MASS-RAB: Robust adaptive beamforming for general-rank signal models via matched spatial spectrum processing

The wavefront of acoustic signal suffers from fast fluctuation after a long distance propagation in a random and inhomogeneous ocean channel, which makes the rank of the covariance matrix for the desired signal (signal of interest) remarkably higher than one. Consequently, the assumption of rank-one point signal model for existing adaptive beamforming algorithms is no longer suitable. In this paper, a matched spatial spectrum processing based robust adaptive beamforming (MASS-RAB) algorithm is presented for general-rank signal models. First, the interference-plus-noise covariance matrix and the desired signal covariance matrix are reconstructed using the matched spatial spectrum processing method. Second, the weight vector is directly calculated using these reconstructed covariance matrices for the minimum variance distortionless response (MVDR) algorithm, which is developed for the general-rank signal models. Due to covariance matrix reconstruction, the MASS-RAB algorithm is more robust than those methods relying on the sample covariance matrix. The cases of the rank-one point signal model and the full-rank non-point signal model are considered by several numerical examples. Experimental results have demonstrated the superiority of the proposed MASS-RAB method.     

Frequency-invariant robust adaptive beamforming based on interference covariance matrix reconstruction

Consider the problems of frequency-invariant beampattern optimization and robustness in broadband beamforming.Firstly,a global optimization algorithm,which is based on phase compensation of the array manifolds,is used to construct the frequency-invariant beampattern.Compared with some methods presented recently,the proposed algorithm is not only available to get the global optimal solution,but also simple for physical realization.Meanwhile,a robust adaptive broadband beamforming algorithm is also derived by reconstructing the covariance matrix.The essence of the proposed algorithm is to estimate the space-frequency spectrum using Capon estimator firstly,then integrate over a region separated from the desired signal direction to reconstruct the interference-plus-noise covariance matrix,and finally caleulate the adaptive beamformer weights with the reconstructed matrix.The design of beamformer is formulated as a convex optimization problem to be solved.Simulation results show that the performance of the proposed algorithm is almost always close to the optimal value across a wide range of signal to noise ratios.     

基于干扰协方差矩阵重构的恒定束宽鲁棒自适应波束形成

针对宽带波束形成中的恒定束宽波束响应优化设计问题与鲁棒性问题展开研究。首先,提出一种基于相位补偿的恒定束宽全局优化设计方法,通过对阵列流形向量进行相位补偿来设计恒定束宽波束,与现有的一些方法相比,该方法不仅能获得全局最优解,而且物理实现简单。同时,还提出一种基于协方差矩阵重构的鲁棒自适应宽带波束形成算法。该算法采用Capon估计器估计样本数据的空间一频率谱密度函数,然后对期望信号波达方向之外的角度区间进行积分来重构干扰加噪声协方差矩阵,最后利用重构的协方差矩阵设计自适应波束形成器权系数。该波束形成器设计问题被表述成凸优化问题求解。仿真结果表明,在整个输入信噪比范围内,该算法几乎都能获得接近理想值的输出信干噪比。      

Weak signal direction of arrival estimation for colocated multiple-input multiple-output sonar array

In order to suppress the influence of symmetrical noise component on multiple-input multiple-output(MIMO)sonar's direction of arrival(DOA)estimation under the condition of low signal-to-noise ratio,we propose a DOA estimation algorithm based on covariance matrix reconstruction method.Firstly,the noise field can be decomposed into symmetrical noise field and asymmetrical noise field.We utilize symmetry property of colored noise matrix and the feature that the imaginary part of covariance matrix has no relation with the symmetry noise to remove the real part of covariance matrix.This operation helps to suppress the influence of colored noise on DOA estimation accuracy.Based on the principle of the imaginary matrix part displacement and the dimension reduction transformation method,the real part of covariance matrix is reconstructed,which helps to suppress the bilateral spectrum interference.Thereafter,Toeplitz method is applied for the covariance matrix decorrelation amendment,and a noise subspace is formed by singular value decomposition(SVD).Finally,we can estimate the DOA of target signals.Both theoretical analysis results and numerical simulation results verify the symmetrical noise suppression performance of this algorithm,and the estimation performance of target azimuth is improved obviously.This method has the characteristics of lower operational complexity,higher degrees of freedom and stronger target resolution.     

海洋环境噪声场对称性分析及噪声消除方法

实际的海洋环境是非常复杂的,存在着海洋自噪声、舰船噪声、生物发声等,阵元接收到的噪声信号存在一定的相关性,此时基于传统阵列信号处理的目标方位估计方法的性能将变差,针对这一问题,提出了一种实部消除方法.首先从阵元接收环境噪声的物理机理出发,将圆环阵接收的噪声场分解为对称噪声场和非对称噪声场,并且研究发现对称噪声场只影响数据协方差矩阵的实部.然后通过消除协方差矩阵实部,达到消除对称噪声场的目的,提高信噪比,但是同时产生了虚假声源.针对虚假声源的问题,提出了基于优化算法重构协方差矩阵实部的方法,消除了虚假声源的影响.仿真分析与海试数据处理结果表明:该方法明显消除了对称噪声,提高了信噪比,改善了阵列信号处理算法的性能.实部消除方法易于实现,有一定的工程应用价值.     

