天基空间目标监视的短弧段定轨技术

利用两个短弧段的天基测角资料实现对空间目标的轨道确定是天基空间目标监视系统需解决的重要问题之一。提出利用二体轨道的角动量和能量守恒方程计算空间目标初轨的新方法,该方法将短弧段的主要测量信息表示为弧段属性,由两个短弧段的弧段属性建立守恒方程,采用变量替换法求解守恒方程获得多个初轨,通过方差分析从中选择合适的初轨。针对轨道改进中的迭代发散和收敛于局部极小点的问题,提出了选取多个迭代初值进行轨道改进的采样方法。仿真结果表明,初轨确定算法是可行的,轨道改进能成功解算最小二乘轨道。     

天基空间监视交会计算和可观测时段预报的误差分析

将卫星和目标的轨道预报误差引入天基空间目标监视的任务规划中,研究了交会计算和可观测时段预报的误差分析方法。在协方差转换基本方法和交会信息计算公式的基础上,推导了从RSW轨道坐标系到RAE参数（距离、方位角、俯仰角）的协方差转换方法。对LEO和GEO目标观测分别引入相对速度和角距变化率,给出了可观测时段误差的分析方法。算例表明本文的计算结果与Monte-Carlo仿真结果相对误差不大于4%,典型轨道误差下LEO和GEO目标的可观测时段误差分别为0.2秒和3秒量级。该方法对任务规划和姿态及相机导引具有指导意义,还可用于分析成功观测对轨道预报精度的需求。     

Particle filter using a new resampling approach applied to LEO satellite autonomous orbit determination with a magnetometer

Particle filter (PF) is widely used in nonlinear and non-Gaussian systems. Resampling is one of the significant steps in PF. However, PF using conventional resampling approaches may lead to divergent solutions because of the degeneracy phenomenon or sample impoverishment associated with a multidimensional system. In this article, an efficient alternative to conventional resampling approaches, called adaptive partial systematic resampling (APSR) with Markov chain Monte Carlo move and intelligent roughening is proposed for satellite orbit determination using a magnetometer. The results of the new resampling approach are compared with conventional resampling approaches and with unscented Kalman filter (UKF) for various initial errors in position and velocity, measurement sampling periods, and measurement noises to evaluate and verify the performance of the new resampling approach. The results of the new resampling approach in all cases are significantly better than the results of conventional resampling approaches. The velocity accuracy of the orbit determination of APSR is slightly poorer than UKF for relatively small initial errors, and small Gaussian measurement noise. However, the proposed approach yields more robust and stable convergence than UKF under large initial errors, long measurement sampling period, large Gaussian measurement noise, or non-Gaussian noise.     

Design and development of correlation techniques to maintain a space surveillance system catalogue

A growing interest exists in a future, autonomous European Space Surveillance System (ESSS). Currently, most of the knowledge about Earth-orbiting space objects is based on information provided by the USASPACECOM. This paper presents the required initial orbit determination (IOD) and correlation techniques to process optical measurements. Former studies were focused on the handling of radar measurements, which are summarised with the aim of describing a global procedure for processing hybrid measurement types (combination of radar and optic data for catalogue maintenance). The introduction of manoeuvres are presented due to their importance in the space object catalogue maintenance.The detection of uncatalogued objects and the successful correlation of already catalogued objects involve two different tasks for telescopes: survey and tasking. Assumptions for both strategies are developed on the basis of the previous work developed at the University of Berne (see [T. Flohrer, T. Schildknecht, R. Musci, E. Stöveken, Performance estimation for GEO space surveillance, Advances in Space Research 35 (2005). [1]; T. Flohrer, T. Schildknecht, R. Musci, Proposed strategies for optical observations in a future European Space Surveillance Network, presented in the 36th COSPAR Scientific Assembly (2006). [2]; R. Musci, T. Schildknecht, M. Ploner, Orbit improvement for GEO objects using follow-up observations, Advances in Space Research 34 (2004). [3]; R. Musci, T. Schildknecht, M. Ploner, G. Beutler, Orbit improvement for GTO objects using follow-up observations, Advances in Space Research 35 (2005). [4]; R. Musci, T. Schildknecht, T. Flohrer, G. Beutler, Concept for a catalogue of space debris in GEO, Proceedings of the Fourth European Conference on Space Debris, (ESA SP-587, 2005). [5]]). When a new object appears in the field of view, initial orbit determination must be performed. When only one telescope per site is available, the initial measurements are separated by only a few seconds. Therefore, the initial orbit determination is quite inaccurate due to bad mathematical conditioning of the problem. In order to improve the accuracy of the initial orbit determination, several follow-up observations of the object are required. This implies that the telescope needs to track the detected objects over a long period, and therefore the time available for surveying is reduced. By processing the additional follow-up measurements, separated now by a few hours, the initial orbit determination gives more accurate results and the object can be recovered after an orbital revolution. When several telescopes per site are available, the optical strategies may be modified. The survey tasks can be distributed between the available telescopes. In this way the number of images corresponding to each object increases and to track the detected object over long periods is not always needed. Numerical results will be shown in order to evaluate the accuracy and features of the different telescope strategies. A key point for performing efficiently the cataloguing process is the calculation of the estimated state vector covariance matrix. The covariance matrix analysis allows an adaptive tasking-survey telescope scheduling. Moreover, the implementation of a proper batch orbit determination process by means of a square root information filter (SRIF) requires a realistic initial covariance matrix.Hybrid measurements are available from objects that can be observed through both radar and optical sensors (e.g. GTO objects). The batch orbit determination and correlation process of hybrid measurements is also based on SRIF using an extended measurement model. Both the initial orbit determination methods using radar and optical measurements have to be sufficiently accurate to initialise SRIF correctly. In order to avoid filter divergence, the estimated covariance must be correctly updated after processing both kinds of measurements. The implemented algorithms are explained and their performance is shown through realistic simulations.Techniques to detect and characterise object manoeuvres during the cataloguing process have been developed and implemented. Four main groups of manoeuvre objects have been established by means of their observed permitted orbital ranges (GEO, LEO, MEO–GPS, Molniya). The study is based on the historical TLEs files. When an object with an uncatalogued orbit appears, a comparison between the new orbit and the orbits contained in the permitted ranges of one of the manoeuvre groups is performed. If the required Δa and/or Δi to convert the lost orbit into the detected orbit seems to be feasible, a manoeuvre will be identified and the orbit will be updated in the catalogue. Otherwise, it will be decided that a new object was found. For this purpose, a procedure to estimate the manoeuvres and reset orbits have been developed.     

