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).     

Improved detection of faint streaks based on a streak-like spatial filter

This paper presents an algorithm to detect very faint object streaks on CCD images acquired with an optical system. The proposed detection method uses image filters simulating the geometrical form and orientation of possible streaks on the CCD image. The method searches for a matching between streak and filter evaluating the convolutions of the image with all possible filters. Based on the statistics of the image background a threshold is applied in order to accept, respectively reject, the possible streak candidates. The detection probabilities and the effect of different parameter settings are estimated with tests on simulated images, while subframes of real images are used to evaluate the applicability of the algorithm to real cases. The detection probability of this method depends on the length and on the signal-to-noise ratio of the streak. For long streaks, a detection for signal-to-noise values around 0.5 is achieved. The further characterization of the detected streak (e.g. centroid and length), which is not performed in the current algorithm, and the reduction of the computation time, which is relatively high for full acquired frames, as well as possible improvements are briefly addressed.     

一种CCD星图星点快速定位算法

大尺寸CCD星图快速处理是制约天基光学观测器件性能的关键因素之一,在星敏感器、空间监视载荷等研制中具有重要意义.通过对CCD星图图像特点的分析,提出了以最大概率实现背景噪声滤除的星图预处理准则;在此基础上,提出了通过两次投影检测实现星点位置测量的算法.与传统方法相比,该算法实现简单,节约了计算量和存储量.对分辨率为2048×2048的CCD实拍星图的实验研究表明了该算法的有效性.      

掩星大气探测系统误差源分析

根据掩星大气探测反演原理,研究了影响系统产品精度的误差源,并对多普勒观测误差、天线相位中心变化误差、多路径误差、卫星质心变化误差、导航卫星钟飘、卫星姿态变化误差和精密定轨速度误差进行分析,根据工程实现可行性提出了系统误差分配建议,为掩星大气探测系统设计提供参考.      

基于视惯融合的大型空间碎片质心位置辨识

大型自由翻滚碎片的质心是在轨操作基坐标系下的不动点，也是碎片连体基下动力学参数向卫星坐标系转换的基准，对其精确识别是提高碎片动力学参数辨识精度的关键。提出基于惯性单元测量数据与双目视觉定位数据融合的大型空间碎片质心位置识别方法。基于无力矩欧拉方程，获取附着到空间碎片表面的惯性单元间转换关系，利用该转换关系对惯性单元冗余测量数据优化，再优化求解惯性单元到质心点距离；利用双目视觉获取惯性单元上标记点动态坐标，再利用惯性单元到质心点距离，基于三点定位原理识别大型空间碎片的质心位置。以加入高斯白噪声的惯性单元与双目视觉测量数据进行仿真，结果表明优化解算后惯性单元实时测量数据的误差降低到1%以下，解算的质心位置三轴误差小于0.47mm；开展了地面试验，结果表明，解算的质心位置三轴误差小于0.49mm。仿真和试验证明，该方法能够为大型空间碎片的消旋、捕获任务提供准确的数据基准。     

高精度星载SAR多普勒参数估算方法

提出了一种基于空间坐标转换,利用卫星位置、速度参数精确估算星载SAR(Synthetic Aperture Radar)全观测带多普勒参数的方法.利用卫星速度、位置,通过星载SAR空间几何模型和坐标转换关系,建立SAR图像中斜距同卫星下视角之间的四次方程,解出下视角并进一步计算出该斜距处的多普勒参数值.仿真结果表明,该方法在无卫星位置、速度误差情况下估算精度达到0.02Hz(多普勒中心频率)和2×10-4Hz/s(多普勒调频率);存在卫星位置测量误差(300m)以及速度测量误差(0.3m/s)的情况下,估算精度达到0.8Hz(多普勒中心频率)和0.07Hz/s(多普勒调频率).该方法适用于单星SAR以及分布式SAR高精度多普勒参数的估算.      

空间目标预警阈值确定分析

针对目前通常采用计算碰撞概率来进行空间目标碰撞预警的方法,为提高其评判标准的精度以达到提高航天器精准预警的目的,分析了目前空间目标碰撞概率阈值确定过程的总体框架.对阈值确定过程中所涉及的误差协方差矩阵确定方法、碰撞概率计算以及碎片通量计算方法进行了研究.以国际空间站（ISS）为例,通过计算其所在空间的碎片通量,分析其轨道受空间环境的影响情况,并与早期结果进行比较,得出其以往的碰撞概率阈值可能被高估的结论.      

Atmospheric drag modelling for orbital micro-debris at LEO altitudes

Data from satellite impact experiments and the scanning of recovered spacecraft offers an extended timebase to examine, using a consistent methodology, the microparticle fluxes. New penetration data from the TiCCE experiment on Eureca /1, 2/ adds to this database and shows that - despite an expected growth in the micro-debris flux - the observed flux is not greater than either LDEF or SMM. The question arises: “is this consistent with the micro particle flux being dominated by space debris or by meteoroids”.

To assist this assessment, numerical modelling using the Gear method /3/ of explicit time integration of the atmospheric drag lifetime of micron dimensioned orbital debris in both circular (LEO) and eccentric (GTO) orbits has been performed for the relevant space exposures. Results are applied to the data to examine whether the recent variations in flux can be attributed to varying levels of, orbital micro-debris caused by atmospheric drag and its changes during the solar cycle.     

