System identification from noisy measurements by using instrumental variables and subspace fitting

This paper considers the estimation of the parameters of a linear discrete-time system from noise-perturbed input and output measurements. The conditions imposed on the system are fairly general. In particular, the input and output noises are allowed to be auto-correlated and they may be cross-correlated as well. The proposed method makes use of an instrumental variable (IV)-vector to produce a covariance matrix that is pre- and postmultiplied by some prechosen weights. The singular vectors of the so-obtained matrix possess complete information on the system parameters. A weighted subspace fitting (WSF) method is then applied to the aforementioned singular vectors to consistently estimate the parameters of the system. The IV-WSF technique suggested herein is noniterative and easy to implement, and has a small computational burden. The asymptotic distribution of its estimation errors is derived and the result is used to motivate the choice of the weighting matrix in the WSF step and also to predict the estimation accuracy. Numerical examples are included to illustrate the performance achievable by the method.This work has been supported by the Swedish Research Council of Engineering Sciences under contract 93-669 and by the Göran Gustafsson Foundation.     

A locally convergent Jacobi iteration for the tensor singular value problem

Multi-linear functionals or tensors are useful in study and analysis multi-dimensional signal and system. Tensor approximation, which has various applications in signal processing and system theory, can be achieved by generalizing the notion of singular values and singular vectors of matrices to tensor. In this paper, we showed local convergence of a parallelizable numerical method (based on the Jacobi iteration) for obtaining the singular values and singular vectors of a tensor.     

TDDM-BOC信号组合码序列及信息序列盲估计

该文针对低信噪比下TDDM-BOC(Time Division Data Modulation-Binary Offset Carrier)信号的组合码序列(将伪码序列和副载波序列看成一个整体序列)及信息序列盲估计问题,提出一种改进的基于奇异值分解的方法。该方法首先利用双信息符号周期、间隔一信息符号周期的时间窗对接受信号进行分段,并构成观测矩阵。然后对观测矩阵进行奇异值分解,通过左奇异向量实现组合码序列的盲估计。同时,通过右奇异向量实现信息序列的盲估计。仿真分析表明,该方法能够在较低的信噪比下达到精确估计的目的。这对于从事卫星导航接收机设计具有一定的参考价值。     

基于数据矩阵奇异值分解的时—空二维信号处理

本文提出一种利用阵列接收信号数据矩阵奇异值分解的时－空二维信号谱估计方法，该方法对线阵接收信号构成的数据矩阵进行奇异值分解，构造出噪声奇异向量，利用信号空间与噪声空间的正交性获得时－空二维谱，该方法可用于高分辨测向测速系统中，计算机模拟表明了该算法的有效性。     

利用特征极值比的盲信道阶数估计方法

确定性辨识方法是盲信道辨识的主流方法,然而确定性方法性能受信道阶数估计的严重影响。本文针对大多数信道阶数估计算法在坏信道条件下失效问题,分析子空间方法中噪声子空间矢量构成特殊矩阵的奇异性与信道阶数之间的关系,对该特殊矩阵最大特征值最小特征值的变化情况进行对比分析,利用特征极值的比值来反映信号子空间到噪声子空间的变化情况,从而提出特征极值比定理。针对观测数据有限且含噪声的实际应用条件,提出一种盲信道阶数估计算法,该算法以不同信道阶数的特征极值比作为参数构造目标函数,得到在真实信道阶数处目标函数取全局最大值,同时对该算法进行了复杂度分析。最后针对两种常用仿真信道参数对算法进行了验证,结果表明,在短数据和低信噪比条件下,本文算法能以较高的估计概率得到好信道和坏信道的有效阶数。      

基于累量的近场源快速定位算法

本文提出了一种基于累量的近场源参数快速估计方法。具体地,本文首先构造了一个累量矩阵,对其进行奇异值分解后,利用得到的右奇异向量和左奇异向量分别使用类Root-MUSIC方法得到了近场波达方向和距离估计的闭式解。该方法利用高阶累量矩阵,减少了阵列孔径损失,提高了能分辨的最大信源数,而且与其他基于高阶累积量的方法相比,该方法在近场的波达方向与距离的估计过程中只需要构造一个累量矩阵和进行一次奇异值分解,并且使用闭式解完全避免了峰值搜索,大大降低了运算量,同时还提高了估计的分辨概率和精度。此外,该方法在几乎没有增加额外计算量的情况下可以推广到混合场源的情况。仿真结果表明,该算法的分辨率和精度都有较大的优越性。      