空间目标轨道信息软件平台的建设

空间目标轨道信息是空间态势感知的重要要素,是空间碰撞预警、空间碎片环境模型和许多空间应用的基础。因而,空间目标轨道确定成为空间态势感知的主要任务之一。文章介绍武汉大学测绘学院正在开发建设的空间目标轨道信息服务软件平台,该平台拥有的主要功能有:利用多源数据的卫星/空间碎片轨道确定(包括初轨确定)与预报、大气质量密度模型精化、空间碰撞预警和半解析法快速精密轨道传播等。文章还针对软件平台功能的研究进展进行了综述,介绍了软件平台发展规划。     

空间目标碰撞预警技术研究综述

随着在轨空间目标数量的不断增加,空间目标碰撞预警工作变得越来越重要。通过对国内外相关文献的调研分析,对空间目标碰撞预警的相关技术及其研究进展进行了全面地介绍。给出了空间目标碰撞预警的总体框架、关键技术和涉及的理论问题,对主要技术问题的研究进展进行了综述,提出了一些需要解决的问题,可供从事空间目标监视和碰撞预警等任务和研究的技术人员参考。     

重力梯度对自由漂浮空间机器人姿态扰动分析

分析重力梯度对在轨运行的自由漂浮空间机器人姿态运动影响。由Lagrange方法建立自由漂浮空间机器人受重力梯度扰动的非线性动力学模型。首先,考虑无控关节自由状态,分析重力梯度对关节运动的影响。其次,利用相平面轨迹分析重力梯度对自由漂浮系统姿态运动影响。最后,由速度偏差曲线分析重力梯度对机械臂的影响。结果表明,当作用时间接近轨道周期或更长时,重力梯度引起的关节偏差已十分显著,且这种扰动作用主要由轨道偏心率决定;关节锁定时俯仰姿态受扰运动有周期振动与翻滚两种形式,若初始角速度满足一定限值可以保证俯仰运动不发生翻滚;当机械臂长时间工作时,忽略重力梯度将产生明显的末端定位误差。     

航天器轨道机动的闭环控制精度分析

利用线性协方差分析法对航天器在闭环控制作用下轨道机动的精度问题进行了研究。首先,分析了存在的主要误差,给出了误差影响下航天器轨道机动闭环控制的系统框图。然后建立了开环和闭环控制系统协方差分析的数学模型,并根据轨道方程线性化给出了脉冲速度修正算法。对赤道大椭圆轨道卫星开环和闭环控制下轨道机动的精度问题进行了分析,与Monte Carlo仿真结果与一致,校验了方法的有效性与正确性。     

A simplified approach to uncertainty quantification for orbits in impulsive deflection scenarios

For the majority of near-Earth Asteroid (NEA) impact scenarios, optimal deflection strategies use a massive impactor or a nuclear explosive, either of which produce an impulsive change to the orbit of the object. However, uncertainties regarding the object composition and the efficiency of the deflection event lead to a non-negligible uncertainty in the deflection delta-velocity. Propagating this uncertainty through the resulting orbit will create a positional uncertainty envelope at the original impact epoch. We calculate a simplified analytic evolution for impulsively deflected NEAs and perform a full propagation of uncertainties that is nonlinear in the deflection delta-velocity vector. This provides an understanding of both the optimal deflection velocities needed for a given scenario, as well as the resulting positional uncertainty and corresponding residual impact probability. Confidence of a successful deflection attempt as a function of launch opportunities is also discussed for a specific case.     