密布式多输入多输出声呐阵列目标波达方向估计

针对低信噪比条件下多输入多输出声呐受对称噪声分量影响导致测向性能降低的情况,提出了一种基于协方差矩阵重构方法的波达方向估计算法。首先,将噪声场分为对称噪声和非对称噪声两部分,利用协方差矩阵虚部与对称信号无关的性质,去掉协方差矩阵的实部来降低对称噪声对目标波达方向估计精度的影响,采用降维转换方法和矩阵虚部置换原理重构协方差矩阵的实部,避免了双频谱的干扰。然后利用Toeplitz方法对重构的协方差矩阵进行解相干修正,通过奇异值分解获得噪声子空间,最后对目标的波达方向进行估计,可实现微弱信号的准确测向。理论分析和实验结果表明,该方法明显抑制了对称噪声,提高了目标的波达方向估计性能,具有运算速度快、自由度高和目标分辨力强的特点。      

相关变量随机数序列产生方法

当采用蒙特卡罗方法对很多问题进行研究时,有时需要对多维相关随机变量进行抽样.之前的研究表明:在协方差矩阵满足正定条件时,可以采用Cholesky分解方法产生多维相关随机变量.本文首先对产生多维相关随机变量的理论公式进行了推导,发现采用Cholesky分解并不是产生多维相关随机变量的唯一方法,其他的矩阵分解方法只要能满足协方差矩阵的分解条件,同样可以用来产生多维相关随机变量.同时给出了采用协方差矩阵、相对协方差矩阵和相关系数矩阵产生多维随机变量的公式,以方便以后使用.在此基础上,利用一个简单测试题和Jacobi矩阵分解方法对上述理论进行了验证.通过对大亚湾中微子能谱进行抽样分析,Jacobi矩阵分解和Cholesky矩阵分解结果一致.针对核工程中的不确定性分析常用的~(238)U辐射俘获截面协方差矩阵进行分解时,由于协方差矩阵的矩阵本征值有负值,导致很多矩阵分解方法无法使用,在引入置零修正以后发现,与Cholesky对角线置零修正相比,Jacobi负本征值置零修正的误差更小.     

协方差矩阵重构的稳健自适应波束形成算法

针对协方差矩阵含有期望信号成分以及波束指向角失配时,传统自适应波束形成器性能严重下降的问题,提出了协方差矩阵重构的稳健自适应波束形成算法。该算法将全空域划分成若干互不重叠的区域,分别对应干扰区域与信号区域,先利用Capon波束形成器对干扰区域积分,由此构造出干扰协方差矩阵。然后,利用标准Capon波束形成器的波束域MUSIC谱估计法对信号区域积分,重构出信号协方差矩阵,以其主特征向量作为期望信号导引向量估计。由于算法重构了干扰加噪声协方差矩阵并对导引向量进行了修正,保证了自适应波束形成器的性能。理论分析和仿真实验结果表明,算法在训练数据含有期望信号成分和波束指向角度失配情况下具有良好的性能。      

Measurement of correlations between low-frequency vibrational modes and particle rearrangements in quasi-two-dimensional colloidal glasses

We investigate correlations between low-frequency vibrational modes and rearrangements in two-dimensional colloidal glasses composed of thermosensitive microgel particles, which readily permit variation of the sample packing fraction. At each packing fraction, the particle displacement covariance matrix is measured and used to extract the vibrational spectrum of the "shadow" colloidal glass (i.e., the particle network with the same geometry and interactions as the sample colloid but absent damping). Rearrangements are induced by successive, small reductions in the packing fraction. The experimental results suggest that low-frequency quasilocalized phonon modes in colloidal glasses, i.e., modes that present low energy barriers for system rearrangements, are spatially correlated with rearrangements in this thermal system.     

