Orbital error propagation considering atmospheric density uncertainty

Due to the influence of various errors, the orbital uncertainty propagation of artificial celestial objects while orbit prediction is required, especially in some applications such as conjunction analysis. In the orbital error propagation of artificial celestial objects in low Earth orbits (LEOs), atmospheric density uncertainty is one of the important factors that require special attention. In this paper, on the basis of considering the uncertainties of position and velocity, the atmospheric density uncertainty is also taken into account to further investigate the orbital error propagation of artificial celestial objects in LEOs. Artificial intelligence algorithms are introduced, the MC Dropout neural network and the heteroscedastic loss function are used to realize the correction of the empirical atmospheric density model, as well as to provide the quantification of model uncertainty and input uncertainty for the corrected atmospheric densities. It is shown that the neural network we built achieves good results in atmospheric density correction, and the uncertainty quantization obtained from the neural network is also reasonable. Moreover, using the Gaussian mixture model - unscented transform (GMM-UT) method, the atmospheric density uncertainty is taken into account in the orbital uncertainty propagation, by adding a sampled random term to the corrected atmospheric density when calculating atmospheric density. The feasibility of the GMM-UT method considering atmospheric density uncertainty is proved by the further comparison of abundant sampling points and GMM-UT results (with and without considering atmospheric density uncertainty).     

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。     

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。     

适用于时变不确定系统的并行模型自适应估计

摘要： 针对受到潜在模型不确定性影响的系统,设计一种并行模型自适应估计(PMAE)算法.以往基于不确定性系统模型设计的滤波算法,在模型精确的情况下,性能往往不及传统卡尔曼滤波（KF）.为了解决该问题,设计基于多个并行滤波器的自适应状态估计算法,其中一个滤波器为KF,用于在未出现模型不确定性的情况下,对系统进行最优状态估计;另一个滤波器为扩维卡尔曼滤波（AKF）,用于在出现模型不确定性的情况下,对不确定性模型参数进行辨识.以空间目标监视为例,分析算法的性能.仿真结果表明,利用PMAE算法能够自适应地对两个并行滤波器进行切换和折衷,从而有效应对模型中存在不确定性和不存在不确定性两种情况.     

月球探测器天文导航的遗传粒子滤波方法

天文导航系统是典型的非线性和噪声非高斯分布的系统.针对传统的扩展卡尔曼滤波不适于非线性和噪声非高斯分布的系统,和一般粒子滤波存在的粒子退化和采样枯竭问题,提出了一种基于遗传算法进行再采样的月球探测器自主天文导航粒子滤波新方法.计算机仿真结果显示了该方法可以有效的克服传统粒子滤波方法的缺点,提高天文导航系统的定位精度.      

Accurate estimation of relative atmospheric density error on the example of uncertain geomagnetic activity information

Errors in neutral atmospheric density are the dominant contributor to unrealistic orbital state-vector covariances in low Earth orbits (LEO). Density uncertainty is caused by model-uncertainty at spatial scales below and within the model resolution, as well as input-uncertainty of the environmental parameters supplied to the semi-empirical atmospheric model.The paper at hand provides multiple contributions. First, analytic equations are derived to estimate the relative density error due to an input parameter uncertainty in any of the environmental parameters supplied to the model. Second, it is shown on the example of uncertain geomagnetic activity information, how to compute the required inputs to facilitate the accurate estimation of the relative density error.A clamped cubic splining approach for the conversion from geomagnetic amplitude (ap) to the kp index is postulated to perform this uncertainty propagation, as other algorithms were found unsuitable for this task. Results of numerical simulations with three popular semi-empirical models are provided to validate the set of derived equations. It is found that geomagnetic input uncertainty is especially important to consider in case of low global geomagnetic activity. The findings seamlessly integrate with prior work by the authors to perform density-uncertainty considering orbit estimation.     

