基于子空间拟合波达方向估计方法研究

传统波达方向(DOA)估计方法由于受阵列尺寸的限制,对处于同一波束内的多个信号源无法得到正确的估计.为此提出了基于子空间拟合的信号到达方位角(DOA)估计算法--信号子空间拟合算法和噪声子空间拟合算法.算法通过对接收数据的子空间与实际信号导向矢量组成的子空间的拟合,来构造信号功率谱尖峰,从而估计目标信号的到达方位角.仿真实验对两种算法的性能进行了分析,分析表明基于噪声子空间拟合算法能突破空域瑞利限的限制,具有空间分辨率高、稳定性好的估计性能.信号子空间拟合算法只有在阵元数较大时,才能正确分辨距离较近的信号源,但具有对环境噪声不敏感的特点.     

DOA估计算法的一种修正MUSIC算法的研究

传统改进 MUSIC 算法通过对接收信号协方差矩阵作预处理,使信号协方差矩阵分解得到信号子空间与噪声子空间正交,从而降低噪声的影响。但当信号间隔很小时,随着信噪比的降低,传统改进MUSIC算法已无法分辨出信号。基于此问题提出的修正MUSIC算法在使信号子空间与噪声子空间正交的基础上,充分利用了噪声子空间及其特征值对噪声子空间的修正,进而构造谱峰搜索函数估计出信号。通过仿真实验,证实了在信噪比很低的情况下,信号间隔很小且存在相关信号时,修正MUSIC算法能准确地估计出传统改进MUSIC算法不能估计的信号。     

Krylov子空间方法及其并行计算

Krylov子空间方法在提高大型科学和工程计算效率上起着重要作用。本文阐述了Krylov子空间方．法产生的背景、Krylov子空间方法的分类,在此基础上,研完了分布式并行计算环境下Krylov子空间方法的并行计算方法,给出了Krylov子空间方法的并行化策略。     

基于MDL准则的MUSIC信号频率估计算法

在正弦信号频率估计方法中,高分辨率谱估计的MUSIC算法利用信号子空间和噪声子空间的正交性进行信号频率的估计,可以得到很高的测频精度.但是信号源数的选择将会影响此方法的有效性.本文研究了基于最小描述长度(MDL)准则的MUSIC算法,信号子空间和噪声子空间的估计以及信号源数的确定同时进行,解决了MUSIC算法中信号源数对估计结果的影响.仿真结果表明利用该方法可准确地估计多个正弦信号的频率值.     

基于ULV更新算法的DS-CDMA自适应检测研究

通过研究多径信号码空间和数据矢量空间,采用噪声子空间技术进行异步DS-CDMA系统期望信号矢量估计,以利于把盲线性滤波优化技术应用于稳健的干扰抑制。提出一种修改的ULV更新算法进行噪声子空间跟踪,该算法不需要相关矩阵的秩估计,直接估计噪声子空间,不进行信号子空间跟踪。仿真结果验证了该文算法的有效性。     

基于正交复用循环机制的WSN信源精确定位算法

无线传感器网络(WSN)信源精确定位算法无法同步优化时延估计与角度估计,且不能将噪声子空间与信号子空间进行分割。为此,提出改进的WSN信源精确定位算法。采用并发方式构建信号解析机制,完成信号空间在频域域上的并发实时解析分割,将噪声信号子空间及信号子空间分割为独立的矩阵信号,获取信源精确定位的时延估计与角度估计。基于能量谱密度估计,设计正交复用循环机制,对单路信号进行特征值分解,得到定位信号数字特征的精确估计,提升时延估计与角度估计精度,并从该估计集合中筛选出同时具备最低时延估计与最低角度估计的信号子空间,从而完成时延与角度的并发实时估计,提高信源定位过程中的定位精度。仿真结果表明,与DT-IPL算法、CD-CPP算法相比,在高衰落信道条件下,该算法具有更高的信源定位精度,且获取的信源位置与实际位置间的误差更低。     

低信噪比条件下的高分辨DOA估计算法

提出一种基于多级维纳滤波器（MSWF）的信号波达方向（DOA）估计算法。通过测试信号子空间的估计值与噪声子空间的正交性实现DOA粗估计,通过测试MSWF分解的互相关函数实现信号DOA的精估计。仿真实验表明,在低信噪比条件下,该算法比已有的子空间类算法有更好的分辨率和误差性能。     

一种多径平坦衰落信道下的盲信噪比估计方法

提出一种多径平坦衰落信道下的盲信噪比估计方法.该算法首先利用数字通信信号的循环平稳统计特性构造接收信号的循环自相关矩阵,然后对该矩阵进行奇异值分解,由分解出的特征值信号子空间和噪声子空间,最后通过利用AIC信息准则分别估计信号子空间和噪声子空间的维数并最终估计出信道的平均信噪比.以MPSK信号为例进行了计算机仿真,结果表明了算法的有效性.     

