脉冲噪声中非平稳源的盲分离方法

盲源分离的目的在于只利用观测数据把被瞬时线性混合的源信号恢复出来.本文讨论的是一种在服从α-稳定的噪声中的非平稳源盲分离方法,我们首先用一个经验门限值对观测数据进行预处理,充分利用源信号的非平稳性和时间相关特性,对加权后的观测数据用滑窗的方法得到不同的时延相关矩阵,然后利用多个特征矩阵的近似联合对角化方法来估计源信号和混合矩阵.这种方法适用于特征指数α趋于1的情况,仿真结果说明该方法具有良好的性能.     

利用盲源分离算法实现DOA估计

提出一种基于快速盲源分离算法实现波达方向（DOA）估计的方法。构造了具有对角化结构的相关矩阵组,引入解盲源分离问题的联合对角化代价函数,采用一种快速的复数域乘性迭代算法求解代价函数,得到混迭矩阵逆的估计,进而实现DOA估计。与同类算法相比,该算法具有更广的适用性和更精确的DOA估计性能。仿真实验结果验证了算法的快速收敛性和优越的估计性能。     

Convolutive blind source separation based on joint block Toeplitzation and block-inner diagonalization

This paper takes a close look at the block Toeplitz structure and block-inner diagonal structure of auto correlation matrices of source signals in convolutive blind source separation (BSS) problems. The aim is to propose a one-stage time-domain algorithm for convolutive BSS by explicitly exploiting the structure in autocorrelation matrices of source signals at different time delays and inherent relations among these matrices. The main idea behind the proposed algorithm is to implement the joint block Toeplitzation and block-inner diagonalization (JBTBID) of a set of correlation matrices of the observed vector sequence such that the mixture matrix can be extracted. For this purpose, a novel tri-quadratic cost function is introduced. The important feature of this tri-quadratic contrast function enables the development of an efficient algebraic method based on triple iterations for searching the minimum point of the cost function, which is called the triply iterative algorithm (TIA). Through the cyclic minimization process in the proposed TIA, it is expected that the JBTBID is achieved. The source signals can be retrieved. Moreover, the asymptotic convergence of the proposed TIA is analyzed. Convergence performance of the TIA and the separation results are also demonstrated by simulations in comparison with some other prominent two-stage time-domain methods.     

Blind source separation for convolutive mixtures based on the joint diagonalization of power spectral density matrices

This paper studies the problem of blind separation of convolutively mixed source signals on the basis of the joint diagonalization (JD) of power spectral density matrices (PSDMs) observed at the output of the separation system. Firstly, a general framework of JD-based blind source separation (BSS) is reviewed and summarized. Special emphasis is put on the separability conditions of sources and mixing system. Secondly, the JD-based BSS is generalized to the separation of convolutive mixtures. The definition of a time and frequency dependent characteristic matrix of sources allows us to state the conditions under which the separation of convolutive mixtures is possible. Lastly, a frequency-domain approach is proposed for convolutive mixture separation. The proposed approach exploits objective functions based on a set of PSDMs. These objective functions are defined in the frequency domain, but are jointly optimized with respect to the time-domain coefficients of the unmixing system. The local permutation ambiguity problems, which are inherent to most frequency-domain approaches, are effectively avoided with the proposed algorithm. Simulation results show that the proposed algorithm is valid for the separation of both simulated and real-word recorded convolutive mixtures.     

Joint blind source separation by generalized joint diagonalization of cumulant matrices

In this paper, we show that the joint blind source separation (JBSS) problem can be solved by jointly diagonalizing cumulant matrices of any order higher than one, including the correlation matrices and the fourth-order cumulant matrices. We introduce an efficient iterative generalized joint diagonalization algorithm such that a series of orthogonal procrustes problems are solved. We present simulation results to show that the new algorithms can reliably solve the permutation ambiguity in JBSS and that they offer superior performance compared with existing multiset canonical correlation analysis (MCCA) and independent vector analysis (IVA) approaches. Experiment on real-world data for separation of fetal heartbeat in electrocardiogram (ECG) data demonstrates a new application of JBSS, and the success of the new algorithms for a real-world problem.     