Square-root quaternion cubature Kalman filtering for spacecraft attitude estimation

A novel quaternion estimator called square-root quaternion cubature Kalman filter is proposed for spacecraft attitude estimation. The filter approach uses a gyro-based model for quaternion propagation and a reduced quaternion measurement model to substantially reduce the computational costs. The process and measurement noises of the system model exhibit the same kind of linear state-dependence. The properties of the state-dependent noises are extended and more general expressions for the covariance matrices of such state-dependent noises are developed. The new filter estimates the quaternion directly in vector space and uses a two-step projection method to maintain the quaternion normalization constraint along the estimation process. The square-root forms enjoy a consistently improved numerical stability because all the resulting covariance matrices are guaranteed to stay positive semi-definite. Extensive Monte-Carlo simulations for several typical scenarios are performed, and simulation results indicate that the proposed filter provides lower attitude estimation errors with faster convergence rate than a multiplicative extended Kalman filter, a quaternion Kalman filter, and a generalized Rodrigues parameters (GRPs)-based cubature Kalman filter for large initialization errors.     

PCE方法在空间实验室轨道预报误差分析中的应用

应用多项式混沌展开法(PCE)进行空间实验室轨道预报误差分析。通过构建PCE模型对轨道预报的不确定性传播过程进行近似，进而对轨道预报后航天器位置和速度的误差进行分析。分析了不同PCE模型阶数、预报时长以及样本点的数目对构建PCE模型的影响。综合考虑精度和计算效率，给出了适用于空间实验室轨道预报误差分析的PCE模型。将PCE方法与传统方法进行对比，结果表明PCE方法有较好的非线性近似能力，且计算效率高，验证了PCE方法应用于空间实验室轨道预报误差分析的有效性。     

基于均匀设计的空间目标监视卫星覆盖能力仿真分析

将均匀设计方法应用到空间目标监视卫星覆盖能力仿真分析中是一种有益的尝试。在本文中,提出了利用均匀设计方法安排试验、STK仿真软件模拟试验的研究思路,能够更简单、更省时地分析空间目标监视卫星覆盖能力指标与各影响因素之间的关系。通过回归分析与规划求解得到最好的覆盖能力指标及各因素配置方案,对空间目标监视卫星覆盖能力的提高、轨道部署的优化和应用的拓展很有裨益。
     

Probability of Collision Error Analysis

The decision for the International Space Station (ISS) to maneuver to avoid a potential collision with another space object will be based on the probability of collision, P _C. The calculation of P _C requires the covariance of both objects at conjunction. It is well known that the covariance computed by US Space Command is optimistic (too small), especially at altitudes where atmospheric drag is the dominant perturbation, because its computation assumes there are no dynamic model errors. In this paper the effect of errors in the covariance on P _C and the sensitivity of P _C to the encounter geometry are investigated.     

基于半参数回归模型的批处理确定卫星轨道方法

由于卫星轨道观测数据中含有非线性影响因素,必然会降低定轨精度。在半参数 回归模型的基础上,应用小波阈值去噪算法估计并消除观测数据中存在的非线性影响因素, 提出了基于半参数回归模型的批处理确定卫星轨道的方法,以提高定轨精度;然后,在理论 上证明了在测量数据存在非线性影响因素的情形下,基于半参数回归模型的批处理确定卫星 轨道方法的定轨精度高于经典的批处理定轨精度;最后,对中低轨卫星应用批处理定轨进行 了仿真。结果表明：基于半参数回归模型的批处理确定卫星轨道方法分离出观测数据中的 白噪声和非线性影响因素,从而可以在观测数据中消除非线性影响因素,提高定轨的精度。     

编队飞行自主控制的自适应方法

自主的高精度相对控制是实现卫星编队任务的关键技术,自主性要求控制器尽可能只利用星载设备所能提供的测量信息以减少星间通信量,高精度要求控制器连续的消除干扰力、期望轨迹推演以及参考星轨道控制与机动所造成的跟踪误差,为此,本文推导了描述星间相对运动的完整动力学模型以及对期望轨迹的跟踪误差模型,基于Lyapunov方法设计了自适应控制器,并证明了此控制器可以保证闭环系统的最终跟踪误差小于指定的界。本文给出的控制器仅需要星间的相对位置和相对速度测量,不需要主星的轨道参数、轨道位置和轨道机动信息,从而具有较高的自主性。仿真结果表明本文给出的控制器可以完成对期望轨迹的跟踪。     

