航天器与短期空间碎片云碰撞概率算法

讨论了航天器与碎片云碰撞概率的提法,介绍了不同碰撞概率间的转换方法。在航天器轨道和碎片云中心轨道都确定情况下,研究了碰撞概率的一般算法;并根据C-W方程推导了只在短时间内有效的简化碰撞概率算法。最后通过蒙特卡洛法验证了简化算法的正确性。     

空间目标碰撞预警的协方差计算与应用

碰撞概率是碰撞预警工程中空间目标危险交会的重要判据之一,其计算精度会受到预报协方差计算精度的影响. 本文统计计算了两种形式的预报协方差. 一是利用精密数值预报模型对卫星精密根数进行预报,将预报根数与精密根数的差作为样本,统计得出1～7天不同预报期的预报协方差;二是采用 SGP4/SDP4预报模型对TLE数据进行预报,将预报根数与TLE根数的差作为样本,统计得出1～7d不同预报期的预报协方差. 分别分析两种方法中包含变轨过程和无变轨情况下的轨道预报精度. 结合2012年某低轨道卫星的危险交会,分析了采用不同协方差时,协方差精度对碰撞预警精度的影响. 协方差计算可为实际碰撞预警工程提供参考.      

Advanced ensemble modeling method for space object state prediction accounting for uncertainty in atmospheric density

For objects in the low Earth orbit region, uncertainty in atmospheric density estimation is an important source of orbit prediction error, which is critical for space traffic management activities such as the satellite conjunction analysis. This paper investigates the evolution of orbit error distribution in the presence of atmospheric density uncertainties, which are modeled using probabilistic machine learning techniques. The recently proposed “HASDM-ML,” “CHAMP-ML,” and “MSIS-UQ” machine learning models for density estimation (Licata and Mehta, 2022b; Licata et al., 2022b) are used in this work. The investigation is convoluted because of the spatial and temporal correlation of the atmospheric density values. We develop several Monte Carlo methods, each capturing a different spatiotemporal density correlation, to study the effects of density uncertainty on orbit uncertainty propagation. However, Monte Carlo analysis is computationally expensive, so a faster method based on the Kalman filtering technique for orbit uncertainty propagation is also explored. It is difficult to translate the uncertainty in atmospheric density to the uncertainty in orbital states under a standard extended Kalman filter or unscented Kalman filter framework. This work uses the so-called “consider covariance sigma point (CCSP)” filter that can account for the density uncertainties during orbit propagation. As a test-bed for validation purposes, a comparison between CCSP and Monte Carlo methods of orbit uncertainty propagation is carried out. Finally, using the HASDM-ML, CHAMP-ML, and MSIS-UQ density models, we propose an ensemble approach for orbit uncertainty quantification for four different space weather conditions.     

基于随机点模拟方法分析空间目标危险交会

基于SGP4模型在空间目标轨道预报中的应用, 在预报的位置速度信息和误差 信息基础上, 提出一种空间两目标碰撞预警的分析方法, 即随机点模拟方法. 与传统的交会平面积分方法相比, 其主要有两点不同: 一是在误差信息中考虑 了误差均值的影响, 即误差椭球不再以预报位置为中心分布; 二是在分析方 法上侧重于真实模拟可能的交会情形, 而不忽略任一方向上的误差. 通过算例分 析验证了该方法的可行性, 结果表明误差均值的非零性使得最大碰撞概率不 一定出现在预报的最近交会距离时刻. 同时仿真结果还表明, 两目标在相对速 度方向上的相对位置仍然存在误差, 这可能造成随机点模拟的碰撞概率计算 值较交会平面积分方法偏小. 不同的碰撞预警分析方法对应不同的预警门限, 根据文中实例, 初步确定10-6为随机点模拟方法的红色预警值.      

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。      

Drag coefficient modeling for grace using Direct Simulation Monte Carlo

Drag coefficient is a major source of uncertainty in predicting the orbit of a satellite in low Earth orbit (LEO). Computational methods like the Test Particle Monte Carlo (TPMC) and Direct Simulation Monte Carlo (DSMC) are important tools in accurately computing physical drag coefficients. However, the methods are computationally expensive and cannot be employed real time. Therefore, modeling of the physical drag coefficient is required. This work presents a technique of developing parameterized drag coefficients models using the DSMC method. The technique is validated by developing a model for the Gravity Recovery and Climate Experiment (GRACE) satellite. Results show that drag coefficients computed using the developed model for GRACE agree to within 1% with those computed using DSMC.     