Video quality measurement based on 3-D. Singular value decomposition

This paper presents a new full reference Video Quality Assessment (VQA) method based on using 3 Dimensional Singular Value Decomposition (3-D SVD). The method compares the structural properties and the luminance characteristics between the reference and the distorted videos. This aim is obtained by applying 3-D SVD that is singular value decomposition in a 3-D space. In principal, the distorted and the original videos are projected on the singular vectors of the original video. The weighted difference between the reflections coefficients could be considered to quantify the quality of videos. For our experiments, we have used the LIVE and EPFL-PoliMI video quality databases to evaluate the performance of our metric. The results show a great correlation between the measure scores and the subjective scores.     

一种基于旋转矩阵单位四元数分解的运动估计算法

本文基于旋转矩阵单位四元数分解定理,提出一种由3D特征点空间位置估计运动参数的算法。单位四元数表示旋转矩阵时不存在奇异点,故基于单位四元数的运动估计方法具有更大的实用价值,而本文算法无需Horn(1987)和Su等人(1989)提出的单位四元数方法的迭代运算。本文给出了解的唯一性分析和模拟实验结果,可见其性能是令人满意的。     

基于K-均值聚类的SVD杂波抑制算法

针对强地物静止杂波及慢速杂波严重环境下,慢速运动目标被淹没其中而无法有效检测的问题,本文设计了一种基于K-均值聚类的SVD杂波抑制方法。该方法对回波信号矩阵进行奇异值分解,依据回波信号特性,得到相应的奇异值谱分布,以及奇异向量的空间相关性和平均多普勒频率三个统计量特征,然后基于这些特征采用K-均值聚类算法对各奇异分量进行聚类,无需人为设定阈值参数估计杂波基,可以自适应确定杂波子空间所对应的奇异向量,最后通过正交子空间投影来抑制回波信号中的杂波成分。实验结果表明,该方法在低信杂比条件下相比于传统子空间方法,能够得到较好杂波抑制效果。     

AN ALGORITHM OF MOTION ESTIMATION BASED ON UNIT QUATERNION DECOMPOSITION OF THE ROTATION MATRIX

Based on the unit quaternion decomposition of rotation matrix, this paper puts forward an algorithm to estimate motion parameters from the space position vectors of 3D feature points. Rotation matrix's representation with the unit quaternion has no singular points, so the unit quaternion-based estimation method is of more practical importance, and the algorithm in this paper does not need iteration computation compared to those unit quaternion-based methods proposed by Horn(1987) and Su, et al.(1989). Solution's uniqueness analysis of the algorithm and simulation experiment results are also presented, it can be seen that performance of our method is satisfactory.     

Analysis of the time-reversal operator for a small spherical scatterer in an electromagnetic field

The time-reversal operator (TRO) for a planar array of crossed dipole elements illuminating a small conducting and/or dielectric sphere is investigated in order to determine the general properties of an electromagnetic time-reversing array system. The behavior of such a system for a given frequency is analyzed by studying the eigenvalues and eigenvectors of the TRO. Each eigenvector specifies a set of complex driving currents for the array elements that produce received voltages that are proportional to the conjugates of the drive currents. The proportionality constant is equal to the square root of the associated eigenvalue and is the same for all elements. The eigenvalues and eigenvectors can be determined by performing a singular value decomposition (SVD) on the multistatic data matrix of the array. The eigenvalues of the TRO are the squares of the singular values, and the eigenvectors are identical to the singular vectors. We have shown that the maximum number of singular vectors associated with the sphere is equal to the number of orthogonal orientations of the dipole moments induced in the sphere when irradiated by the array, so there is a maximum of six for a conducting sphere but only three are significant when the conductivity is small and the sphere may be considered being just a dielectric. Numerical results are presented for linear and circular arrays to show the general behavior of the system.     

