H-infinity deconvolution filtering:a Krein space approach in state-space setting

This note is concerned with the H-infinity deconvolution filtering problem for linear time-varying discretetime systems described by state space models, The H-infinity deconvolution filter is derived by proposing a new approach in Krein space. With the new approach, it is clearly shown that the central deconvolution filter in an H-infinity setting is the same as the one in an H2 setting associated with one constructed stochastic state-space model. This insight allows us to calculate the complicated H-infinity deconvolution filter in an intuitive and simple way. The deconvolution filter is calculated by performing Riccati equation with the same order as that of the original system.

Krein space approach to robust H_∞ filtering for linear uncertain systems

A novel Krein space approach to robust H∞ filtering for linear uncertain systems is developed. The parameter uncertainty, entering into both states and measurement equations, satisfies an energy-type constraint. Then a Krein space approach is used to tackle the robust H∞ filtering problem. To this end, a new Krein space formal system is designed according to the original sum quadratic constraint （SQC） without introducing any nonzero factors into it and, consequently, the estimate recursion is obtained through the filter gain in Krein space. Finally, a numerical example is given to demonstrate the effectiveness of the proposed approach.

Krein Space-based H∞ Fault Estimation for Linear Discrete Time-varying Systems

这份报纸处理 H 差错评价的问题因为有 L2 标准的线性分离变化时间的系统的一个类围住未知输入。主要贡献是 H 差错评价的一条新 Krein 基于空间的途径的发展。H 差错评价的问题第一被等同到一种分级的二次的形式的最小。由在 Krein 空格介绍一个相应系统，然后，一个 H 差错评估者的存在上的一个足够、必要的条件被导出，它的参数矩阵的一个答案以矩阵 Riccati 方程被获得。最后，二个数字例子被给表明建议方法的效率。

Factorization of Operators in Krein Spaces and Linear-Fractional Relations of Operator Balls

We consider plus-operators in Krein spaces and generated operator linear fractional relations of the following form: . We study some special type of factorization for plus-operators T, among them the following one: T = BU, where B is a lower triangular plus-operator, U is a J-unitary operator. We apply the above factorization to the study of basical properties of relations (1), in particular, convexity and compactness of their images with respect to the weak operator topology. Obtained results we apply to the known Koenigs embedding problem, the Krein-Phillips problem of existing of invariant semidefinite subspaces for some families of plus-operators and to some other fields.

Krein space representation and Lorentz groups of analytic Hilbert modules

This paper aims to introduce some new ideas into the study of submodules in Hilbert spaces of analytic functions. The effort is laid out in the Hardy space over the bidisk H^2(D^2). A closed subspace M in H^2(D^2) is called a submodule if ziM ? M(i = 1, 2). An associated integral operator(defect operator) CM captures much information about M. Using a Kre??n space indefinite metric on the range of CM, this paper gives a representation of M. Then it studies the group(called Lorentz group) of isometric self-maps of M with respect to the indefinite metric, and in finite rank case shows that the Lorentz group is a complete invariant for congruence relation. Furthermore, the Lorentz group contains an interesting abelian subgroup(called little Lorentz group) which turns out to be a finer invariant for M.

Krein空间中无穷维Hamilton算子的极大确定不变子空间的存在性问题(英文)

本文研究了不定度规空间空间中的无穷维Hamilton算子. 利用Plus算子存在极大不变子空间的性质, 获得了无穷维Hamilton算子在Krein空间中存在极大确定不变子空间的充分条件.

Krein空间上J-正常算子的可定化性

对于Krein空间上J-正常算子的各种可定化性进行了研究.利用可定化J-正常算子的谱函数,给出了临界线的概念,得到了可定化的J-正常算子成为强可定化算子和一致可定化算子的充要条件.

Krein空间的再生核

介绍了再生核Krein空间,并给出了两个不同的Krein空间,它们以同一个函数为再生核的有趣性质.

关于Krein空间上J-正常算子可定化性的一个注记

利用可定化J-自伴算子的谱函数,对于Krein空间上J-正常算子N的可定化性与其实部、虚部的可定化性之间的关系做了讨论.指出若N的实部或虚部中有一个为可定化算子(强可定化算子、一致可定化算子),则N是可定化的(强可定化的、一致可定化的),且通过例子说明该结论的逆命题并不成立.

一类参数边界条件的Sturm-Liouville问题的Krein空间描述

文章考虑边界条件含有参数的Sturm-Liouville问题,用Krein空间的语言描述此问题,得到它可构造Krein空间上的自伴算子.

Krein空间内一类Sturm-liouville算子的谱

研究Krein空间内定义在有限区间[-1,1]上的一类具有分离型边界条件的左定Sturm-Liouville算子的谱。证明该算子只有实的纯点谱(特征值),并具体计算出其特征值的形式。

PT Symmetric Quantum Models Living in an Auxiliary Pontryagin Space

In the traditional theoretical descriptions of microscopic physical systems （typically, atoms and molecules） people strongly relied upon analogies between the classical mechanics and quantum theory. Naturally, such a methodical framework proved limited as it excluded, up to the recent past, multiple, less intuitively accessible phenomenological models from the serious consideration. For this reason, the classical-quantum parallels were steadily weakened, preserving still the basic and robust abstract version of the key Copenhagen-school concept of treating the states of microscopic systems as elements of a suitable linear Hilbert space. Less than 20 years ago, finally, powerful innovations emerged on mathematical side. Various less standard representations of the Hilbert space entered the game. Pars pro toto, one might recall the Dyson＇s representation of the so-called interacting boson model in nuclear physics, or the steady increase of popularity of certain apparently non-Hermitian interactions in field theory. In the first half of the author＇s present paper the recent heuristic progress as well as phenomenologieal success of the similar use of non-Hermitian Ham iltonians will be reviewed, being characterized by their self-adjoint form in an auxiliary Krein space K. In the second half of the author＇s text a further extension of the scope of such a mathematically innovative approach to the physical quantum theory is proposed. The author＇s key idea lies in the recommendation of the use of the more general versions of the indefinite metrics in the space of states （note that in the Krein-space case the corresponding indefinite metric P is mostly treated as operator of parity）. Thus, the author proposes that the operators P should be admitted to represent, in general, the indefinite metric in a Pontryagin space. A constructive version of such a generalized quantization strategy is outlined and found feasible.

