A two-stage frequency-domain blind source separation method for underdetermined instantaneous mixtures

In order to decrease the probability of missing some data points or noises being added in the inverse truncated mixing matrix （ITMM） algorithm, a two-stage frequency- domain method is proposed for blind source separation of underdetermined instantaneous mixtures. The separation process is decomposed into two steps of ITMM and matrix completion in the view that there are many soft-sparse （not very sparse） sources. First, the mixing matrix is estimated and the sources are recovered by the traditional ITMM algorithm in the frequency domain. Then, in order to retrieve the missing data and remove noises, the matrix completion technique is applied to each preliminary estimated source by the traditional ITMM algorithm in the frequency domain. Simulations show that, compared with the traditional ITMM algorithms, the proposed two-stage algorithm has better separation performances. In addition, the time consumption problem is considered. The proposed algorithm outperforms the traditional ITMM algorithm at a cost of no more than one- fourth extra time consumption.

Underdetermined DOA estimation and blind separation of non-disjoint sources in time-frequency domain based on sparse representation method

This paper deals with the blind separation of nonstation-ary sources and direction-of-arrival （DOA） estimation in the under-determined case, when there are more sources than sensors. We assume the sources to be time-frequency （TF） disjoint to a certain extent. In particular, the number of sources presented at any TF neighborhood is strictly less than that of sensors. We can identify the real number of active sources and achieve separation in any TF neighborhood by the sparse representation method. Compared with the subspace-based algorithm under the same sparseness assumption, which suffers from the extra noise effect since it can-not estimate the true number of active sources, the proposed algorithm can estimate the number of active sources and their cor-responding TF values in any TF neighborhood simultaneously. An-other contribution of this paper is a new estimation procedure for the DOA of sources in the underdetermined case, which combines the TF sparseness of sources and the clustering technique. Sim-ulation results demonstrate the validity and high performance of the proposed algorithm in both blind source separation （BSS） and DOA estimation.

A robust clustering algorithm for underdetermined blind separation of sparse sources

In underdetermined blind source separation, more sources are to be estimated from less observed mixtures without knowing source signals and the mixing matrix. This paper presents a robust clustering algorithm for underdetermined blind separation of sparse sources with unknown number of sources in the presence of noise. It uses the robust competitive agglomeration （RCA） algorithm to estimate the source number and the mixing matrix, and the source signals then are recovered by using the interior point linear programming. Simulation results show good performance of the proposed algorithm for underdetermined blind sources separation （UBSS）.

Source Recovery in Underdetermined Blind Source Separation Based on Artificial Neural Network

We propose a novel source recovery algorithm for underdetermined blind source separation, which can result in better accuracy and lower computational cost. On the basis of the model of underdetermined blind source separation, the artificial neural network with single-layer perceptron is introduced into the proposed algorithm. Source signals are regarded as the weight vector of single-layer perceptron, and approximate ι~0-norm is taken into account for output error decision rule of the perceptron, which leads to the sparse recovery. Then the procedure of source recovery is adjusting the weight vector of the perceptron. What's more, the optimal learning factor is calculated and a descent sequence of smoothed parameter is used during iteration, which improves the performance and significantly decreases computational complexity of the proposed algorithm. The simulation results reveal that the algorithm proposed can recover the source signal with high precision, while it requires lower computational cost.

Algorithm for source recovery in underdetermined blind source separation based on plane pursuit

In order to achieve accurate recovery signals under the underdetermined circumstance in a comparatively short time,an algorithm based on plane pursuit(PP) is proposed. The proposed algorithm selects the atoms according to the correlation between received signals and hyper planes, which are composed by column vectors of the mixing matrix, and uses these atoms to recover source signals. Simulation results demonstrate that the PP algorithm has low complexity and higher accuracy as compared with basic pursuit(BP), orthogonal matching pursuit(OMP), and adaptive sparsity matching pursuit(ASMP) algorithms.

Mixing matrix estimation of underdetermined blind source separation based on the linear aggregation characteristic of observation signals

Under the underdetermined blind sources separation(UBSS) circumstance,it is difficult to estimate the mixing matrix with high-precision because of unknown sparsity of signals.The mixing matrix estimation is proposed based on linear aggregation degree of signal scatter plot without knowing sparsity,and the linear aggregation degree evaluation of observed signals is presented which obeys generalized Gaussian distribution(GGD).Both the GGD shape parameter and the signals' correlation features affect the observation signals sparsity and further affected the directionality of time-frequency scatter plot.So a new mixing matrix estimation method is proposed for different sparsity degrees,which especially focuses on unclear directionality of scatter plot and weak linear aggregation degree.Firstly,the direction of coefficient scatter plot by time-frequency transform is improved and then the single source coefficients in the case of weak linear clustering is processed finally the improved K-means clustering is applied to achieve the estimation of mixing matrix.The proposed algorithm reduces the requirements of signals sparsity and independence,and the mixing matrix can be estimated with high accuracy.The simulation results show the feasibility and effectiveness of the algorithm.

