Short-arc tracklet association for geostationary objects

Measurement association and initial orbit determination is a fundamental task when building up a database of space objects. This paper proposes an efficient and robust method to determine the orbit using the available information of two tracklets, i.e. their line-of-sights and their derivatives. The approach works with a boundary-value formulation to represent hypothesized orbital states and uses an optimization scheme to find the best fitting orbits. The method is assessed and compared to an initial-value formulation using a measurement set taken by the Zimmerwald Small Aperture Robotic Telescope of the Astronomical Institute at the University of Bern. False associations of closely spaced objects on similar orbits cannot be completely eliminated due to the short duration of the measurement arcs. However, the presented approach uses the available information optimally and the overall association performance and robustness is very promising. The boundary-value optimization takes only around 2% of computational time when compared to optimization approaches using an initial-value formulation. The full potential of the method in terms of run-time is additionally illustrated by comparing it to other published association methods.     

基于扩展卡尔曼滤波的XPNAV-1卫星自主定轨算法研究

X射线脉冲星导航1号（XPNAV-1）是全球首颗脉冲星导航专用试验卫星。利用该卫星观测的单颗脉冲星数据,采用几何约束方法,能够有效抑制轨道误差增长,但存在长时间定轨发散问题。针对XPNAV-1卫星拓展试验任务及脉冲星导航后续发展需求,利用多颗脉冲星的观测数据,研究基于扩展卡尔曼滤波（EKF）的卫星自主定轨算法。首先,建立该卫星的轨道力学模型和观测方程;然后,详细论述EKF滤波算法和分段式定常系统（PWCS）的可观测性分析方法;最后,通过综合分析XPNAV-1卫星的观测数据、脉冲星对该卫星轨道的覆盖性以及系统状态的可观测性,进行自主定轨算法试验。试验结果表明,基于EKF的自主定轨算法滤波过程收敛,验证了该算法的合理性和有效性。     

基于TLE的弹道系数计算方法及应用分析

针对仅使用两行要素(Two Line Element,TLE)作为数据源的应用需求,研究了基于TLE轨道衰减的弹道系数计算方法。介绍了一种常用的基于两组TLE的直接计算法,分析TLE选取间隔对结果精度的影响;提出了一种基于多组TLE的迭代计算方法,以降低异常TLE对计算结果的影响;从弹道系数计算效果、在再入预报中的应用等方面对这两种方法进行比较分析。结果表明,两种方法各有优劣,基于多组TLE的迭代计算法稳定性更高、受TLE精度的影响更小;由于数据区间更短,基于两组TLE的计算结果对短期轨道衰减特性反应得更准确,用于临近再入时的预报效果更好。     

基于跟踪微分器的多目标数据关联算法

根据目标在运动过程中位置与速度只能连续变化这一事实,提出了杂波环境下基于跟踪微分器的一种多目标数据关联算法.算法利用跟踪微分器得到目标波门内所有量测的位置与速度,通过将其与目标前一时刻的位置和速度的比较来实现在未知杂波环境下的多目标数据关联.该算法直接利用量测数据,不需要目标运动、传感器噪声及杂波的先验统计知识,在目标数已知杂波不很密集的情况下具有良好的数据关联能力.此算法计算量小、结构简单,与目标状态滤波估计算法完全分离,便于模块化设计和与其他滤波算法结合,易于工程实现.仿真结果验证了算法的有效性.     

基于正弦拟合的空间目标短弧关联算法

星敏感器是一种高精度姿态传感器,具有断续拍摄空间目标的能力,可作为空间目标监视平台。将星敏感器断续观测的短弧准确关联是实现空间目标精确定轨的前提。通过对空间目标的大量观测数据统计发现,空间目标的赤纬随赤经的变化始终满足一条周期为360°的正弦曲线且峰值与轨道倾角有关。对新旧航迹的赤经赤纬变化规律进行研究,提出一种基于正弦拟合的空间目标短弧关联算法,避免了空间目标初定轨的步骤,节约了算法运行时间。仿真中观测时长最短为50s,通过对目标密集的GEO带增加额外约束,可区分倾角相差0.01°的轨道。当航迹段间隔3h时,3组噪声水平目标关联的准确率均达90%以上。     