一种改善逆波束形成显示效果方法

在低信噪比条件下,由于协方差矩阵中主对角元素相比其他元素所含噪声能量大,致使逆波束形成(IBF)所得空间谱中目标方位处能量与其他方位处能量差别小、显示效果不好。对此,本文采用对协方差矩阵主对角元素进行修正法来降低噪声对IBF的影响,进而扩大目标方位与其他方位处能量差别,改善空间谱显示效果。 Matlab数值仿真和湖试数据处理结果均表明：在低信噪比条件下,本方法可改善IBF所得空间谱的显示效果。本文所述方法简单有效,可满足实际工程应用,为改善方位历程显示效果提供一个参考。     

General second-order covariance of Gaussian maximum likelihood estimates applied to passive source localization in fluctuating waveguides

A method is provided for determining necessary conditions on sample size or signal to noise ratio (SNR) to obtain accurate parameter estimates from remote sensing measurements in fluctuating environments. These conditions are derived by expanding the bias and covariance of maximum likelihood estimates (MLEs) in inverse orders of sample size or SNR, where the first-order covariance term is the Cramer-Rao lower bound (CRLB). Necessary sample sizes or SNRs are determined by requiring that (i) the first-order bias and the second-order covariance are much smaller than the true parameter value and the CRLB, respectively, and (ii) the CRLB falls within desired error thresholds. An analytical expression is provided for the second-order covariance of MLEs obtained from general complex Gaussian data vectors, which can be used in many practical problems since (i) data distributions can often be assumed to be Gaussian by virtue of the central limit theorem, and (ii) it allows for both the mean and variance of the measurement to be functions of the estimation parameters. Here, conditions are derived to obtain accurate source localization estimates in a fluctuating ocean waveguide containing random internal waves, and the consequences of the loss of coherence on their accuracy are quantified.     

基于矢量水听器阵列空域预滤波处理的多重信号分类算法研究

矢量水听器能同时拾取声压和振速信息,在相同的信噪比、阵元数及阵列孔径下,矢量阵定向性能优于声压阵列。目前,以多重信号分类算法(Multiple signal classification,MUSIC)为代表的高分辨定向算法已经广泛应用于矢量水听器阵列中。但是随着信噪比降低、信号源方位间隔减小,传统MUSIC算法定向精度及分辨概率显著下降。本文采用最小二乘法设计适用于矢量水听器水平阵列的矩阵空域滤波器,用于阵列数据的空间滤波预处理,可以对阻带扇面噪声进行有效抑制。由滤波后的数据协方差矩阵可以得到新的噪声子空间,在传统MUSIC算法基础上修正通带扇面内阵列流型的畸变后即可得到滤波后MUSIC算法的方位谱。仿真结果表明,当信噪比较低时,改进算法有效提高了通带扇面内目标方位分辨性能。最后本文对四基元矢量水平阵列海试数据进行了处理,改进算法对窄带信号定向较常规算法-3 dB束宽减小了13°,旁瓣级降低约8 dB。对有一定带宽的行船辐射噪声定向处理得到了更加精确的航迹图,海试数据处理结果证明了该算法的可行性和有效性。     

Random matrix theory and fund of funds portfolio optimisation

The proprietary nature of Hedge Fund investing means that it is common practise for managers to release minimal information about their returns. The construction of a fund of hedge funds portfolio requires a correlation matrix which often has to be estimated using a relatively small sample of monthly returns data which induces noise. In this paper, random matrix theory (RMT) is applied to a cross-correlation matrix C, constructed using hedge fund returns data. The analysis reveals a number of eigenvalues that deviate from the spectrum suggested by RMT. The components of the deviating eigenvectors are found to correspond to distinct groups of strategies that are applied by hedge fund managers. The inverse participation ratio is used to quantify the number of components that participate in each eigenvector. Finally, the correlation matrix is cleaned by separating the noisy part from the non-noisy part of C. This technique is found to greatly reduce the difference between the predicted and realised risk of a portfolio, leading to an improved risk profile for a fund of hedge funds.     

Covariance NMR spectroscopy by singular value decomposition

Covariance NMR is demonstrated for homonuclear 2D NMR data collected using the hypercomplex and TPPI methods. Absorption mode 2D spectra are obtained by application of the square-root operation to the covariance matrices. The resulting spectra closely resemble the 2D Fourier transformation spectra, except that they are fully symmetric with the spectral resolution along both dimensions determined by the favorable resolution achievable along omega2. An efficient method is introduced for the calculation of the square root of the covariance spectrum by applying a singular value decomposition (SVD) directly to the mixed time-frequency domain data matrix. Applications are shown for 2D NOESY and 2QF-COSY data sets and computational benchmarks are given for data matrix dimensions typically encountered in practice. The SVD implementation makes covariance NMR amenable to routine applications.     

基于稳健背景子空间的高光谱图像异常检测

在RX算法中,局部背景协方差矩阵估计会由于背景受到异常像元的“污染”而不能准确反映背景分布,从而导致检测性能下降.针对这一问题,提出一种基于稳健背景子空间的异常检测算法.利用空间秩深度度量背景中每个样本相对于整个背景样本分布空间的位置,将“游离”于背景分布空间之外的样本看作是潜在的异常样本,并将其映射到背景分布空间之内.在此基础上,通过估计背景的协方差矩阵,利用主成分分析构造能更精确地刻画背景的子空间,在该子空间进行了基于马氏距离的检测异常.模拟和真实数据验证了该算法的有效性.     

