The high-speed development of space defense technology demands a high state estimation capacity for spacecraft tracking methods.However,reentry flight is accompanied by complex flight environments,which brings to the ...The high-speed development of space defense technology demands a high state estimation capacity for spacecraft tracking methods.However,reentry flight is accompanied by complex flight environments,which brings to the uncertain,complex,and strongly coupled non-Gaussian detection noise.As a result,there are several intractable considerations on the problem of state estimation tasks corrupted by complex non-Gaussian outliers for non-linear dynamics systems in practical application.To address these issues,a new iterated rational quadratic(RQ)kernel high-order unscented Kalman filtering(IRQHUKF)algorithm via capturing the statistics to break through the limitations of the Gaussian assumption is proposed.Firstly,the characteristic analysis of the RQ kernel is investigated in detail,which is the first attempt to carry out an exploration of the heavy-tailed characteristic and the ability on capturing highorder moments of the RQ kernel.Subsequently,the RQ kernel method is first introduced into the UKF algorithm as an error optimization criterion,termed the iterated RQ kernel-UKF(RQ-UKF)algorithm by derived analytically,which not only retains the high-order moments propagation process but also enhances the approximation capacity in the non-Gaussian noise problem for its ability in capturing highorder moments and heavy-tailed characteristics.Meanwhile,to tackle the limitations of the Gaussian distribution assumption in the linearization process of the non-linear systems,the high-order Sigma Points(SP)as a subsidiary role in propagating the state high-order statistics is devised by the moments matching method to improve the RQ-UKF.Finally,to further improve the flexibility of the IRQ-HUKF algorithm in practical application,an adaptive kernel parameter is derived analytically grounded in the Kullback-Leibler divergence(KLD)method and parametric sensitivity analysis of the RQ kernel.The simulation results demonstrate that the novel IRQ-HUKF algorithm is more robust and outperforms the existing advanced UKF with respect to the kernel method in reentry vehicle tracking scenarios under various noise environments.展开更多
In view of its use as reactivity theory,Conceptual Density Functional Theory(DFT),introduced by Parr et al.,has mainly concentrated up to now on the E = E[N,v] functional.However,different ensemble representations can...In view of its use as reactivity theory,Conceptual Density Functional Theory(DFT),introduced by Parr et al.,has mainly concentrated up to now on the E = E[N,v] functional.However,different ensemble representations can be used involving other variables also,such as ρ and μ.In this study,these different ensemble representations(E,?,F,and R) are briefly reviewed.Particular attention is then given to the corresponding second-order(functional) derivatives,and their analogieswith the second-order derivatives of thermodynamic state functions U,F,H,and G,which are related to each other via Legendre transformations,just as the DFT functionals(Nalewajski and Parr,1982).Starting from an analysis of the convexity/concavity of the DFT functionals,for which explicit proofs are discussed for some cases,the positive/negative definiteness of the associated kernels is derived and a detailed comparison is made with the thermodynamic derivatives.The stability conditions in thermodynamics are similar in structure to the convexity/concavity conditions for the DFT functionals.Thus,the DFT functionals are scrutinized based on the convexity/concavity of their two variables,to yield the possibility of establishing a relationship between the three second-order reactivity descriptors derived from the considered functional.Considering two ensemble representations,F and ?,F is eliminated as it has two dependent(extensive)variables,N and ρ.For ?,on the other hand,which is concave for both of its intensive variables(μ and υ),an inequality is derived from its three second-order(functional) derivatives:the global softness,the local softness,and the softness kernel.Combined with the negative value of the diagonal element of the linear response function,this inequality is shown to be compatible with the Berkowitz-Parr relationship,which relates the functional derivatives of ρ with υ,at constant N and μ.This was recently at stake upon quantifying Kohn's Nearsightedness of Electronic Matter.The analogy of the resulting inequality and the thermodynamic inequality for the G derivatives is highlighted.Potential research paths for this study are briefly addressed;the analogies between finite-temperature DFT response functions and their thermodynamic counterparts and the quest for analogous relationships,as derived in this paper,for DFT functionals that are analogues of entropy-dimensioned thermodynamic functions such as the Massieu function.展开更多
交叉熵法可显著加速电网可靠性评估,但往往聚焦于独立随机变量,若将其拓展至相关性变量可进一步提升加速性能。为有效获取相关性变量的重要抽样密度函数以实现其重要抽样,针对相关性建模中广泛使用的核密度估计模型(kernel density esti...交叉熵法可显著加速电网可靠性评估,但往往聚焦于独立随机变量,若将其拓展至相关性变量可进一步提升加速性能。为有效获取相关性变量的重要抽样密度函数以实现其重要抽样,针对相关性建模中广泛使用的核密度估计模型(kernel density estimation,KDE)开展了交叉熵优化研究。因KDE模型不属于指数分布家族,传统交叉熵优化难以实施,故利用复合抽样算法特点提出了新颖的直接交叉熵优化方法,推导出KDE模型最优权重参数的解析表达式。因权重参数数量级较小,直接优化易导致准确性退化,故基于子集模拟思想进一步提出间接交叉熵优化方法,将较小的权重参数优化转换成较大的条件概率优化,提升了优化准确性。通过MRTS79和MRTS96可靠性测试系统的评估分析,验证了所提方法在含相关性变量电网可靠性评估中的高效加速性能。展开更多
基金supported by the National Natural Science Foundation of China under Grant No.12072090.