基于MUSIC算法的宽带频谱感知

利用MUSIC算法进行宽带频谱感知时,主用户信号个数估计是关键问题。为此,提出一种动态门限搜索匹配的信号个数估计算法。利用信号子空间和噪声子空间的正交性动态调整门限,搜索与预设维度最匹配的信号个数作为最终的估计值。仿真结果表明,在低信噪比的情况下,该算法能准确估计信号个数,提高宽带频谱感知性能。     

求解大型非对称稀疏线性方程组的FIMinpert算法

在Krylov子空间方法日益流行的今天,提出了又一求解大型稀疏线性方程组的Krylov子空间方法：灵活的IMinpert算法（即FIMinpert算法）。FIMinpert算法是在Minpert算法的截断版本即IMinpert算法的基础上结合右预处理技术,对原方程组作某些预处理来降低系数矩阵的条件数,从而大大加快迭代方法的收敛速度。给出了新算法的详细的理论推理过程和具体执行,并且通过数值实验表明,FIMinpert算法的收敛速度确实比IMinpert算法和GMRES算法快得多。     

基于Krylov-Schur重启技术的Arnoldi模型降阶方法

Krylov子空间模型降阶方法是模型降阶中的典型方法之一,Arnoldi模型降阶方法是这类方法中的一类基本方法。运用重正交化的Arnoldi算法得到[r]步Arnoldi分解;执行Krylov-Schur重启过程,导出基于Krylov-Schur重启技术的Arnoldi模型降阶方法。运用此方法对大规模线性时不变系统进行降阶,得到具有较高近似精度的稳定的降阶系统,从而改善了Krylov子空间降阶方法不能保持降阶系统稳定性的不足。数值算例验证了此方法是行之有效的。     

The communication-hiding pipelined BiCGstab method for the parallel solution of large unsymmetric linear systems

A High Performance Computing alternative to traditional Krylov subspace methods, pipelined Krylov subspace solvers offer better scalability in the strong scaling limit compared to standard Krylov subspace methods for large and sparse linear systems. The typical synchronization bottleneck is mitigated by overlapping time-consuming global communication phases with local computations in the algorithm. This paper describes a general framework for deriving the pipelined variant of any Krylov subspace algorithm. The proposed framework was implicitly used to derive the pipelined Conjugate Gradient (p-CG) method in Hiding global synchronization latency in the preconditioned Conjugate Gradient algorithm by P. Ghysels and W. Vanroose, Parallel Computing, 40(7):224–238, 2014. The pipelining framework is subsequently illustrated by formulating a pipelined version of the BiCGStab method for the solution of large unsymmetric linear systems on parallel hardware. A residual replacement strategy is proposed to account for the possible loss of attainable accuracy and robustness by the pipelined BiCGStab method. It is shown that the pipelined algorithm improves scalability on distributed memory machines, leading to significant speedups compared to standard preconditioned BiCGStab.     

Parallel Performance of Block ILU Preconditioners for a Block-tridiagonal Matrix

The parallelizable block ILU (incomplete LU) factorization preconditioners for a block-tridiagonal matrix have been recently proposed by the author. In this paper, we describe a parallelization of Krylov subspace methods with the block ILU factorization preconditioners on distributed-memory computers such as the Cray T3E, and then parallel performance results of a preconditioned Krylov subspace method are provided to evaluate the effectiveness and efficiency of the block ILU preconditioners on the Cray T3E.     