Blind Source Separation for Non-Stationary Mixing

Blind source separation attempts to recover independent sources which have been linearly mixed to produce observations. We consider blind source separation with non-stationary mixing, but stationary sources. The linear mixing of the independent sources is modelled as evolving according to a Markov process, and a method for tracking the mixing and simultaneously inferring the sources is presented. Observational noise is included in the model. The technique may be used for online filtering or retrospective smoothing. The tracking of mixtures of temporally correlated is examined and sampling from within a sliding window is shown to be effective for destroying temporal correlations. The method is illustrated with numerical examples.     

A unifying criterion for instantaneous blind source separation based on correntropy

Correntropy has recently been introduced as a generalized correlation function between two stochastic processes, which contains both high-order statistics and temporal structure of the stochastic processes in one functional form. Based on this blend of high-order statistics and temporal structure in a single functional form, we propose a unified criterion for instantaneous blind source separation (BSS). The criterion simultaneously exploits both spatial and spectral characteristics of the sources. Consequently, the new algorithm is able to separate independent, identically distributed (i.i.d.) sources, which requires high-order statistics; and it is also able to separate temporally correlated Gaussian sources with distinct spectra, which requires temporal information. Performance of the proposed method is compared with other popular BSS methods that solely depend on either high-order statistics (FastICA, JADE) or second-order statistics at different lags (SOBI). The new algorithm outperforms the conventional methods in the case of mixtures of sub-Gaussian and super-Gaussian sources.     

一种多维信源衰减延时混合的欠定盲源分离方法

为解决衰减延时混合信号的欠定盲源分离问题，该文研究了一种基于信源数估计的欠定盲源分离方法。首先，采用对时频域观测信号求能量来构造稀疏域；其次，在能量域中利用势函数估计信源数；再次，根据信源数将能量和峰值对应的频点筛选出来预测时频掩码从而获得估计信源的短时频谱；最后，填充线用来解决时域分离信号的边界效应问题。实验表明，所提方法可以有效分离衰减延时混合的模拟信号，并且在不同信噪比下优于稀疏聚类算法和子空间法；此外，在对实测悬臂梁锤击测试的过程中可以估计出模态阶数并且准确识别出结构的各阶模态固有频率。     

基于三阶统计量的欠定盲源分离方法

盲源分离(BSS)在缺失源信号信息及信息混合方式信息的情况下,仅利用观测信号实现源信号恢复,是信号处理中的重要手段。欠定盲源分离(UBSS)中观测信号少于源信号数目,因此,相较于正定/超定情形,其更接近现实情况。然而,观测信号往往受到噪声干扰,传统基于2阶统计量和信号稀疏性的欠定盲源分离结果对噪声较为敏感。鉴于3阶统计量在处理对称分布噪声时的优势,该文利用观测信号的3阶统计信息实现混合矩阵的估计。考虑到源信号的自相关特性,计算多时延下观测信号一系列的3阶统计信息,并堆叠成4阶张量,进而将混合矩阵估计问题转化为4阶张量的典范双峰分解问题。该文进一步利用广义高斯模型和期望最大算法实现源信号的恢复。1000次蒙特卡罗实验表明该文算法能够有效抑制噪声的影响。针对3×4混合模型,当信噪比为15 dB时,该文算法对混合矩阵的平均估计误差达到–20.35 dB,所恢复出的源信号与真实源信号之间的平均绝对相关系数达0.84,与现有方法相比,取得了最好的分离结果。     

一种新的联合对角化盲源分离算法分析

盲源分离是一种多通道的信号处理方法。应用盲源分离理论,可以在不知道传输通道的情况下,仅依靠采集到的信号,提取出各种源信号。构建累积量联合矩阵,进行对角化处理,得到分离矩阵,是一种很常见的盲源分离方法。针对通常算法精度不高的问题,提出了一种将基于二阶累积量和基于四阶累积量综合在一起的盲源分离算法。该方法结合了两种方法的优点,既考虑了二阶时空间上的不相关,又考虑了四阶累积量度量的独立性。     

Matrix-Group Algorithm via Improved Whitening Process for Extracting Statistically Independent Sources From Array Signals