一种基于奇异值分解的特征抽取方法

特征抽取是模式识别的基本问题之一,Fisher线性鉴别分析是特征抽取中最为经典和广泛使用的方法之一。该文分析了Fisher线性鉴别分析在求解过程中可能存在的问题:鉴别矢量的分量可能是复数;特征值对扰动的敏感性;鉴别矢量之间未必具有正交性。由此提出了均衡散布矩阵的概念,并利用均衡散布矩阵构造了一种新的线性鉴别准则。利用奇异值分解定理,将求取鉴别矢量转化为对矩阵求奇异向量。用该方法进行求解可以有效地避免前述的问题。试验结果表明,该鉴别准则具有良好的鉴别能力。     

A Novel Method for the Diagnosis of the Incipient Faults in Analog Circuits Based on LDA and HMM

Diagnosis of incipient faults for electronic systems, especially for analog circuits, is very important, yet very difficult. The methods reported in the literature are only effective on hard faults, i.e., short-circuit or open-circuit of the components. For a soft fault, the fault can only be diagnosed under the occurrence of large variation of component parameters. In this paper, a novel method based on linear discriminant analysis (LDA) and hidden Markov model (HMM) is proposed for the diagnosis of incipient faults in analog circuits. Numerical simulations show that the proposed method can significantly improve the recognition performance. First, to include more fault information, three kinds of original feature vectors, i.e., voltage, autoregression-moving average (ARMA), and wavelet, are extracted from the analog circuits. Subsequently, LDA is used to reduce the dimensions of the original feature vectors and remove their redundancy, and thus, the processed feature vectors are obtained. The LDA is further used to project three kinds of the processed feature vectors together, to obtain the hybrid feature vectors. Finally, the hybrid feature vectors are used to form the observation sequences, which are sent to HMM to accomplish the diagnosis of the incipient faults. The performance of the proposed method is tested, and it indicates that the method has better recognition capability than the popularly used backpropagation (BP) network.     

Higher Order SVD Analysis for Dynamic Texture Synthesis

Videos representing flames, water, smoke, etc., are often defined as dynamic textures: "textures" because they are characterized by the redundant repetition of a pattern and "dynamic" because this repetition is also in time and not only in space. Dynamic textures have been modeled as linear dynamic systems by unfolding the video frames into column vectors and describing their trajectory as time evolves. After the projection of the vectors onto a lower dimensional space by a singular value decomposition (SVD), the trajectory is modeled using system identification techniques. Synthesis is obtained by driving the system with random noise. In this paper, we show that the standard SVD can be replaced by a higher order SVD (HOSVD), originally known as Tucker decomposition. HOSVD decomposes the dynamic texture as a multidimensional signal (tensor) without unfolding the video frames on column vectors. This is a more natural and flexible decomposition, since it permits us to perform dimension reduction in the spatial, temporal, and chromatic domain, while standard SVD allows for temporal reduction only. We show that for a comparable synthesis quality, the HOSVD approach requires, on average, five times less parameters than the standard SVD approach. The analysis part is more expensive, but the synthesis has the same cost as existing algorithms. Our technique is, thus, well suited to dynamic texture synthesis on devices limited by memory and computational power, such as PDAs or mobile phones.     

An eigen-based MIMO multiuser scheduler with partial feedback information

An eigen-based MIMO multiuser scheduler which is robust to spatial channel correlation is proposed. The proposed scheduler uses the principal right singular vector for reduced feedback information and exploits the eigen-mode transmission using a precoder matrix, whose columns are the principal right singular vectors of selected users. Since the proposed scheduler uses only each principal eigen channel of the user, it is hot affected by spatial channel correlation even if all spatial channels are equal. Moreover, since the distribution of a singular value is concentrated on the principal singular value under the spatially correlated environments, more channel gain can be obtained. By computer simulations, it is shown that the proposed scheduler has better performance for both capacity and fairness under the moderate spatial channel correlation than the existing schedulers.     