Strategies for reducing large fMRI data sets for independent component analysis

In independent component analysis (ICA), principal component analysis (PCA) is generally used to reduce the raw data to a few principal components (PCs) through eigenvector decomposition (EVD) on the data covariance matrix. Although this works for spatial ICA (sICA) on moderately sized fMRI data, it is intractable for temporal ICA (tICA), since typical fMRI data have a high spatial dimension, resulting in an unmanageable data covariance matrix. To solve this problem, two practical data reduction methods are presented in this paper. The first solution is to calculate the PCs of tICA from the PCs of sICA. This approach works well for moderately sized fMRI data; however, it is highly computationally intensive, even intractable, when the number of scans increases. The second solution proposed is to perform PCA decomposition via a cascade recursive least squared (CRLS) network, which provides a uniform data reduction solution for both sICA and tICA. Without the need to calculate the covariance matrix, CRLS extracts PCs directly from the raw data, and the PC extraction can be terminated after computing an arbitrary number of PCs without the need to estimate the whole set of PCs. Moreover, when the whole data set becomes too large to be loaded into the machine memory, CRLS-PCA can save data retrieval time by reading the data once, while the conventional PCA requires numerous data retrieval steps for both covariance matrix calculation and PC extractions. Real fMRI data were used to evaluate the PC extraction precision, computational expense, and memory usage of the presented methods.     

Data error covariance in matched-field geoacoustic inversion

Many approaches to geoacoustic inversion are based implicitly on the assumptions that data errors are Gaussian-distributed and spatially uncorrelated (i.e., have a diagonal covariance matrix). However, the latter assumption is often not valid due to theory errors, and can lead to reduced accuracy for geoacoustic parameter estimates and underestimation of parameter uncertainties. This paper examines the effects of data error (residual) covariance in matched-field geoacoustic inversion. An inversion approach is developed based on a nonparametric method of estimating the full covariance matrix (including off-diagonal terms) from the data residuals and explicitly including this covariance in the misfit function. Qualitative and quantitative statistical tests for Gaussianity and for correlations in complex residuals are considered to validate the inversion results. The approach is illustrated for Bayesian geoacoustic inversion of broadband, vertical-array acoustic data measured in the Mediterranean Sea.     

一种改进的快速Mini-Norm算法

Ｋｕｍａｒｅｓａｎ和Ｔｕｆｔｓ提出的Ｍｉｎｉ－Ｎｏｒｍ算法通过对空间协方差矩阵进行特征分解，随后构造噪声子空间向量来求解方位。     

基于石墨烯纳米带的齿形表面等离激元滤波器的研究

提出了一种基于石墨烯纳米带的齿形表面等离激元波导滤波器, 并且用时域有限差分法研究了这种结构. 单个齿形的滤波器可以实现带阻滤波, 其滤波特性可以用基于散射矩阵的解析模型解释. 滤波器的透射谱特性可以通过调节齿的长度、宽度以及石墨烯的化学势来改变. 由于石墨烯的化学势可以用门电路来调节, 这种结构的滤波器可以在器件加工完成后灵活地调节其工作波长. 同时研究了多齿滤波器, 这种结构可以实现宽带滤波, 文中对具有不同齿数、周期的滤波器的透射谱进行了细致的研究. 研究结果对实现基于石墨烯的大规模集成光电子器件提供了重要的理论参考.     

原位能量色散X射线荧光分析中岩样基体效应及其修正研究

原位能量色散X射线荧光现场分析岩样矿物成分时,岩样基体效应会对测量结果产生影响。本文以Cu元素作为待测元素,研究了17种不同岩样基体对原位能量色散X射线荧光分析Cu元素特征X射线强度的影响及其修正方法。采用蒙特卡罗方法模拟获得了Cu元素含量相同的17种不同岩样测量谱线,综合各类岩石元素构成的相似性,并依据模拟谱线Cu元素Kα射线强度与谱线参数之间的相关性,反映了原位能量色散X射线荧光分析岩样Cu元素的基体效应并不完全受岩体元素构成或岩石分类的控制,需要依据岩石样分析谱线参数的相关性进行归类讨论。针对基体影响Cu元素特征射线强度相似的15种岩样进一步研究,并对Cu元素特征X射线与谱线主要参数的主成分进行分析,发现散射本底、X光管靶材料特征X射线及其非相干散射峰强度能够很好的描述Cu元素特征X射线强度受岩样基体影响的变化,据此可以对基体效应影响相似的岩体进行Cu元素测量结果修正。采用本文方法同样也能为不同岩性岩体其他待测元素基体效应的修正提供参考。