基于混合粒子滤波的载波估计算法

针对粒子滤波载波估计算法的高复杂度、粒子退化及贫化问题,提出了一种基于混合粒子滤波的载波估计方法.该方法引入多阶马尔科夫模型,采用多个非零均值高斯分布的加权和来近似重要性函数的最佳选择,并根据最大后验概率准则规范粒子的迭代计算.仿真结果表明,在非高斯噪声环境下,低轨卫星通信TDMA/DEQPSK(Time Division Multiple Address/Differential Quadrature Phase Shift Keying)数据帧非合作接收载波估计时,与基于经典粒子滤波的载波估计算法相比,提高了粒子"效率",在误码性能相当的情况下,有效降低了计算复杂度.     

Optimising filtering of two-line element sets to increase re-entry prediction accuracy for GTO objects

Predicting re-entry epoch of space objects enables managing the risk to ground population. Predictions are particularly difficult for objects in highly-elliptical orbits, and important for objects with components that can survive re-entry, e.g. rocket bodies (R/Bs). This paper presents a methodology to filter two-line element sets (TLEs) to facilitate accurate re-entry prediction of such objects. Difficulties in using TLEs for precise analyses are highlighted and a set of filters that identifies erroneous element sets is developed. The filter settings are optimised using an artificially generated TLE time series. Optimisation results are verified on real TLEs by analysing the automatically found outliers for exemplar R/Bs. Based on a study of 96 historical re-entries, it is shown that TLE filtering is necessary on all orbital elements that are being used in a given analysis in order to avoid considerably inaccurate results.     

Precise orbit determination using the batch filter based on particle filtering with genetic resampling approach

In this study, genetic resampling (GRS) approach is utilized for precise orbit determination (POD) using the batch filter based on particle filtering (PF). Two genetic operations, which are arithmetic crossover and residual mutation, are used for GRS of the batch filter based on PF (PF batch filter). For POD, Laser-ranging Precise Orbit Determination System (LPODS) and satellite laser ranging (SLR) observations of the CHAMP satellite are used. Monte Carlo trials for POD are performed by one hundred times. The characteristics of the POD results by PF batch filter with GRS are compared with those of a PF batch filter with minimum residual resampling (MRRS). The post-fit residual, 3D error by external orbit comparison, and POD repeatability are analyzed for orbit quality assessments. The POD results are externally checked by NASA JPL’s orbits using totally different software, measurements, and techniques. For post-fit residuals and 3D errors, both MRRS and GRS give accurate estimation results whose mean root mean square (RMS) values are at a level of 5 cm and 10–13 cm, respectively. The mean radial orbit errors of both methods are at a level of 5 cm. For POD repeatability represented as the standard deviations of post-fit residuals and 3D errors by repetitive PODs, however, GRS yields 25% and 13% more robust estimation results than MRRS for post-fit residual and 3D error, respectively. This study shows that PF batch filter with GRS approach using genetic operations is superior to PF batch filter with MRRS in terms of robustness in POD with SLR observations.     

Orbit determination by genetic algorithm and application to GEO observation

This paper demonstrates an initial orbit determination method that solves the problem by a genetic algorithm using two well-known solutions for the Lambert’s problem: universal variable method and Battin method. This paper also suggests an intuitive error evaluation method in terms of rotational angle and orbit shape by separating orbit elements into two groups. As reference orbit, mean orbit elements (original two-lines elements) and osculating orbit elements considering the J2 effect are adopted and compared. Our proposed orbit determination method has been tested with actual optical observations of a geosynchronous spacecraft. It should be noted that this demonstration of the orbit determination is limited to one test case. This observation was conducted during approximately 70 min on 2013/05/15 UT. Our method was compared with the orbit elements propagated by SGP4 using the TLE of the spacecraft. The result indicates that our proposed method had a slightly better performance on estimating orbit shape than Gauss’s methods and Escobal’s method by 120 km. In addition, the result of the rotational angle is closer to the osculating orbit elements than the mean orbit elements by 0.02°, which supports that the estimated orbit is valid.     