This paper addresses the problem of blind separation of multiple independent sources from observed array output signals. The main contributions in this paper include an improved whitening scheme for estimation of signal subspace, a novel biquadratic contrast function for extraction of independent sources, and an efficient alterative method for joint implementation of a set of approximate diagonalization-structural matrices. Specifically, an improved whitening scheme is first developed by estimating the signal subspace jointly from a set of diagonalization-structural matrices based on the proposed cyclic maximizer of an interesting cost function. Moreover, the globally asymptotical convergence of the proposed cyclic maximizer is analyzed and proved. Next, a novel biquadratic contrast function is proposed for extracting one single independent component from a slice matrix group of any order cumulant of the array signals in the presence of temporally white noise. A fast fixed-point algorithm that is a cyclic minimizer is constructed for searching a minimum point of the proposed contrast function. The globally asymptotical convergence of the proposed fixed-point algorithm is analyzed. Then, multiple independent components are obtained by using repeatedly the proposed fixed-point algorithm for extracting one single independent component, and the orthogonality among them is achieved by the well-known QR factorization. The performance of the proposed algorithms is illustrated by simulation results and is compared with three related blind source separation algorithms     

一种利用结构特点实现复数域联合对角化解盲源分离新算法研究及应用

联合对角化方法是求解盲源分离问题的有力工具.但是现存的联合对角化算法大都只能求解实数域盲源分离问题,且对目标矩阵有诸多限制.为了求解更具一般性的复数域盲源分离问题,提出了一种基于结构特点的联合对角化（Structural Traits Based Joint Diagonalization,STBJD）算法,既取消了预白化操作解除了对目标矩阵的正定性限制,又允许目标矩阵组为复值,具有极广的适用性.首先,引入矩阵变换,将待联合对角化的复数域目标矩阵组转化为新的具有鲜明结构特点的实对称目标矩阵组.随后,构建联合对角化最小二乘代价函数,引入交替最小二乘迭代算法求解代价函数,并在优化过程中充分挖掘所涉参量的结构特点加以利用.最终,求得混迭矩阵的估计并据此恢复源信号.仿真实验证明与现存的有代表性的对目标矩阵无特殊限制的复数域联合对角化算法FAJD算法及CVFFDIAG算法相比,STBJD算法具有更高的收敛精度,能有效地解决盲源分离问题.     

On the Use of Spatial Time Frequency Distributions for Signal Extraction

This paper deals with the extraction of signals from their instantaneous linear mixtures using time-frequency distributions. Fundamentally, this problem is a signal synthesis from the time-frequency (t-f) plane. However with the incorporation of the spatial information provided by a multisensor array, the problem can be posed as special case of blind source separation. So far, the blind source separation has been solved using only statistical information available on the source signals. Herein, we propose to solve the aforementioned problem using time-frequency signal representations and the spatial array aperture. The proposed approach relies on the difference in the t-f signatures of the sources to be separated. It is based on the diagonalization of a combined set of spatial time-frequency distribution matrices. A numerical example is provided to illustrate the effectiveness of our method.     

多维盲信源分离的联合块对角化方法

根据多维盲信源分离中源信号组内相关、组间独立的特点,提出一种利用联合块对角化解决该问题的方法,并用经过改造的雅克比算法实现。源信号自相关矩阵具有块对角结构,使得白化后观测数据的时延相关矩阵具有可联合块对角化的结构,因此可以通过联合块对角化来辨识分离矩阵中的正交部分以恢复源信号。针对联合块对角化的特点,对传统的雅克比方法加以改造,将GIVENS旋转矩阵中参数的选择问题转化为一元四次三角函数多项式的优化问题,同时调整旋转的循环顺序。这样,通过连续的GIVENS旋转即可实现联合块对角化。实验仿真和分析表明了算法的有效性。      