Chebyshev不等式在空间碎片碰撞概率置信度中的应用

空间碎片的碰撞预警与规避能有效避免碰撞事件的发生.碰撞概率是碰撞预警的主要判据,也是航天器规避机动决策的主要依据.由于计算碰撞概率的各相关参数带有误差,导致计算得到的碰撞概率值并不准确,难以做出规避机动决策,因此评估碰撞概率值的可信程度是亟需解决的问题.本文给出了一种碰撞概率置信度的计算方法,利用各影响参数的标准差,通过误差传递的方法计算碰撞概率的标准差,结合单边Chebyshev不等式,给出碰撞概率值大于10-4阈值时的置信度,并结合实际案例进行了分析.      

星敏感器中星图图像的星体细分定位方法研究

介绍了星敏感器的基本工作原理和星图图像的预处理的主要方法,将传统质心法、带阈值的质心法、平方加权质心法和高斯曲面拟合法应用于星敏感器中星图图像的星体细分定位,并进行了较为系统的仿真研究.仿真结果表明,带阈值的质心法是一种较为理想的星体细分定位方法.就噪声水平、阈值选择及低通滤波对细分定位精度的影响进行了仿真研究.最后,利用仿真结果对模拟星图图像的星体进行了细分定位实验,取得了较为满意的结果.      

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.     

基于拉普拉斯变换的空间目标碰撞概率计算方法

碰撞概率是空间碎片碰撞预警中评判碰撞发生可能性大小的重要依据,对航天器机动规避具有重要意义。基于拉普拉斯变换的碰撞概率计算方法利用拉普拉斯变换以及幂级数的定义,推导了在短时间接近情况下碰撞概率的幂级数表达式,分析了碰撞概率的截断误差并确定了在不同精度要求下的幂级数项数。针对2009年美俄卫星的碰撞事件,将基于拉普拉斯变换的碰撞概率计算结果与Chan方法、Monte Carlo方法的计算结果进行比较,验证了基于拉普拉斯变换方法在计算精度上的优势。      

带偏置点的绳系拖拽离轨系统动力学研究

考虑空间拖船利用飞网/飞爪对空间残骸捕获结束后绳系拖拽系统的动力学特性,开展了基于简化的带偏置点构型的建模及仿真研究.首先,捕获后的组合体包括空间拖船、系绳和空间残骸,系绳在空间残骸一端的牵挂点看作偏置点,给出相应的的绳系拖拽系统构型;其次,以降轨离轨过程为例,建立系统能量方程,并根据欧拉-拉格朗日方程给出系统的动力学表达式并估算系绳张紧情况下的平衡点;最后,设定离轨推力,在不同的初始角速度、系绳张紧或松弛以及不同松弛程度条件下,分析绳系拖拽离轨系统的动力学行为.研究表明,空间残骸小的初始角速度和张紧或略微松弛的系绳能够保证安全离轨.     

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.     

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.      

Application of CCD drift-scan photoelectric technique on monitoring GEO satellites

Geosynchronous Earth Orbit (GEO) satellites are widely used because of their unique characteristics of high-orbit and remaining permanently in the same area of the sky. Precise monitoring of GEO satellites can provide a key reference for the judgment of satellite operation status, the capture and identification of targets, and the analysis of collision warning. The observation using ground-based optical telescopes plays an important role in the field of monitoring GEO targets. Different from distant celestial bodies, there is a relative movement between the GEO target and the background reference stars, which makes the conventional observation method limited for long focal length telescopes. CCD drift-scan photoelectric technique is applied on monitoring GEO targets. In the case of parking the telescope, the good round images of the background reference stars and the GEO target at the same sky region can be obtained through the alternating observation of CCD drift-scan mode and CCD stare mode, so as to improve the precision of celestial positioning for the GEO target. Observation experiments of GEO targets were carried out with 1.56-meter telescope of Shanghai Astronomical Observatory. The results show that the application of CCD drift-scan photoelectric technique makes the precision of observing the GEO target reach the level of 0.2″, which gives full play to the advantage of the long focal length of the telescope. The effect of orbit improvement based on multi-pass of observations is obvious and the prediction precision of extrapolating to 72-h is in the order of several arc seconds in azimuth and elevation.     

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.     

卫星遥感图像信息作为姿态敏感器的应用研究

陆标敏感器可以从卫星遥感图像信息中提取卫星的姿态信息,它根据卫星实时图像与基准图像之间的偏移量,计算出卫星的姿态。对陆标敏感器的总体方案进行了设计,在图像匹配技术中采用基于区域特征的先粗匹配、后精匹配的匹配算法,在姿态确定算法中对可能达到的姿态测量精度进行了理论分析,研究表明陆标敏感器可以获得较高精度的卫星姿态信息,作为新型光学姿态敏感器具有重要的研究意义。     

Advances in auroral imaging from space

Space imaging of the aurora provides unique quantitative information on the instantaneous global distribution and pattern of the aurora - a direct result of particle acceleration and precipitation processes occurring throughout the magnetosphere. Techniques for imaging from space have usually involved systematically scanning a detector across the earth using some combination of satellite motion and spin, scanning mirrors, and/or electronic scanning. The recent advent of CCD image sensor arrays opens up possibilities for vastly improved sensitivity and resolution in satellite imagers, although scanning systems retain significant advantages in situations where scattered light is a problem and where narrow band optical interference filters are needed.A new type of imaging instrument being built in Canada for the Swedish Viking satellite will employ a two-dimensional CCD array detector which is fibre-optically coupled to a micro-channel plate intensifier. It will produce images of low light level auroral emissions at the rate of one image per spin of the satellite (20 seconds). The instrument operates in the vacuum ultraviolet and uses a fast inverse Cassegrain optical system. Charge is shifted in the CCD imaging array in synchronism with the moving image so that exposure times of approximately one second will be achieved.     

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.