基于范数优化的对角加载稳健自适应波束形成

本文提出了一种基于范数优化的对角加载自适应波束形成算法。算法利用p-范数来代替2-范数对误差不确定性进行总体修正,从而解决导向矢量和样本方差矩阵同时存在失配误差时所导致的波束形成器性能下降问题。最优范数p通过遗传算法求得。仿真结果验证了在不同实验条件下,相比于传统的对角加载算法,使用最优p范数比2-范数约束具有更好的性能。     

基于稳健最小二乘的鲁棒波束形成

为解决Capon波束形成器在存在导向矢量失配时的性能急剧下降问题,提出了一种结合广义旁瓣对消器和稳健最小二乘的鲁棒波束形成算法.该算法利用广义旁瓣对消器原理将Capon波束形成器转化为最小二乘问题,然后在数据协方差矩阵误差的范数约束下将其转化为二阶锥规划问题,并利用高效内点法得到最优解.所提出的算法经推导证明属于对角加载类.仿真分析表明,该算法在导向矢量失配和快拍不足时仍具有较好的性能.     

线性干扰参数约束的稳健LSMI波束形成算法

 针对稳健的加载样本矩阵求逆(LSMI)波束形成算法,给出了一种新的求解方法,获得了加载电平的准确计算公式,而且得出最优加载量为负值,且与约束参数的选取无关.为了改善LSMI波束形成算法的抗干扰性能,提出利用线性干扰参数约束(LJC)来实现,其中对LJC-LSMI波束形成算法进行了建模和求解,得到了最优加权矢量的表达式,并给出了具体的求解方法.仿真分析验证了算法的正确性和有效性,结果表明LJC-LSMI相对于LSMI具有较强的干扰抑制能力,相对于线性约束最小功率(LCMP)波束形成算法具有稳健的波束指向性能.     

一种波束形成中的自适应对角加载方法

在自适应波束形成中，由于采样快拍数有限，导致协方差矩阵的估计误差，由此得到的自适应波束旁瓣很高。对角加载方法是一种改善波束性能的有效方法。文章介绍了对角加载的原理，给出了一种对角加载值的确定方法和仿真效果。该方法能根据采样数据自适应调整对角加载的数值，实现容易，能得到很好的旁瓣特性。     

一种加载量迭代搜索的稳健波束形成

当阵列的导向矢量并不精确已知时,自适应波束形成有较大的性能损失.为提高波束形成的稳健性,对角加载成为一种常用的方式.但困扰这类方法的核心问题是合适的加载量如何确定.粗估导向矢量经对角加载后得到修正的导向矢量,如果加载量合适,则修正后的导向矢量接近真实导向矢量,即与噪声子空间的正交性变好.基于以上分析,构造修正导向矢量向信号子空间和噪声子空间投影的加权代价函数来评价加载量的合适与否,进而提出一种迭代搜索合适加载量的方法.计算机仿真验证了方法的有效性,与同类方法对比显示其优越性.     

一种空间色噪声环境下的鲁棒自适应波束

该文提出了一种基于对角加载的鲁棒自适应波束形成算法,以提高空间色噪声环境中自适应波束对方向矢量误差的鲁棒性。该算法首先利用噪声协方差矩阵对阵列相关矩阵进行预白化,同时定义了一个与噪声矩阵相对应的椭圆方向矢量模糊集,然后,通过在该模糊集内进行最坏情况性能优化来确定对角加载因子。和现有的通过迭代求解加载因子的方法不同,该文给出了最优加载因子的近似解析表达式,降低了运算量,揭示了哪些因素可以影响最优加载因子,以及如何影响。仿真结果表明,在空间色噪声环境中,该算法具有很好的鲁棒性,并且,给出的加载因子表达式是其真实最优解的一个准确近似。     

最差性能最优通用信号模型稳健波束形成算法

针对空间分布散射信号源的稳健波束形成问题,提出了一种新的通用信号模型稳健波束形成算法,不仅得到了封闭形式的最优加权矢量,而且获得了最优的性能改善.其中分析了与传统对角加载的关系,给出了最优加载量的计算方法,并得出具有最优负加载的解才可以获得最优的性能改善.最后的仿真分析验证了所提出算法的正确性和有效性,而且发现最优加权矢量只取决于给定的接收数据和未知的失配量,与失配约束参数的选择无关,而失配约束参数只是参与最优权计算的辅助参数.     

最坏情况下的鲁棒自适应波束形成算法性能分析

研究了最坏情况下的鲁棒自适应波束形成算法,它通过对角加载提高波束对方向矢量误差的鲁棒性.给出了其最优对角加载因子的近似解析达式,揭示了各种因素如何影响最优加载因子.在此基础上,对该算法进行了性能分析,推导出了关于目标功率估计和信号干扰噪声比的近似表达式.计算机仿真验证了本文的分析.     