Model-order reductions for MIMO systems using global Krylov subspace methods

This paper presents theoretical foundations of global Krylov subspace methods for model order reductions. This method is an extension of the standard Krylov subspace method for multiple-inputs multiple-outputs (MIMO) systems. By employing the congruence transformation with global Krylov subspaces, both one-sided Arnoldi and two-sided Lanczos oblique projection methods are explored for both single expansion point and multiple expansion points. In order to further reduce the computational complexity for multiple expansion points, adaptive-order multiple points moment matching algorithms, or the so-called rational Krylov space method, are also studied. Two algorithms, including the adaptive-order rational global Arnoldi (AORGA) algorithm and the adaptive-order global Lanczos (AOGL) algorithm, are developed in detail. Simulations of practical dynamical systems will be conducted to illustrate the feasibility and the efficiency of proposed methods.     

Model order reduction of nonlinear models based on decoupled multi-model via trajectory piecewise linearization

In this paper a novel model order reduction method for nonlinear models, based on decoupled multi-model, via trajectory piecewise-linearization is proposed. Through different strategies in trajectory piecewise-linear model reduction, model order reduction of a trajectory piecewise-linear model based on output weighting (TPWLOW), has been developed by authors of current work. The structure of mentioned work was founded based on Krylov subspace method, which is appropriate for high order models. Indeed the size of the Krylov subspaces may increase with the number of inputs of the system. As a result, the use of Krylov subspace method may become deficient the case for multi-input systems of order few decades. This paper aims to generalize the idea of model reduction of TPWLOW model by concentrating on balanced truncation technique which is appropriate for medium size systems. In addition, the proposed method either guarantees or provides guaranteed stability in some mentioned conditions. Finally, applicability of the reduced model, instead of high-order decoupled multi-model in weighting multi-model controllers, is investigated through the control of a nonlinear Alstom gasifier benchmark.     

互连线高效时域梯形差分模型降阶算法

为了进一步提高现有互连电路模型降阶方法的精度和效率,提出一种基于时域梯形法差分的互连线模型降阶方法.首先将互连电路的时域方程用梯形法差分离散后获得一种关于状态变量的递推关系,形成了一个非齐次Krylov子空间;然后利用非齐次Arnoldi算法求得非齐次Krylov子空间的正交基,再通过正交基对原始系统进行投影得到降阶系统.该算法可以保证时域差分后降阶系统和原始系统的状态变量在离散时间点的匹配,保证时域降阶精度,同时也保证了降阶过程的数值稳定性及降阶系统的无源性.与现有的时域模型降阶方法相比,文中算法可降低计算复杂度;与频域降阶方法相比,由于避免了时频域转换误差,其在时域具有更高的精度.     

Application of block Krylov subspace algorithms to the Wilson-Dirac equation with multiple right-hand sides in lattice QCD

It is well known that the block Krylov subspace solvers work efficiently for some cases of the solution of differential equations with multiple right-hand sides. In lattice QCD calculation of physical quantities on a given configuration demands us to solve the Dirac equation with multiple sources. We show that a new block Krylov subspace algorithm recently proposed by the authors reduces the computational cost significantly without losing numerical accuracy for the solution of the O(a)-improved Wilson-Dirac equation.     

解大规模非对称矩阵特征问题的精化Arnoldi方法的一种变形

§1.引言 传统的投影类方法是计算大规模非对称矩阵特征问题Ax=λx部分特征对的主要方法,它们包括Arnoldi方法、块Arnoldi方法、同时迭代法、Davidson方法和Jacobi-Davidson方法,贾提出的精化投影类方法目前被公认为是另一类重要     

A Fast Preconditioned Iterative Algorithm for the Electromagnetic Scattering from a Large Cavity

In this paper, a fast preconditioned Krylov subspace iterative algorithm is proposed for the electromagnetic scattering from a rectangular large open cavity embedded in an infinite ground plane. The scattering problem is described by the Helmholtz equation with a nonlocal artificial boundary condition on the aperture of the cavity and Dirichlet boundary conditions on the walls of the cavity. Compact fourth order finite difference schemes are employed to discretize the bounded domain problem. A much smaller interface discrete system is reduced by introducing the discrete Fourier transformation in the horizontal and a Gaussian elimination in the vertical direction, presented in Bao and Sun (SIAM J. Sci. Comput. 27:553, 2005). An effective preconditioner is developed for the Krylov subspace iterative solver to solve this interface system. Numerical results demonstrate the remarkable efficiency and accuracy of the proposed method.