基于频域数据采样和时域信号同步的超宽带时间反转成像

提出一种基于频域数据取样和时域信号同步的超宽带（Ultrawideband,UWB）时间反转（Time-Reversal,TR）成像方法.单个发射机发射UWB脉冲信号到探测区域,时间反转镜（Time Reversal Mirror,TRM）的每个天线单元对散射信号进行细频和粗频数据采样,得到各自单元的频率-频率-多站数据矩阵（individual-FF-MDM）.把所有单元的该矩阵堆砌起来,形成一个全体单元的频率-频率-多站数据矩阵（full-FF-MDM）,并对full-FF-MDM进行奇异值分解（Singular Value Decomposition,SVD）,得到耦合了目标位置信息的左奇异值向量.将每一个左奇异值向量变换成时域脉冲回传辐射,则来自TRM各单元的回传辐射信号在相应目标处同时到达波形的最大值,而在非该目标处则不能同时达到最大值.于是,定义各单元的回传信号乘积作为目标成像函数,可获得良好的横向和纵向分辨率.     

Blind MIMO eigenmode transmission based on the algebraic power method

Identification of the channel matrix is of main concern in wireless multiple input multiple output (MIMO) systems. To maximize the SNR, the best way to utilize a MIMO system is to communicate on the top singular vectors of the channel matrix. Here, we present a new approach for direct blind identification of the main independent singular modes, without estimating the channel matrix itself. The right and left singular vectors with maximum corresponding singular values are determined using payload data and are continuously updated while at the same time being used for communication. The feasibility of the approach is demonstrated by simulating the performance over a noisy, fading time-varying channel. Mathematically, the technique is related to the iterative numerical Power method for finding eigenvalues of a matrix as well as the "time reversal mirror" technique developed within acoustics.     

Design of two-dimensional rectangular array beamformers withpartial adaptivity

This paper considers the problem of designing a two-dimensional (2-D) rectangular array beamformer with partial adaptivity. Using the eigenstructure of the signal data received by a 2-D rectangular array beamformer, we first show that the optimal weight matrix when using full adaptivity can be obtained from a set of singular vectors. Then the design problem of using partial adaptivity is formulated. As a result, the optimal solution for the partially adaptive weight matrix can be found by solving two basic problems, namely determining the proper dimension of the partially adaptive weight matrix and the set of the singular vectors. We develop the detection formulas for the information theoretic criteria AIC and MDL to find the proper dimension. Next, an efficient method is presented so that the optimal solution for the set of the singular vectors can be found analytically. We also investigate the required computational complexity. It is shown that 2-D partially adaptive beamforming using the proposed technique requires less computational complexity than 2-D fully adaptive beamforming using conventional techniques. Moreover, computer simulations demonstrate that the proposed 2-D partially adaptive technique provides satisfactory array performance when compared with conventional fully adaptive techniques     

毫米波大规模MIMO系统中低复杂度混合预编码方法

针对毫米波大规模多输入多输出(MIMO)系统混合预编码方案设计的难点,提出了一种低复杂度混合预编码方法。首先基于奇异值分解,构造初始射频(RF)预编码矩阵,然后构造数字预编码矩阵。进而将残差矩阵最大左奇异矢量构造的矢量添加到RF矩阵的最后一列,以更新初始RF矩阵。经过多次迭代,从而形成最终RF预编码矩阵。最后基于最小二乘准则设计数字预编码矩阵。理论分析和仿真结果表明,相比于基于正交匹配追踪(OMP)算法的混合预编码设计方法,该方法在计算复杂度大幅下降的同时,其性能远远优于基于OMP算法的混合预编码方法,同时在数据流数相对较小时,其性能接近最优的全数字预编码设计方法。     

基于奇异值分解的基图像的人脸识别

研究了基于奇异值分解的人脸识别问题。首先证明了图像的大量信息主要体现在图像矩阵奇异值分解的前几个最大奇异值所对应的左、右奇异向量中,然后给出了模板图像的基图像,并将图像展开成基图像的线性表示,提取其组合系数作为图像的代数特征并用于人脸识别中。实验表明,较以投影系数向量为代数特征的人脸识别方法,该方法所需的运行时间明显降低,而且与基于奇异值向量作为图像特征的方法相比,该方法的识别精度明显提高。