基于广义正则化最小二乘的天基测向初定轨

传统天基测向初定轨的不足,主要是由于观测数据存在系统误差和观测方程组的系数矩阵病态或不可逆。文章建立观测方程的半参数回归模型,提出基于补偿最小二乘估计和岭估计的广义正则化最小二乘估计,推导了估计公式,并证明了相关统计性质。引入选主列Givens-QR分解算法,提高观测方程求解效率和数值计算稳定性。仿真结果表明:该方法应用于天基测向初定轨可行,可以提高定轨精度和解算成功率。     

基于多模型的不等长序列数据关联算法

单模型在处理不等长序列数据关联时不能兼顾计算精度、复杂度和抗扰性,为此提出了基于多模型(MM)的不等长序列数据关联算法。将基于滑动窗口和动态时间弯曲(DTW)的不等长序列相似度度量模型作为MM的输入模型,以2种模型计算得到的时似变化比作为模型判断指标进行模型转换,实现了2种模型的优势互补,并得到模型的应用条件,最后输出MM作用后的不等长序列相似度,以此作为关联指标进行关联判定。仿真实验验证了MM关联算法在处理不等长序列数据关联的有效性,并对序列长度和突变率变化对关联效果的影响进行了分析。     

Onboard orbit determination using GPS observations based on the unscented Kalman filter

Spaceborne GPS receivers are used for real-time navigation by most low Earth orbit (LEO) satellites. In general, the position and velocity accuracy of GPS navigation solutions without a dynamic filter are 25 m (1σ) and 0.5 m/s (1σ), respectively. However, GPS navigation solutions, which consist of position, velocity, and GPS receiver clock bias, have many abnormal excursions from the normal error range for space operation. These excursions lessen the accuracy of attitude control and onboard time synchronization. In this research, a new onboard orbit determination algorithm designed with the unscented Kalman filter (UKF) was developed to improve the performance. Because the UKF is able to obtain the posterior mean and covariance accurately by using the second-order Taylor series expansion through the sampled sigma points that are propagated by using the true nonlinear system, its performance can be better than that of the extended Kalman filter (EKF), which uses the linearized state transition matrix to predict the covariance. The dynamic models for orbit propagation applied perturbations due to the 40 × 40 geo-potential, the gravity of the Sun and Moon, solar radiation pressure, and atmospheric drag. The 7(8)th-order Runge–Kutta numerical integration was applied for orbit propagation. Two types of observations, navigation solutions and C/A code pseudorange, can be used at the user’s discretion. The performances of the onboard orbit determination were verified using real GPS data of the CHAMP and KOMPSAT-2 satellites. The results of the orbit determination were compared with the precision orbit ephemeris (POE) of the CHAMP and KOMPSAT-2 satellites.     

基于TLE的Starlink星座第一阶段部署情况分析

近年来,随着卫星技术的快速发展和低轨（low earth orbit,LEO）卫星宽带互联网建设需求的不断增加,低轨大规模星座发展日新月异。针对Starlink星座初始化部署问题,首先论述了“星链”（Starlink）星座现状,分析在轨卫星高度变化。然后利用公开的两行轨道根数（two-line element,TLE）,从卫星发射入轨、轨道面分布两个方面,简要分析了Starlink星座的部署情况,给出升交点的变化规律;同时仿真分析了Starlink星座对地面的覆盖性能。最后,给出星座轨道面和相位分布、故障卫星处置以及可见卫星数量。所分析的结果以期为中国未来部署大规模LEO星座的建设提供借鉴。     

一种基于有效修剪的最大频繁项集挖掘算法

对关联挖掘中的最大频繁项集挖掘问题进行了研究,提出了一种基于项集格修剪机制的最大频繁项集挖掘算法.采用项集格生成树的数据结构,将最大频繁项集挖掘过程转化为对项集格生成树进行深度优先搜索获取所有最大频繁节点的过程. 其中提高算法效率的一个重要措施是在遍历项集格生成树的过程中对生成树进行修剪.给出了项集格生成树的三个性质,并在此基础上提出了直接超集修剪、间接超集修剪与事务集等价修剪三种修剪机制,尽可能忽略非频繁节点及其所生成的扩展节点以减少遍历的节点数目.试验结果表明,三种修剪机制都能够有效地减少搜索空间,其中事务集等价修剪机制的效果最好,算法的性能与输入数据集的稠密程度相关.      