一种改进的多级维纳滤波器误差加载算法

对角加载是目前广泛采用的提高自适应波束形成稳健性的技术之一.在分析多级维纳滤波器结构实现空时自适应处理算法的基础上,提出了一种改进的能够等价递推实现对角加载的误差加载算法.该算法在每一级递推计算中均对加载值进行一次修正,有效克服了传统方法的最终对角加载结果总是小于期望的加载值的缺点,避免了加载不足,其每级迭代计算过程只增加了两次实数乘法和加法运算.仿真结果证明了该算法的有效性.     

复广义高斯分布多通道最大似然联合去噪去混响波束形成器

提出了一种基于复超高斯分布的多通道联合去噪去混响波束形成器。本文采用复超高斯模型对语音信号建模,在最大似然准则下首次推导出联合去噪去混响波束形成器的解析表达式,并证明了该式是现有多种联合去噪去混响波束形成器的一般化形式。同时通过理论推导证明本文所提算法性能优于传统多通道预测误差算法级联最小功率无失真波束形成器。仿真实验与实际实验结果均表明,本文提出的算法在多个客观指标上明显优于现有联合去噪去混响算法。      

基于Huber范数和概率运动场的鲁棒图像超分辨重建算法

传统超分辨(SR)算法对配准误差、模型误差以及噪声过于敏感,这限制了其在实际中的应用。为了提高算法的鲁棒性,该文从配准和重建两方面对传统算法进行了改进。在配准阶段,通过引入概率运动场避免了算法对配准精度的依赖,同时利用Heaviside函数实现权重映射,进一步提高了算法的自适应性;在重建阶段,采用基于Huber范数的正则化估计,在提高重建鲁棒性的同时也保证了算法数值解的稳定性。实验表明该算法具有很好的鲁棒性,其重构性能优于现有的一些超分辨重建方法。     

Robust Power Control for Multiuser Underlay Cognitive Radio Networks Under QoS Constraints and Interference Temperature Constraints

Since the nature of mobility and unreliability in wireless communication system may degrade the communication performance, robustness is one of the main concerns in cognitive radio networks (CRNs). In CRNs, the existing power control algorithms based on the assumption of exact system information may not guarantee the communication requirements due to the parameter uncertainties in real system. In this paper, we propose a robust distributed power control algorithm for underlay CRNs. The novelty in our paper is that we consider all possible parameter uncertainties: channel uncertainty and interference uncertainty. Our objective is to maximize the total throughput of secondary users while channel gain and interference plus noise are uncertain. According to the robust optimization theory, uncertain parameters are modeled by additive uncertainties with bounded errors. Through the worst case principle, we transform the robust power control problem into a deterministic optimization one, which is solved by using Lagrange dual decomposition method. Numerical simulation results show that the proposed algorithm can satisfy the QoS requirements of both secondary users and primary users for all uncertainty realizations.     

Robust position control of a magnetic levitation system via dynamic surface control technique

This paper considers the position-tracking problem of a magnetic levitation system in the presence of modeling errors due to uncertainties of physical parameters. A robust nonlinear controller is designed to achieve excellent position-tracking performance. The recently developed dynamic surface control is modified and applied to the system under study, to over-come the problem of "explosion of terms" associated with the backstepping design procedure. Input-to-state stability of the control system is analyzed, and the advantages of the dynamic surface control technique over the conventional backstepping technique are verified through both theoretical and experimental studies.     

基于失配误差正交分解的稳健自适应波束形成

针对自适应波束形成中期望信号导向矢量的失配问题,该文提出了一种利用失配误差的正交分量来逐步修正期望信号导向矢量的自适应波束形成方法。该方法首先构造两个正交子空间,正交分解失配误差以后,通过引入松弛变量,把修正过程转化为解决迭代的二次凸优化问题。提出的方法没有假定失配误差模约束或概率约束,从而避免了上限估计和概率分布建模。仿真结果验证了方法的有效性。     

高光谱图像Pareto优化稀疏解混

高光谱解混是学术界的一个难题,稀疏高光谱解混指的是利用已知光谱库进行解混,旨在从先验光谱库中找到一些可以表征图像的数个纯光谱向量作为高光谱图像的端元,并利用这些端元求解相应的端元丰度,这是一个NP难的组合优化问题。目前多通过将L0范数凸松弛为L1范数进行稀疏解混,但该方法得到的仅仅是近似解。文中提出了一种基于Pareto优化的稀疏解混算法（ParetoSU）,将稀疏解混问题转化为一个两目标优化问题,其中一个优化目标是建模误差,另一个目标是端元稀疏度。ParetoSU直接解决稀疏解混中的组合优化问题,不需要对L0范数进行近似。最后利用仿真数据验证了该解混算法的有效性。     