Blind source separation by weighted K-means clustering

Blind separation of sparse sources （BSSS） is discussed. The BSSS method based on the conventional K-means clustering is very fast and is also easy to implement. However, the accuracy of this method is generally not satisfactory. The contribution of the vector x（t） with different modules is theoretically proved to be unequal, and a weighted K-means clustering method is proposed on this grounds. The proposed algorithm is not only as fast as the conventional K-means clustering method, but can also achieve considerably accurate results, which is demonstrated by numerical experiments.

UBSS and blind parameters estimation algorithms for synchronous orthogonal FH signals

By using the sparsity of frequency hopping（FH） signals,an underdetermined blind source separation（UBSS） algorithm is presented. Firstly, the short time Fourier transform（STFT） is performed on the mixed signals. Then, the mixing matrix, hopping frequencies, hopping instants and the hooping rate can be estimated by the K-means clustering algorithm. With the estimated mixing matrix, the directions of arrival（DOA） of source signals can be obtained. Then, the FH signals are sorted and the FH pattern is obtained. Finally, the shortest path algorithm is adopted to recover the time domain signals. Simulation results show that the correlation coefficient between the estimated FH signal and the source signal is above 0.9 when the signal-to-noise ratio（SNR） is higher than 0 d B and hopping parameters of multiple FH signals in the synchronous orthogonal FH network can be accurately estimated and sorted under the underdetermined conditions.

Source number estimation and separation algorithms of underdetermined blind separation

Recently,sparse component analysis (SCA) has become a hot spot in BSS re-search. Instead of independent component analysis (ICA),SCA can be used to solve underdetermined mixture efficiently. Two-step approach (TSA) is one of the typical methods to solve SCA based BSS problems. It estimates the mixing matrix before the separation of the sources. K-means clustering is often used to estimate the mixing matrix. It relies on the prior knowledge of the source number strongly. However,the estimation of the source number is an obstacle. In this paper,a fuzzy clustering method is proposed to estimate the source number and mixing matrix simultaneously. After that,the sources are recovered by the shortest path method (SPM). Simulations show the availability and robustness of the proposed method.

基于UBSS算法的电力系统低频振荡辨识方法

低频振荡监测和分析对电力系统故障诊断和电网恢复至关重要。该文提出一种基于欠定盲源分离原理的低频振荡模式辨识方法,包括欠定盲源分离(underdetermined blind source separation,UBSS)和希尔伯特变换(Hilbert transform,HT)。首次系统地提出并论证含欠定盲源分离、模式定阶和振荡参数的辨识方法。提出的UBSS-HT方法利用能量比函数确定故障时刻,利用贝叶斯信息准则(Bayesian information criterion,BIC)实现模式定阶,阐述维度空间理论,论证构建虚拟多通道的可行性,通过盲源分离来实现源信号分离,最后通过HT在希尔伯特空间来辨识振荡参数。通过大量的系统建模仿真和现场录波数据试验评估所提方法的性能,验证该方法的有效性、准确性和抗干扰能力。

Non-invasive foetal heartbeat rate extraction from an underdetermined single signal

Extraction of foetal heartbeat rate from a single passive sound sensor on the mother’s abdomen is demonstrated. The extraction is based on the assumption that a disjoint band of frequencies exist and foetal signal is concentrated in this band, and further that it can be represented conveniently as a set of wavelet coefficients. The algorithm has been applied to each stream of data obtained from six different channels and the detection performance is elaborated. The algorithm has also been tested on signals from non-pregnant abdomens to show successful rejection of adult heartbeat. The extraction of the desired signal is done in two stages so as to eliminate components from the maternal heart-beat.

Adaptive blind separation of underdetermined mixtures based on sparse component analysis

The independence priori is very often used in the conventional blind source separation （BSS）. Naturally, independent component analysis （ICA） is also employed to perform BSS very often. However, ICA is difficult to use in some challenging cases, such as underdetermined BSS or blind separation of dependent sources. Recently, sparse component analysis （SCA） has attained much attention because it is theoretically available for underdetermined BSS and even for blind dependent source separation sometimes. However, SCA has not been developed very sufficiently. Up to now, there are only few existing algorithms and they are also not perfect as well in practice. For example, although Lewicki-Sejnowski＇s natural gradient for SCA is superior to K-mean clustering, it is just an approximation without rigorously theoretical basis. To overcome these problems, a new natural gradient formula is proposed in this paper. This formula is derived directly from the cost function of SCA through matrix theory. Mathematically, it is more rigorous. In addition, a new and robust adaptive BSS algorithm is developed based on the new natural gradient. Simulations illustrate that this natural gradient formula is more robust and reliable than Lewicki-Sejnowski＇s gradient.