基于聚类最近数据关联的多目标跟踪算法

提出了一种基于聚类最近数据关联的多目标跟踪算法.建立了基于目标位置、目标大小和目标灰度的3层匹配距离,将3个距离加权综合得到目标匹配的距离函数.以目标链为基准寻找与其存在最小匹配距离关系的观测目标作为目标链的数据后继,再以此观测目标为基准寻找与其存在最小匹配距离关系的目标链作为该目标的数据前驱.当且仅当匹配对象之间前驱与后继关系同时成立时认为二者匹配成功.将已有目标链分为4类,将当前帧观测目标分为2类.分析各类数据间可能存在的匹配关系,利用上述方法进行匹配运算.对于目标遮挡等情况,基于目标运动轨迹的瞬时直线性和均值滤波原理,将某时间段内的目标质心坐标作为输入数据得到回归直线,预测下一时刻的目标质心位置.目标大小和灰度预测数据由该时间内均值滤波得到.本算法在多人体跟踪实验中取得良好效果.     

基于模糊逻辑的交互式多模型滤波算法

针对交互式多模型（IMM）滤波算法在对反舰导弹的"蛇形"机动方式进行跟踪时收敛速度慢、滤波精度低的问题。在三维空间内,假定目标以匀速直线和"蛇形"机动2种方式进行运动,以相对距离和视线角为观测信息,对IMM滤波算法的模型概率更新模块进行改进,提出了基于模糊逻辑的交互式多模型（FLIMM）滤波算法。通过仿真对比分析,改进后的算法能够有效地提高收敛速度,进而获得更高的跟踪精度。      

基于SSUKF的航天器自主导航算法

针对航天器自主导航系统对稳定性、精确性和实时性的要求,将超球面分布采 样点变换SSUT(Spherical Simplex Unscented Transformation)和Unscented卡尔曼滤波(UK F)相结合,研究了基于SSUT的UKF(SSUKF)导航滤波算法.由于SSUT减少了采样点个 数,在保证滤波精度和标准UKF相当的条件下减轻了计算负担.根据UKF和扩展卡尔曼滤波(E KF)计算过程相似的特点,设计了SSUKF和EKF相结合的混合卡尔曼滤波算法.算法通过能够 度量估计误差的模式切换函数,可以自适应地在SSUKF和EKF之间切换,避免了UKF计算效率低 以及EKF对滤波参数敏感、容易发散的缺点.数值仿真结果表明,混合卡尔曼滤波器提高了 计算效率,保证了估计精度,具有良好的鲁棒性,适合于航天器自主导航系统.      

基于MEDLL的分级搜索抗多径算法

以多径估计延迟锁定环路(MEDLL)为代表的参量式基带抗多径算法以其能够同时估计直达信号和多径信号各参数而受到广泛关注,然而该类算法估计精度的提高是以计算复杂度的增加为代价的。为了在保证估计精度的同时降低资源消耗并加快搜索速度,提出了一种MEDLL最大似然(ML)估计搜索方法,将粗搜索后得到的参数估计值作为下一级搜索的先验信息,缩小搜索范围后减小搜索步进,完成逐级精细的参数估计。推导了原始MEDLL及树状分级结构的MEDLL(T-MEDLL)算法计算复杂度表达式;其中在存在一路多径信号的情况下,对于0.01 chip的多径延迟分辨率,复杂度可以降低为传统盲搜索的30%~50%。进一步基于自研的数字中频(IF)GPS信号模拟器和软件GPS接收机平台对不同多径情况下盲搜索法与分级搜索算法的参数估计精度及码伪距多径误差等性能进行了对比,验证了更低计算复杂度的T-MEDLL可以达到与传统MEDLL算法同样的跟踪精度。      

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。