Uncertainty-aware Cube algorithm for medium-term collision risk assessment

The number of Earth orbiting objects is constantly growing, and some orbital regions are becoming risky environments for space assets of interest, which are increasingly threatened by accidental collisions with other objects, especially in Low-Earth Orbit (LEO). Collision risk assessment is performed by various methods, both covariance and non-covariance based. The Cube algorithm is a non-covariance-based method used to estimate the collision rates between space objects, whose concept consists in dividing the space in cubes of fixed dimension and, at each time instant, checking if two or more objects share the same cube. Up to now its application has been limited to the long-term scenarios of orbital debris evolutionary models, where considering the uncertainties is not necessary and impractical. Within operative contexts, instead, medium-term collision risk analysis may be an important task, in which the propagation-related uncertainties play a prominent role, but the timescale poses challenges for the application of standard covariance-based conjunction analysis techniques. In this framework, this paper presents an approach for the evaluation of the medium-term collision frequency for objects in LEO, called Uncertainty-aware Cube method. It is a modified version of the Cube, able to take the possible errors in the space objects’ position into account for the detection of the conjunctions. As an object’s orbit is propagated, the along-track position error grows more and more, and each object could potentially be in a different position with respect to the one determined by numerical propagation and, thus, in a different cube. Considering the uncertainties, at each time instant the algorithm associates more than one cube to each object and checks if they share at least one cube. If so, a conjunction is detected and a degree of confidence is evaluated. The performance of the method is assessed in different LEO scenarios and compared to the original Cube method.     

DSMC方法中的自适应当地时间步长法

理论分析表明,Laux提出的DSMC(Direct Simulation of Monte Carlo)方法中的当地时间步长法尽管能够显著缩短流场达到稳定所需的CPU计算时间,提高DSMC程序的运行效率,却存在仿真分子运动和碰撞计算复杂,并需要耗费额外计算机内存的缺憾.对Laux的方法中仿真分子的运动处理时机提出了改进,并改变了其碰撞抽样方法,从而简化了仿真分子的运动和碰撞计算处理,避免了额外的计算机内存消耗.应用改进后的自适应时间步长法,对圆柱的稀薄气体绕流进行了采用和未采用改进的自适应当地时间步长法的对比计算.结果表明,改进后的自适应当地时间步长法能明显缩短流场达到稳定所需的计算时间,对流场模拟结果产生的影响却非常小.      

考虑分布参数依赖的风险混合不确定性分析方法

在定量化风险评估中,针对变量分布参数存在依赖时的混合不确定性传播问题,提出一种考虑分布参数完全依赖、部分依赖以及独立传播情形的双层混合不确定性刻画与传播框架,内外层分布参数不确定性分别用概率分布与可能性分布刻画,采用蒙特卡罗模拟法与模糊扩展原则相结合的数值求解方法。针对认知不确定性分布参数依赖性,构建了统一的认知不确定性分布参数依赖性模型,并给出依赖性系数的概念。为实现认知不确定性分布参数独立性采样,设计了基于D-S证据理论与随机集相结合的不确定性传播算法,相比于概率刻画下的双层蒙特卡罗方法,计算代价有效降低。以某型氢氧发动机贮箱共底漏气率为算例,验证本文方法的有效性与可行性。     

ESA’s process for the identification and assessment of high-risk conjunction events

ESA’s Space Debris Office provides an operational service for the assessment of collision risks of ESA satellites. Currently, the ENVISAT and ERS-2 missions in low Earth orbits are covered by this service. If an upcoming high-risk conjunction event is predicted based on analysis of Two-Line Element (TLE) data from the US Space Surveillance Network, then independent tracking data of the potential high-risk conjunction object are acquired to improve the knowledge of its orbit. This improved knowledge and the associated small error covariances derived from the orbit determination process scale down the position error ellipsoid at the conjunction epoch. Hence, for the same miss-distance, in most cases an avoidance manoeuvre can be suppressed with an acceptable residual risk.     

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。     

脉冲等离子体推力器放电电离二维PIC建模与仿真

摘要： 针对脉冲等离子体推力器（PPT）的放电过程,利用粒子网格 蒙特卡洛（PIC MCC）方法建立仿真计算模型.以LES 6 PPT为例,加入电离碰撞进行电离仿真.通过粒子运动碰撞与电磁场耦合仿真计算得到电流与电路总电阻的变化规律,揭示了PPT放电过程中等离子体密度分布情况.通过对比不加入粒子预分布与加入粒子预分布的两种条件下的计算结果,得到了加入粒子预分布使带电粒子密度计算结果更接近实验结果的结论.根据PPT的工作过程,在放电之前推力器内存在等离子体,所以在仿真研究中应进行粒子的预分布.文中的研究方法对PPT的粒子方法模拟具有一定的参考意义.     