应用萤火虫算法的混沌信号盲源分离

针对现有的独立成分分析法分离混合混沌信号精度不理想的问题,提出了一种新的混沌信号盲分离方法。该方法以求解最优解混矩阵为目标,利用峭度构造目标函数,将混沌信号的盲源分离转化为一个优化问题,并用萤火虫算法求解。同时,通过预白化和正交矩阵的参数化表示降低优化问题的维数,能有效提高分离精度。仿真结果表明,无论是处理混合的混沌映射信号还是混合的混沌流信号,该方法都能快速收敛,并且其分离精度在各项实验中都优于独立成分分析法等现有的盲源分离方法。     

一种充分利用变量结构的解卷积 混合盲源分离新方法

 针对卷积混合盲源分离问题,提出一种基于接收信号不同延时下自相关矩阵组的联合块内对角化方法.为了求解表征联合块内对角化近似程度的基于最小二乘的三二次代价函数,给出基于梯度下降法的三迭代算法.该算法在充分利用混迭矩阵的块Toeplitz结构和源信号相关矩阵的块内对角化结构的基础上,交替估计代价函数中的三组待定参数,搜索代价函数最小点,从而得到混迭矩阵的估计,实现信道的盲均衡和源信号的盲分离.分析了三迭代算法的收敛性能,证明即使存在估计误差时,该算法依然全局渐进收敛.仿真结果表明,与其他经典的两步算法相比,提出的一步算法能够更好地估计混迭矩阵并恢复出源信号,有效地解决了卷积混合盲源分离问题.     

Underdetermined blind separation of non-disjoint signals in time-frequency domain based on matrix diagonalization

To estimate precisely the mixing matrix and extract the source signals in underdetermined case is a challenging problem, especially when the source signals are non-disjointed in time-frequency (TF) domain. The conventional algorithms such as subspace-based achieve blind source separation exploiting the sparsity of the original signals and the mixtures must satisfy the assumption that the number of sources that contribute their energy at any TF point is strictly less than that of sensors. This paper proposes a new method considering the uncorrelated property of the sources in the practical field which relaxes the sparsity condition of sources in TF domain. The method shows that the number of the sources that exist in any TF neighborhood simultaneously equals to that of sensors. We can identify the active sources and estimate their corresponding TF values in any TF neighborhood by matrix diagonalization. Moreover, this paper proposes a method for estimating the mixing matrix by classifying the eigenvectors corresponded to the single source TF neighborhoods. The simulation results show the proposed algorithm separates the sources with higher signal-to-interference ratio compared to other conventional algorithms.     

动态变化混叠模型下盲源分离中的源数估计

在进行欠定盲分离时,特别是对于源信号数目及混合矩阵动态变化的情况,常规的欠定盲分离及源数估计方法不能对源信号数目的变化时刻做出判断,因此很难实现动态变化的源信号数目实时和准确的估计。针对这个问题,提出了一种动态变化混叠模型下欠定盲源分离中的源数估计方法。首先,建立动态变化混叠情形下盲源分离的数学模型及动态标识矩阵。其次,基于构建的动态标识矩阵统计和判断动态源信号数目的变化情况。最后,通过分段时间内多维观测矢量采样点聚类区间局部峰值统计,实现动态变化混叠模型下盲源分离中的源信号数目的有效估计。仿真结果表明,该方法能有效实现动态变化混叠模型下欠定盲源分离中的源数估计,并且信号估计效果良好。     

基于相关系数的盲源分离排序和相位调整法

针对盲源分离后信号存在排序和相位不确定性的情况,提出一种基于相关系数的盲源分离排序和相位调整法,通过对盲源分离后信号运用该方法进行排序和相位调整,从而消除盲源分离后信号存在的相位和排序不确定性。仿真结果表明,在混合矩阵主对角线元素占优的情况下,此法可以有效地消除盲源分离后信号存在的排序和相位不确定性。     

Robust spatial time-frequency distribution matrix estimation with application to direction-of-arrival estimation

We consider the problem of estimating spatial time-frequency distribution (STFD) matrices in the presence of impulsive noise. STFD matrices are widely used in sensor array processing for direction-of-arrival estimation and blind source separation of non-stationary sources. Conventional methods fail when the noise is non-Gaussian or impulsive. We propose robust techniques for STFD estimation which are based on pre-processing, robust position based estimation and robust covariance based estimation. The proposed methods are compared in terms of direction-of-arrival estimation performance.