利用OH夜气辉反演原子氧数密度时输入参数的不确定度对反演结果的影响

借助OH夜气辉辐射的光化学模式,由OH夜气辉辐射反演中间层-低热层区域的原子氧数密度时,输入参数的不确定性将导致反演得到的原子氧数密度具有不确定性.以在sudden death猝灭模式下通过OH(8-3)振动带体辐射率反演原子氧数密度为例,分别研究了大气参数和OH气辉辐射率的不确定度引起的反演不确定度、化学反应速率常数的不确定度引起的反演不确定度,以及所有输入参数的不确定度共同引起的反演不确定度,找出其不确定度对反演结果影响最大的参数.结果表明,三种反演不确定度均随着高度的升高而增大,温度和体辐射率的不确定度对第一种反演不确定度的贡献最大,反应速率常数b(8)和A(8-3)、的不确定度对第二种反演不确定度的贡献最大.     

Satellite collision probability estimation using polynomial chaos expansions

This paper presents the application of polynomial chaos (PC) to estimating the probability of collision between two spacecraft. Common methods of quantifying this probability for conjunction assessment use either Monte Carlo analyses or include simplifying assumptions to improve tractability. A PC expansion, or PCE, provides a means for approximating the solution to a large set of stochastic ordinary differential equations, which includes orbit propagation. When compared to Monte Carlo methods, non-intrusive, i.e., sampling-based, PCE generation techniques may greatly reduce the number of orbit propagations required to approximate the possibly non-Gaussian, a posteriori probability density function. The presented PC-based method of computing collision probability requires no fundamental simplifying assumptions, and reduces the computation time compared to Monte Carlo. This paper considers two cases where the common conjunction assessment assumptions are no longer valid. The results indeed demonstrate a reduction in computation time when compared to Monte Carlo, and improved accuracy when compared to simplified techniques.     

基于交互式多模型鲁棒滤波的目标机动估计算法

针对雷达导引头的测量信息带有闪烁噪声的问题，研究了交互式多模型和鲁棒滤波在雷达导引头目标机动估计中的应用.采用Huber Based滤波理论改进高阶容积卡尔曼滤波，提出高阶容积鲁棒滤波算法，选取Singer模型、“当前”统计模型、常加速度模型作为目标机动模型，建立雷达导引头测量模型，结合交互式多模型算法框架，设计目标机动估计滤波器.蒙特卡洛数字仿真结果表明，所提算法的鲁棒性较强，与传统高斯滤波相比，所提算法对闪烁噪声具有更高的滤波精度.     

基于并行扩展卡尔曼滤波的自主卫星星座导航方法

针对星间距离测量容易受到外界干扰的问题，提出了一种适用于多颗地球卫星和一颗月球卫星的卫星星座自主导航的并行扩展卡尔曼滤波算法.通过解决噪声统计不确定情况下的测量调度问题来选择适当的测量，降低干扰的影响.为了自适应地选择适当的测量，提出一种基于不同来源的测量构造多个子集的并行扩展卡尔曼滤波器，其中每个扩展卡尔曼滤波器用于处理不同测量子集，并基于残差序列计算子滤波器的权重，组合并行滤波器的估计结果.通过与EKF和传统的多模型自适应估计算法进行比较，表明所提出方法在干扰条件下的三轴位置估计误差的稳定性，体现了性能优势.     

伴飞航天器轨道修正点状态的最小二乘估计

研究了近圆轨道航天器长期伴随飞行在轨道修正时刻相对状态的最小二乘估计方法。针对长期伴飞航天器在固定时刻进行轨道修正的特点,提出采用最小二乘估计方法对轨道修正时刻的相对位置状态进行估计,并基于模型误差特点提出对该算法进行改进的加权最小二乘估计算法。算法具有计算相对简单、算法灵活等特点。仿真结果表明,对于固定时刻的状态估计,这种加权最小二乘估计算法和扩展卡尔曼滤波算法的效果相当,能够满足在轨长期伴随飞行在轨道修正时刻的相对状态估计精度要求。     