基于BP神经网络的自主定轨自适应Kalman滤波算法

针对Sage Husa自适应滤波方法存在的窗函数开窗大小选择问题,提出一种基于BP神经网络学习估计系统协方差矩阵的自适应Kalman滤波算法。该算法以Kalman滤波预测残差向量作为网络输入,通过网络分段离线学习确定预测残差向量与预测残差协方差矩阵间的非线性关系,自适应地估计Kalman滤波系统协方差矩阵。将其应用到自主定轨系统,仿真结果表明利用本文算法自主定轨60天星座平均URE误差小于1.9米,且能够快速跟踪到系统噪声的突变,较Kalman滤波方法和Sage Husa自适应滤波方法具有更好的性能。     

基于空间目标特性的无缝搜索技术研究

为了解决常规雷达搜索屏拦截空间目标概率不高的问题,利用空间目标过境具有周期性的特征,提出一种高拦截率的无缝搜索方法。当搜索屏经度覆盖范围大于等于目标重访经度差时,目标过境将至少被搜索屏拦截1次。利用这个特征,通过优化相控阵雷达法线仰角和搜索波位的驻留时间改变搜索屏的空间和能量分布,使各个轨道高度处的搜索经度覆盖范围等于目标的重访经度差,从而在最小时间资源开销的条件下实现了空间目标高概率拦截搜索。仿真结果表明,在时间资源开销相同的条件下,提出的无缝搜索方法与常规搜索方法相比,可将空间目标平均拦截率由90.93%提升至99.94%。研究对于提升空间目标监视雷达搜索效率具有较高的应用价值。     

A laser-optical system to re-enter or lower low Earth orbit space debris

Collisions among existing Low Earth Orbit (LEO) debris are now a main source of new debris, threatening future use of LEO space. Due to their greater number, small (1–10 cm) debris are the main threat, while large (>10 cm) objects are the main source of new debris. Flying up and interacting with each large object is inefficient due to the energy cost of orbit plane changes, and quite expensive per object removed. Strategically, it is imperative to remove both small and large debris. Laser-Orbital-Debris-Removal (LODR), is the only solution that can address both large and small debris. In this paper, we briefly review ground-based LODR, and discuss how a polar location can dramatically increase its effectiveness for the important class of sun-synchronous orbit (SSO) objects. With 20% clear weather, a laser-optical system at either pole could lower the 8-ton ENVISAT by 40 km in about 8 weeks, reducing the hazard it represents by a factor of four. We also discuss the advantages and disadvantages of a space-based LODR system. We estimate cost per object removed for these systems. International cooperation is essential for designing, building and operating any such system.     

Estimation of debris dispersion due to a space vehicle breakup during reentry

This paper studies the problem of the estimation of the extent of the airspace containing falling debris due to a space vehicle breakup. A precise propagation of debris to the ground is not practical for many reasons. There is insufficient knowledge of the initial state vector, ambient wind conditions, and the key parameters including the ballistic coefficients. In addition, propagation of all debris pieces to the ground would require extensive computer time. In this paper, a covariance propagation method is introduced for the estimation of debris dispersion due to a space vehicle breakup. The falling debris is simulated, and the data are analyzed to derive the probability of debris evolution in different altitude layers over time. The concept of positional probability ellipsoids is employed for the visualization of the results. Through a case study, it is shown that while the results of the covariance propagation method are in close agreement with those of the Monte Carlo method, the covariance propagation method is much more computationally efficient than the Monte Carlo method.     

空间翻滚非合作目标相对位姿估计的视觉SLAM方法

针对空间翻滚非合作目标相对位姿测量中目标先验信息缺失和模型不确定问题,将移动机器人视觉同步定位与建图（SLAM）贝叶斯滤波估计模型推广到非合作目标相对位姿测量中,提出一种基于视觉SLAM的翻滚非合作目标相对位姿估计方法。首先,构建了相对位姿估计的贝叶斯滤波状态转移模型和量测更新模型。其次,为避免平动噪声协方差过大导致滤波性能下降的问题,对状态转移方程进行优化,采用最小二乘估计方法预测位置参数。最后,采用一种联合无损卡尔曼滤波和粒子滤波的贝叶斯滤波方法实现了目标全部位姿参数的快速平滑估计。基于计算机合成图像数据和真实图像序列的仿真实验表明：提出的方法具有较优的速度和精度,且对目标速度变化、特征提取和数据关联误差等具有较好的鲁棒性。