文摘The high-speed development of space defense technology demands a high state estimation capacity for spacecraft tracking methods.However,reentry flight is accompanied by complex flight environments,which brings to the uncertain,complex,and strongly coupled non-Gaussian detection noise.As a result,there are several intractable considerations on the problem of state estimation tasks corrupted by complex non-Gaussian outliers for non-linear dynamics systems in practical application.To address these issues,a new iterated rational quadratic(RQ)kernel high-order unscented Kalman filtering(IRQHUKF)algorithm via capturing the statistics to break through the limitations of the Gaussian assumption is proposed.Firstly,the characteristic analysis of the RQ kernel is investigated in detail,which is the first attempt to carry out an exploration of the heavy-tailed characteristic and the ability on capturing highorder moments of the RQ kernel.Subsequently,the RQ kernel method is first introduced into the UKF algorithm as an error optimization criterion,termed the iterated RQ kernel-UKF(RQ-UKF)algorithm by derived analytically,which not only retains the high-order moments propagation process but also enhances the approximation capacity in the non-Gaussian noise problem for its ability in capturing highorder moments and heavy-tailed characteristics.Meanwhile,to tackle the limitations of the Gaussian distribution assumption in the linearization process of the non-linear systems,the high-order Sigma Points(SP)as a subsidiary role in propagating the state high-order statistics is devised by the moments matching method to improve the RQ-UKF.Finally,to further improve the flexibility of the IRQ-HUKF algorithm in practical application,an adaptive kernel parameter is derived analytically grounded in the Kullback-Leibler divergence(KLD)method and parametric sensitivity analysis of the RQ kernel.The simulation results demonstrate that the novel IRQ-HUKF algorithm is more robust and outperforms the existing advanced UKF with respect to the kernel method in reentry vehicle tracking scenarios under various noise environments.
基金S.F. wishes to thank the Research Foundation Flanders (FWO) and the European Union＇s Horizon 2020 Marie Sklodowska-Curie grant (No. 706415) for financially suppor(ing his post-doctoral research at the ALGC group. ED.P. and P.G. acknowledge (he Research Fo
文摘In view of its use as reactivity theory,Conceptual Density Functional Theory(DFT),introduced by Parr et al.,has mainly concentrated up to now on the E = E[N,v] functional.However,different ensemble representations can be used involving other variables also,such as ρ and μ.In this study,these different ensemble representations(E,?,F,and R) are briefly reviewed.Particular attention is then given to the corresponding second-order(functional) derivatives,and their analogieswith the second-order derivatives of thermodynamic state functions U,F,H,and G,which are related to each other via Legendre transformations,just as the DFT functionals(Nalewajski and Parr,1982).Starting from an analysis of the convexity/concavity of the DFT functionals,for which explicit proofs are discussed for some cases,the positive/negative definiteness of the associated kernels is derived and a detailed comparison is made with the thermodynamic derivatives.The stability conditions in thermodynamics are similar in structure to the convexity/concavity conditions for the DFT functionals.Thus,the DFT functionals are scrutinized based on the convexity/concavity of their two variables,to yield the possibility of establishing a relationship between the three second-order reactivity descriptors derived from the considered functional.Considering two ensemble representations,F and ?,F is eliminated as it has two dependent(extensive)variables,N and ρ.For ?,on the other hand,which is concave for both of its intensive variables(μ and υ),an inequality is derived from its three second-order(functional) derivatives:the global softness,the local softness,and the softness kernel.Combined with the negative value of the diagonal element of the linear response function,this inequality is shown to be compatible with the Berkowitz-Parr relationship,which relates the functional derivatives of ρ with υ,at constant N and μ.This was recently at stake upon quantifying Kohn's Nearsightedness of Electronic Matter.The analogy of the resulting inequality and the thermodynamic inequality for the G derivatives is highlighted.Potential research paths for this study are briefly addressed;the analogies between finite-temperature DFT response functions and their thermodynamic counterparts and the quest for analogous relationships,as derived in this paper,for DFT functionals that are analogues of entropy-dimensioned thermodynamic functions such as the Massieu function.
文摘交叉熵法可显著加速电网可靠性评估,但往往聚焦于独立随机变量,若将其拓展至相关性变量可进一步提升加速性能。为有效获取相关性变量的重要抽样密度函数以实现其重要抽样,针对相关性建模中广泛使用的核密度估计模型(kernel density estimation,KDE)开展了交叉熵优化研究。因KDE模型不属于指数分布家族,传统交叉熵优化难以实施,故利用复合抽样算法特点提出了新颖的直接交叉熵优化方法,推导出KDE模型最优权重参数的解析表达式。因权重参数数量级较小,直接优化易导致准确性退化,故基于子集模拟思想进一步提出间接交叉熵优化方法,将较小的权重参数优化转换成较大的条件概率优化,提升了优化准确性。通过MRTS79和MRTS96可靠性测试系统的评估分析,验证了所提方法在含相关性变量电网可靠性评估中的高效加速性能。