嫦娥五号月面上升和下降段实时轨道确定

针对月球探测中月面上升和下降段的实时轨道确定问题,提出基于三向测量的实时自适应当前统计方法。首先,通过自适应当前统计模型描述探测器月面上升下降过程,其次,综合利用三向数据进行测量更新,最后,通过UKF滤波算法完成实时轨道确定。由于自适应当前统计模型具有良好的适应性,该方法能对探测器月面上升和下降段进行有效定位,通过嫦娥五号探测器实际上升和下降过程数据进行测试,结果表明,文章提出的基于三向测量的实时自适应当前统计方法比传统的几何定位方法具有更好的抗差性,对深空目标探测具有一定的工程应用价值。     

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.     

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.     

Disturbance observer based model predictive control for accurate atmospheric entry of spacecraft

Facing the complex aerodynamic environment of Mars atmosphere, a composite atmospheric entry trajectory tracking strategy is investigated in this paper. External disturbances, initial states uncertainties and aerodynamic parameters uncertainties are the main problems. The composite strategy is designed to solve these problems and improve the accuracy of Mars atmospheric entry. This strategy includes a model predictive control for optimized trajectory tracking performance, as well as a disturbance observer based feedforward compensation for external disturbances and uncertainties attenuation. 500-run Monte Carlo simulations show that the proposed composite control scheme achieves more precise Mars atmospheric entry (3.8?km parachute deployment point distribution error) than the baseline control scheme (8.4?km) and integral control scheme (5.8?km).     

传导发射测量不确定度评定的验证

为了保证测量不确定度评定结果有足够的可信度,必须对评定的测量不确定度进行验证。概述了采用蒙特卡洛模拟法验证传导发射测量不确定度的方法,介绍了通过埃奇沃思级数估计测量结果概率分布的过程和应用蒙特卡洛方法解决实际问题的基本步骤,最后结合某试验室的实例给出了验证结果,证明在大部分频点上其根据GUM评定的传导发射测量不确定度是可信的。     

多星对合作目标的分布式协同导航滤波算法

针对多颗在轨卫星对空间合作目标的协同导航问题,提出了一种适用于协同导航的分布式球面单形-径向容积求积分卡尔曼滤波（DSSRCQKF）算法。为了计算非线性滤波中的高斯加权积分,分别使用球面单形准则和二阶高斯-拉盖尔求积分准则计算球面积分和径向积分,提出了一种新的球面单形-径向容积求积分准则。将该准则嵌入分布式卡尔曼滤波框架中,结合协同导航的非线性数学模型,给出适用于协同导航的DSSRCQKF算法,该算法要求每颗导航星仅与其邻居星进行通信,通过数据的分布式融合实现对目标星轨道状态的一致估计,从而避免了传统集中式处理中较高的通信和计算压力。仿真实验结果表明,与分布式卡尔曼滤波相比,本文算法将对合作目标的实时定位精度提高了11 m,定速精度提高了0.02 m/s,从而验证了本文算法的有效性。      

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.     

结构振动主动控制系统的非概率可靠性分析

为了解决结构主动振动控制系统的可靠性问题,考虑结构参数的不确定性,研究了结构振动主动控制系统可靠性分析的非概率方法.对不确定变量用区间数或区间向量进行描述,基于区间数学,提出了含区间不确定参数的闭环控制系统响应的计算方法,在此基础之上结合非概率可靠性分析方法,建立了适用于振动控制系统的非概率可靠性分析方法.该方法无需不确定量的概率信息,只需明确参数所在区间范围即可,对开环系统和闭环控制系统的可靠性分析与基于可靠性的控制器设计具有一定的理论意义.通过数值算例,将非概率可靠性分析方法与蒙特卡洛方法进行了比较,结果表明了本文所提方法的有效性和对复杂结构振动主动控制系统的适用性.