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 This paper considers two cases where the common conjunction assessment assumptions are no longer valid.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.     

微波双通带滤波器多项式综合技术

文章提出了一种新的微波双通带滤波器多项式综合技术,这种方法将频率转换与优化方法结合,与频率转换方法相比较,文章中提出的新方法不仅能够有效地综合出具有等波纹响应特性的对称双通带滤波器的s参数多项式,而且对于两个不对称度很高的双通带也同样有效。文章最后给出了相应的设计实例,验证了该方法对所有双通带多项式综合的有效性。     

Impact time control guidance against maneuvering targets based on a nonlinear virtual relative model

Aiming at the problem of high-precision interception of air-maneuvering targets with impact time constraints, this paper proposes a novel guidance law based on a nonlinear virtual relative model in which the origin is attached to the target. In this way, the original maneuvering target is transformed into a stationary one. A polynomial function of the guidance command in the range domain with two unknown coefficients is introduced into the virtual model, one of the coefficients is determined to ...     

两种模型用于卫星钟差预报的性能分析

利用二次多项式和GM（1，1）灰色系统两种模型对GPS卫星钟差进行了预报分析。计算结果表明：在短期（1d）预报中，两者的预报误差在1ns量级以内；在长期（210d）预报中，灰色模型预报精度明显高于二次多项式模型预报精度，并且灰色模型长期（210d）预报Cs钟的精度高于Rb钟。     

横流转捩模型参数不确定度量化分析与应用研究

为获得横流转捩模型重要参数在不同工况下对转捩结果的定量影响规律并尝试获得更加准确可靠的转捩模型预测结果,开展了基于非嵌入式多项式混沌(NIPC)方法的横流转捩模型参数不确定度量化分析、参数敏感性分析及其应用研究。不确定度量化分析方面,对基于γ-Re_(θt)模型的完全当地化横流转捩模型的重要模型参数进行了拉丁超立方抽样,通过有限参数样本的S-K低速平板和无限展长后掠翼的数值计算,运用非嵌入式多项式混沌方法,定量分析了模型参数在不同类型转捩流场中的影响效能。在应用研究方面,以不确定度与参数敏感性定量分析结果为指导,对模型参数进行了横流诱导转捩条件下的筛选与标定,在NLF(2)-0415后掠翼、6:1标准椭球体以及DLR-F4翼身组合体算例中进行了验证,标定后的模型对多个算例的三维边界层横流转捩进行了较好的预测。     

Polynomial networks based adaptive attitude tracking control for NSVs with input constraints and stochastic noises

This paper proposes a backstepping technique and Multi-dimensional Taylor Polynomial Networks (MTPN) based adaptive attitude tracking control strategy for Near Space Vehicles (NSVs) subjected to input constraints and stochastic input noises. Firstly, considering the control input has stochastic noises, and the attitude motion dynamical model of the NSVs is actually modeled as the Multi-Input Multi-Output (MIMO) stochastic nonlinear system form. Furthermore, the MTPN is used to estimate the unknown system uncertainties, and an auxiliary system is designed to compensate the influence of the saturation control input. Then, by using backstepping method and the output of the auxiliary system, a MTPN-based robust adaptive attitude control approach is proposed for the NSVs with saturation input nonlinearity, stochastic input noises, and system uncertainties. Stochastic Lyapunov stability theory is utilized to analysis the stability in the sense of probability of the entire closed-loop system. Additionally, by selecting appropriate parameters, the tracking errors will converge to a small neighborhood with a tunable radius. Finally, the numerical simulation results of the NSVs attitude motion show the satisfactory flight control performance under the proposed tracking control strategy.     

基于无奇点根数的空间相对导航插值滤波算法

为了提高椭圆轨道航天器的相对导航精度,将基于Stirling公式的多项式插值滤波方法（DDF2）引入导航算法,降低了传统的卡尔曼滤波方法中泰勒级数展开线性化     

基于FFT的GPS快速并行捕获算法

为了提高GPS接收机的捕获速度和捕获精度,提出了一种新的基于FFT的并行捕获方案。采用一次FFT运算和多次IFFT运算同时完成频域和码相位域的二维搜索,将运算量减少一半。在通过判决捕获到相关峰后,通过简单内插精确确定载波频率,提高频率的分辨率。     

基于多项式拟合SDRE的三维导引律设计

应用多项式拟合的SDRE方法结合改进的极坐标系(MPC)设计了三维次优导引律。介绍了 SDRE方法与多项式拟合的SDRE方法,后者是前者十分优越的逼近;推导了MPC下的弹目相对 运动方程,将球坐标下的六个状态方程减少到了三个并且满足多项式拟合SDRE方法的应用前 提;在此基础上,推导出了三维拟合SDRE导引律(nSDRE)。仿真显示,nSDRE是一种有效的导 引律,较广义理想比例导引律(GIPN)具有更好的导引品质,特别在目标机动时,nSDRE能更 好地应对目标机动引起的视线转率发散而导致脱靶的问题。
     

基于测速定轨的轨道参数精度分析

利用误差传播关系,比较了测速体制下逐点定轨算法和多项式定轨算法的精度,为多项式和样条算法在测速定轨体制中的应用提供理论依据。利用逐点及多项式算法对两条典型轨道进行性能计算,结果表明:多项式算法能获得比逐点算法更高精度的轨道参数,且该算法数据结构简单、具有一定的实时性。