Improved statistical sparse decomposition principle method for underdetermined blind source signal recovery

Aiming at the statistical sparse decomposition principle(SSDP) method for underdetermined blind source signal recovery with problem of requiring the number of active signals equal to that of the observed signals, which leading to the application bound of SSDP is very finite, an improved SSDP(ISSDP) method is proposed. Based on the principle of recovering the source signals by minimizing the correlation coefficients within a fixed time interval, the selection method of mixing matrix’s column vectors used for signal recovery is modified, which enables the choose of mixing matrix’s column vectors according to the number of active source signals self-adaptively. By simulation experiments, the proposed method is validated. The proposed method is applicable to the case where the number of active signals is equal to or less than that of observed signals, which is a new way for underdetermined blind source signal recovery.

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。

基于改进粒子群的密度聚类算法混合矩阵估计

针对混合矩阵估计算法中传统的噪声环境下基于密度的空间聚类(density-based spatial clustering of applications with noise,DBSCAN)算法需要人为设定邻域半径以及核心点数这一问题,提出双约束粒子群优化(double constrained particle swarm optimization,DCPSO)算法,对DBSCAN算法的邻域半径参数进行寻优,将得到的最优参数作为DBSCAN算法的参数输入,然后计算聚类中心,完成混合矩阵估计。针对基于距离排序的源信号数目估计算法存在依靠经验参数的选取且不具备噪声点剔除能力的问题,提出了最大距离排序算法。实验结果表明,所提算法较相应的对比算法皆有提升,源信号数目估计准确率较原算法提高近40%,混合矩阵估计的误差较对比算法提升3 dB以上,且所提算法在收敛速度上优于原算法。

基于EMD-NLPCA的欠定非线性盲源分离算法及应用

对欠定非线性混合信号的盲源分离算法进行研究,提出一种基于经验模式分解与非线性主成分分析(EMD-NLPCA)的盲源分离算法。首先对观测信号做EMD处理,重构信号后引入高阶统计量,再进行主成分分析,完成信号分离。该算法既可以应对欠定环境,又解决了非线性混合问题。仿真实验中,将该算法与稀疏分量分析法的结果进行比照,证明了该算法的正确性以及相较于稀疏分量分析法更具普适性。将该算法用于无人机发动机开车音频信号的分离,效果较好。

基于欠定盲源分离模型的负荷分解方法研究

大规模分布式能源并入电网,其波动性与随机性对网侧的安全稳定带来挑战。而柔性负荷的合理调控可促进需求侧响应,柔性负荷的分解与识别是实现源荷积极互动的前提和关键。传统非侵入式负荷监测需要先验信息,在实际中较难获取。为此,提出一种基于欠定式盲源分离模型的负荷分解方法,利用开源数据集REDD进行实例验证分析。首先,对功率序列进行邻点做差处理,构建负荷功率与时间分布特征,通过聚类识别出独立负荷个数;随后,采用概率归一思想求解欠定混合矩阵,将独立负荷有功功率矩阵的输出转化为几种概率事件;最后,采用盲源分离模型将总功率信号分解为各独立负荷功率的叠加。实例分析结果表明:所提方法具有普适性,分解精度高,可满足实际需求。

欠定和非完全稀疏性的盲信号提取

两步策略已成为欠定盲信号分离的基本方法,混叠矩阵的估计是源恢复的先决条件.本文针对非完全稀疏性情况,提出一个两步的盲提取方法.该方法先利用信号的单源区间样本,估计部分源的基矢量(混叠矩阵的列矢量),后最小干扰地提取所对应的源;除它所对应的基矢量外,它不依赖的其它的基矢量,故回避了混叠矩阵可识别的必要条件.几个仿真实验结果显示了该算法的性能和实用性.

基于CS与K-SVD的欠定盲源分离稀疏分量分析

为了提高盲源分离的准确率,提出了结合压缩感知(CS)与K均值奇异值分解(K-SVD)的稀疏分量分析方法进行盲源分离.首先,分析欠定盲源分离估计源信号与压缩感知问题的等价性,建立压缩感知框架;其次,在此框架下利用K-SVD方法训练稀疏字典;最后利用经典追踪算法计算得到稀疏分量,结合传统的两步法,进行盲源分离.大量实验表明,该算法与其他稀疏表示方法相比获得了较好的分离效果.与传统两步法不同的是,该算法在压缩感知框架下利用K-SVD方法自适应地训练稀疏字典,求出混合信号的稀疏表示,稀疏分量分析方法的改进对盲源分离的准确率起到直接的影响作用.

基于时频分布的欠定混叠盲分离

针对欠定混合信号的盲分离问题,提出了基于时频分布的欠定盲分离算法,首先计算信号的时频分布矩阵并找出信号的自源时频点,然后把自源点对应的时频分布矩阵表示成三阶张量并通过张量分解估计出混合矩阵,最后通过计算矩阵的伪逆和时频合成来完成源信号的恢复.该算法不需要假设源信号是稀疏的或相互独立的.仿真结果表明与已有算法相比本文方法提高了盲分离的性能.