Robust UKF algorithm in SINS initial alignment

In the traditional unscented Kalman filter（UKF）,accuracy and robustness decline when uncertain disturbances exist in the practical system.To deal with the problem,a robust UKF algorithm based on an H-infinity norm is proposed.In Krein space,a robust element is added in the simplified UKF so as to improve the algorithm.The filtering gain is adjusted by the robust element and in this way the performance of the robustness of the filtering algorithm is promoted.In the initial alignment process of the large heading misalignment angle of the strapdown inertial navigation system（SINS）,comparative studies are conducted on the robust UKF and the simplified UKF.The simulation results illustrate that compared with the simplified UKF,the robust UKF is more accurate,and the estimation error of heading misalignment decreases from 16.9＇ to 4.3＇.In short,the robust UKF can reduce the sensitivity to the system disturbances resulting in better performance.

基于多传感器的序贯式融合有限域H∞滤波方法

与集中式和分布式融合滤波器相比,序贯式融合滤波器不仅保证了估计精度相同,而且在对测量值即到达即滤波、部分测量值缺失等方面都具有灵活性、自适应性和实时性等特点.为此,本文针对一类噪声能量有界的多传感器动态系统,给出了一种序贯式融合有限域H∞滤波器.首先,利用测量值扩维的方法,给出一种集中式融合有限域H∞滤波器;然后,利用H∞滤波的性能指标与二次型不等式之间、以及Hilbert空间二次型的稳定点与Krein空间正交投影之间等的对应关系,构造出一种序贯式融合有限域H∞滤波器;最后,从理论与数值仿真两方面验证了新滤波器与集中式融合有限域H∞滤波器的性能等价性.

H-infinity鲁棒滤波增益研究

基于Krein空间状态模型,深入分析H-infinity滤波增益,提出了广义滤波增益、增益失调因子等相关概念,并给出了H-infinity滤波器鲁棒性机理及H-infinity滤波器发散原因等相关结论。在此基础上,建立了一套结构化算法,清晰地描述了H-infinity滤波的两个计算回路和两个更新过程。仿真结果证明了相关结论的正确性。

广义系统H_∞多步预报器设计

基于格林空间中的新息分析方法和卡尔曼滤波理论,首次给出了广义系统H∞多步预报器存在的充要条件和一种简单的计算方法.本文将广义系统的H∞多步预报问题转化为带有当前观测和时滞观测的格林空间中广义系统最小方差估计问题,然后引入新息重组序列解决该最小方差估计问题.通过求解维数与变换后的系统相同的两个黎卡提方程得到了H∞预报器,避免了处理带观测时滞系统时常采用的系统增广方法.数值例子表明利用本文的新息重组方法计算广义系统H∞多步预报器比用系统增广方法计算量小.

二阶段H_∞滤波在捷联惯导/里程计组合导航系统中的应用

针对一类包含未知常值偏置的线性系统的状态估计问题,比如捷联惯导/里程计组合导航系统,由于扩展未知常值偏置为系统状态,导致系统状态维数比较高。当应用H∞滤波进行估计时,就会引起滤波算法的计算量大大增加,进而会影响其估计性能。为了解决这个问题,将H$滤波问题转化为Krein空间下的求解某种二次型的最小值问题,而求解该最小值可以使用Kalman滤波来解决。因此,通过采用二阶段Kalman滤波理论,在Krein空间下建立了二阶段H∞滤波算法,将H$滤波中的高维矩阵计算解耦成并行的低维矩阵计算,有效地解决了高维矩阵计算所带来的数值计算问题,降低了计算量,并且该算法有利于硬件并行运算设计,为进一步提高算法执行速度提供了可能。通过在捷联惯导/里程计组合导航系统中的仿真实验,验证了算法的有效性。

一类与微分算子相关的不定度规空间

该文根据Sturm-Liouville算子的性质,构造了一个与其相关的完备的不定度规空间和它的正则分解,并讨论了它的正的、极大正的等子空间的性质。

Spectrum of a class of fourth order left-definite differential operators

The spectrum of a class of fourth order left-definite differential operators is studied. By using the theory of indefinite differential operators in Krein space and the relationship between left-definite and right-definite operators, the following conclusions are obtained： if a fourth order differential operator with a self-adjoint boundary condition that is left-definite and right-indefinite, then all its eigenvalues are real, and there exist countably infinitely many positive and negative eigenvalues which are unbounded from below and above, have no finite cluster point and can be indexed to satisfy the inequality …≤λ-2≤λ-1≤λ-0〈0〈λ0≤λ1≤λ2≤…

H_∞鲁棒滤波在机动目标跟踪中的应用

在交互多模型中通常使用的卡尔曼滤波器中,引入广义H∞鲁棒滤波器,以一定的精度为代价,换取满意的鲁棒性能。H∞鲁棒滤波算法可以分解为卡尔曼滤波和鲁棒化两个环节,从而形成一种基于增益失调因子的结构化分解算法。为验证算法的有效性,进行了Monte Carlo仿真。仿真结果表明,本文算法跟踪复杂机动目标时跟踪性能有较大提高,有很好的可实现性。