between z and χ, the amplitude estimate is then determined by direct computation. The magnitude of the inner product, when properly normalized, is the MF. To construct the set of model signals, we sample the EISCAT transmission, in the same way as we sample the received signal, and apply linearly changing Doppler-shifts to it. Our initial implementation of the MF-method in 2001 was about four orders of magnitude too slow for real-time applications, but we have now gained the required speed factors. A factor of ten comes from using faster computers, another factor of ten comes from coding our key algorithms in C instead of Matlab. The largest factor, typically 100–300, comes from using a special, approximative, but in practice quite sufficient, method of finding the MF maximum. Test measurements show that we get real-time speed already when using a single dual-processor 2 GHz G5 Macintosh to do the detection computations.     

天基激光移除空间碎片仿真平台研究与开发

为了从空间碎片和天基移除系统两方面分析激光驱动碎片变轨过程,优化移除任务规划和策略,基于真实的可观测空间碎片数据,设计并开发了一套天基激光移除空间碎片三维数值仿真平台。首先从总体设计出发,对三维数值仿真平台的需求分析、总体框架、模块功能进行了明确的描述。其次通过对激光驱动空间碎片变轨过程数学模型的分析,确定了各模块的具体实现方法。最后采用C++/Qt开发了三维数值仿真平台,通过仿真验证了设计平台的有效性。该仿真平台可用于不同天基平台和目标碎片的任务规划、碎片分布热点区域和航天器防护区域的方案设计及空间环境治理体系的优化设计。     

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.      

电路测试响应信号的GP-KSVD稀疏重构算法

电路系统测试响应信号具有周期性强、分布较稀疏的特点,针对电路系统测试响应信号的压缩重构问题进行了研究,提出了基于梯度方向追踪的K奇异值分解(GPKSVD)稀疏重构算法。结合单一响应信号以及混合信号其自身特点进行字典训练,利用更新后字典对含噪信号进行梯度追踪稀疏表征,通过对含噪信号的重构,实现了去噪的目的,算法计算复杂度低,储存量小,具有较好的重构效果。仿真中将GP-KSVD表征与使用随机字典、离散余弦字典(DCT)的表征进行比较,从信噪比(SNR)以及相对均方误差(RMSE)2项指标中得出使用KSVD字典具有更好的重构去噪效果;此外将GP-KSVD稀疏重构算法与正交匹配追踪正交匹配追踪(OMP)-KSVD、预处理共轭梯度追踪(PCGP)算法进行比较,得出GP-KSVD的计算时间最短、重构精度更高的结论,并且进行了实测验证。算法可用来对测试响应信号进行预处理,为电路系统设备性能的评估分析提供了理论依据。     

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。      

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.     

Fuzzy multi-criteria decision-making approach to prioritization of space debris for removal

As private companies and government space agencies begin to seriously consider the task of active space debris removal, it is becoming increasingly more important to determine the highest priority objects to deorbit. This work sets forth an approach for prioritization of space debris through the utilization of Multi-Criteria Decision-Making methodologies and fuzzy logic, as well as both quantitative and qualitative criteria. The proposed debris prioritization approach considers various criteria including the orbit, size, mass, pairwise and total collision probabilities, and decay timeframe of each debris object. The means of assigning attributes to each assessment criterion is discussed in detail. To determine the weighting scheme for the criteria, a questionnaire was prepared and shared with experts in the field of space situational awareness. The work examines over two thousand critical debris objects selected from the existing debris catalog with respect to these criteria. The quantified attributes for each debris object are then aggregated through the fuzzy versions of the Analytic Hierarchy Process and the Technique for Order Preference by Similarity to Ideal Solution. The results of the analysis identify high-priority debris objects for removal from Earth-bound orbits.     

Parallel,adaptive, multi-object trajectory integrator for space simulation applications

Computer simulation is a very helpful approach for improving results from space born experiments. Initial-value problems (IVPs) can be applied for modeling dynamics of different objects – artificial Earth satellites, charged particles in magnetic and electric fields, charged or non-charged dust particles, space debris. An ordinary differential equations systems (ODESs) integrator based on applying different order embedded Runge–Kutta–Fehlberg methods is developed. These methods enable evaluation of the local error. Instead of step-size control based on local error evaluation, an optimal integration method is selected. Integration while meeting the required local error proceeds with constant-sized steps. This optimal scheme selection reduces the amount of calculation needed for solving the IVPs. In addition, for an implementation on a multi core processor and parallelization based on threads application, we describe how to solve multiple systems of IVPs efficiently in parallel.     

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.