Joint Optimal Design of Digital Filters and State-Space Realizations

In this brief, a procedure for digital filters design is presented. The main purpose is to show that a digital filter and its realization can be simultaneously determined such as to minimize an upper bound of the H₂ norm of the estimation error and impose a certain degree of robustness against practical uncertainties as for instance, finite word length implementation, roundoff errors, and numerical precision. The optimal filter and its state-space realization are jointly determined from the solution of a convex programming problem expressed in terms of linear matrix inequalities. A simple illustrative example is presented for comparison purposes making clear the advantages of the reported results     

Passivity Analysis and Passification of Markovian Jump Systems

This paper is concerned with the problems of delay-dependent robust passivity analysis and robust passification for uncertain Markovian jump linear systems (MJLSs) with time-varying delay. The parameter uncertainties are time varying but norm bounded. For the robust passivity problem, the objective is to seek conditions such that the closed-loop system under the state-feedback controller with given gains is passive, irrespective of all admissible parameter uncertainties. For the robust passification problem, desired passification controllers will be designed which guarantee that the closed-loop MJLS is passive. By constructing a proper stochastic Lyapunov–Krasovskii function and employing the free-weighting matrix technique, delay-dependent passivity/passification performance conditions are formulated in terms of linear matrix inequalities. Finally, the effectiveness of the proposed approaches is demonstrated by a numerical example.     

Robust mean-squared error estimation in the presence of model uncertainties

We consider the problem of estimating an unknown parameter vector x in a linear model that may be subject to uncertainties, where the vector x is known to satisfy a weighted norm constraint. We first assume that the model is known exactly and seek the linear estimator that minimizes the worst-case mean-squared error (MSE) across all possible values of x. We show that for an arbitrary choice of weighting, the optimal minimax MSE estimator can be formulated as a solution to a semidefinite programming problem (SDP), which can be solved very efficiently. We then develop a closed form expression for the minimax MSE estimator for a broad class of weighting matrices and show that it coincides with the shrunken estimator of Mayer and Willke, with a specific choice of shrinkage factor that explicitly takes the prior information into account. Next, we consider the case in which the model matrix is subject to uncertainties and seek the robust linear estimator that minimizes the worst-case MSE across all possible values of x and all possible values of the model matrix. As we show, the robust minimax MSE estimator can also be formulated as a solution to an SDP. Finally, we demonstrate through several examples that the minimax MSE estimator can significantly increase the performance over the conventional least-squares estimator, and when the model matrix is subject to uncertainties, the robust minimax MSE estimator can lead to a considerable improvement in performance over the minimax MSE estimator.     

具有同步化特征选择的迭代紧凑非平行支持向量聚类算法

本文提出了一种新的带有同步化特征选择的聚类算法，称为"具有同步化特征选择的迭代紧凑非平行支持向量聚类算法"（IT-NHSVC-SFS）.在具有两个非平行超平面的学习模型中使用迭代（交替）优化算法完成聚类，同时引入两种类型的正则项，分别是欧几里得范数和无穷范数，欧几里得范数用于提升聚类模型的泛化能力，无穷范数实际上是对两个非平行超平面进行同步化地隐式特征抽取，从而降低来自于不相关特征的聚类噪音，保证了模型的聚类精度，并引入一组束缚变量（bounding variables）避免无穷范数的最大化操作，将非凸优化问题转化成二次凸优化问题.同时，由于新提出的模型体现着"最大间隔"的思想，因此具有良好的泛化能力.为了方便实现两个非平行超平面同步化的特征选择过程，文中将非平行超平面SVM（Nonparallel Hyperplane SVM，NHSVM）作为IT-NHSVC-SFS算法的基础模型，因此和TWSVM以及它的变体模型不同的是：只需要求解一个二次规划问题（QP问题）就可以同时得到两个最优超平面.同时，新算法在原有的NHSVM模型的约束条件集合中新添加了两组等式约束条件，从而无需进行原有模型中的两个大矩阵的求逆操作，降低了计算复杂度.此外，在IT-NHSVC-SFS模型中，用拉普拉斯损失函数（Laplacian loss measure）代替了NHSVM模型原有的铰链损失函数（hinge loss function），避免了算法早熟收敛（premature convergence）.在一组标准数据集上的数值实验结果表明，相对于其他已有的聚类算法，IT-NHSVC-SFS算法在聚类精度方面具有更好的表现.