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.     

Collision probabilities in geosynchronous orbit and techniques to control the environment

This paper addresses the physical crowding problem of geosynchronous satellites by summarizing two independent analyses. The first analysis included developing a new technique for predicting the expected time between collisions of active geosynchronous satellites with expired geosynchronous satellites. The unique feature of this new technique is that deterministic methods are used to model the motion of satellites and statistical techniques are employed to estimate collision probability. This allows realistic distributions of active and expired satellites to be used in the prediction process. The results of this new technique compare very closely to the results of previously used techniques. The second analysis addresses disposal options for spent upper stages (PAM-D, IUS, etc.) that are currently left in stable elliptical orbits. These spent upper stages are a hazard to the geosynchronous region as well as low earth orbits. Two propulsive techniques are presented that will reduce the orbit lifetime of the spent upper stages.     

空间目标碰撞概率的显式表达式及影响因素分析

在圆轨道情况下推导了空间目标碰撞概率的显式表达式,将碰撞概率表示为空间目标交会几何条件(过交线高度差、过交线时间差、轨道夹角等)和RSW坐标系误差方差的显式函数.根据显式表达式对碰撞概率的影响因素进行了分析,研究了过交线高度差、过交线时间差、轨道夹角、位置预报误差、等效半径等因素对碰撞概率的影响,得出了一些有意义的结论.     

基于线性协方差方法的交会对接误差分析

将线性协方差分析方法和蒙特卡罗仿真相结合,按交会任务和飞行特征把交会过程分为变轨飞行、自由飞行和中途速度修正三种特征段,研究了状态误差的传播规律和交会过程中各种误差对交会对接精度的影响。在变轨飞行段,分析了追踪航天器的姿态误差、控制系统性能状态估计误差,以及目标航天器轨道摄动对状态误差传播的影响。在自由飞行段,分析了追踪航天器估计状态误差的先验值和测轨误差对状态误差传播的影响。在中途速度修正段,分析了追踪航天器姿态误差和控制系统性能误差对状态误差传播的影响。仿真结果表明,误差分析方法设计合理,可以指导交会对接的轨道设计工作,能对已经设计好的交会策略进行误差分析和设计验证。     

空间碎片预警中的碰撞概率方法研究

由于空间碎片对飞行在地球轨道上的航天器危害日益严重,所以必须采取一些有效的防护措施,对于那些直径大于10 cm的碎片,通常是采用主动规避的方法来进行防护.为了避免传统的Box判据造成的过多错误预警,碰撞概率模型开始被应用于空间碎片预警,本文以空间站为例,将碰撞概率方法与传统Box区域判定法进行比较,介绍碰撞概率计算模型的建立方法,基于位置误差矩阵的碰撞概率Pc的算法,并针对实际交会事例进行了计算和分析.      

Explicit expression of collision probability in terms of RSW and NTW components of relative position

The existing analytical and numerical computing methods for collision probability (P_c) provide sufficiently accurate results, but do not reveal the direct connection between P_c and conjunction geometry or error covariance. This paper derived an explicit expression of P_c under the circular orbit assumption, based on analysis of closest approach distance and Chan’s analytical formulae for P_c. The P_c was expressed as an explicit function of the radial, in-track, cross-track components of relative position and error covariance. The explicit expression is simple and compact, relates P_c with components of relative position, which are two kinds of important conjunction risk criteria. By introducing non-zero flight-path angle and ratio of velocity’s magnitude, a modified expression of P_c was presented for objects in eccentric orbits. For objects with eccentricity less than 0.01 (which account for 62% of all LEO objects), the relative error of the explicit expression is less than 0.107, or 0.252 for typical conjunction cases. What really matters in conjunction risk assessment is the order of magnitude rather than the specific value of P_c, the precision of the explicit expression is sufficient for conjunction risk assessment and decision-making for most LEO objects.     

空间目标碰撞预警中的一种高效筛选方法

在航天器碰撞预警工作中, 为节省计算时间, 需要从大量空间目标中筛选出 可能的危险目标, 计算碰撞概率等参量并进行风险评估. 通常采用的筛选方 法包括高度筛选、几何筛选和时间筛选三步, 不同文献中后两步筛选的算 法略有不同, 同时各方法均难以实现预报三天的快速碰撞预警. 本文通过充 分考虑一阶摄动项对目标轨道的影响, 改进了时间筛选算法, 并在其后增加 了距离筛选, 将筛除比例从通常的大约99%提高到99.97%, 为实现快速碰 撞预警工作提供了理论支持. 通过对实测数据的计算比较, 验证了方 法的正确性及高效性.