一种改进的基于奇异值分解的信源数目估计算法

信源数目估计问题在盲源分离中具有重要的意义。研究了传感器数目大于信源数目时的源数估计问题。首先分析了用奇异值分解法进行信源数目估计的优势与不足,然后提出了一种改进的基于奇异值分解的信源数目估计算法。该算法首先对含噪混合信号进行奇异值分解,然后检测信号分量与噪声分量之间的转折点,将信号分量与噪声分量区分开来,从而得到信号源的数目。实验仿真表明,该算法在低信噪比以及采样点数较少时仍然具有好的性能。     

基于奇异值分解的多卫星信号盲检测

针对非合作低信噪比环境下的卫星通信信号检测问题,在信号子空间维数估计的基础上,提出了一种基于奇异值分解的多卫星信号盲检测方法。该方法充分利用奇异值与特征值之间的关系,设计检测统计量将多个信号能量集中起来进行考虑,以适应更低的信噪比,并从理论上对检测性能进行了推导分析。仿真结果表明,该方法简单高效,针对不同的卫星信号,在虚警概率小于1%、信噪比为-11 dB时,盲检测概率均可达90%以上;同时能够在低信噪比环境下适应多信号环境,且其计算量相对特征值方法减少了一个数量级,更适合应用在星载设备上。     

一种基于奇异值分解的改进信噪比盲估计算法

针对空间分解类信噪比(SNR)估计算法中子空间维数估计复杂度较高,低信噪比下估计偏差较大的问题,提出了一种改进的子空间维数估计算法。该算法首先利用样本自相关矩阵的奇异值序列进行后向差分得到梯度序列,对梯度序列每一项与后5项之和的比值进行搜索,最大比值所对应的奇异值序号作为信号子空间维数,最后计算信噪比。合适数据长度下的仿真结果表明：在信噪比-5 dB~20 dB范围内,常规通信信号的信噪比估计平均偏差小于0.5 dB,标准差小于1 dB;该算法提升了低信噪比下的估计性能,运算量较小,无需知道调制方式、载波频率、符号率等先验信息,在低信噪比时对信噪比时变的跟踪估计更为准确,且对复杂高阶调制信号同样适用。     

一种基于Toeplitz矩阵重构的相干信源DOA估计算法

提出一种基于Toeplitz矩阵重构的相干信号源DOA估计算法。首先对各个阵元的接收数据与参考阵元（第一个阵元）的接收数据的相关函数进行排列,形成Hermitian Toeplitz矩阵,然后通过奇异值分解可以得到信号子空间和噪声子空间,从而实现相干信源的DOA估计。该算法在不减少阵列有效孔径的情况下,增加了可估计相干信号源数目,并在低信噪比条件下能够得到较好的估计性能,计算机仿真结果证实了算法的有效性。     

基于奇异谱分析的抗数字射频存储距离波门拖引干扰

针对基于数字射频存储(DRFM)技术的转发式欺骗干扰难以检测和抑制问题,该文根据DRFM的延时量化会导致干扰信号产生细微的中心频率频移及谐波分量寄生的特性,提出一种基于奇异谱分析(SSA)的抗距离波门拖引干扰方法。该方法首先提取干扰信号谐波分量与目标回波经SSA分解后奇异值能量的分布差异特征,实现对有源欺骗干扰的检测,然后依据干扰中心频率频移特性,通过划分合适的奇异值子空间重构目标信号,实现对欺骗干扰的抑制。该方法不需要估计噪声参数,在干扰检测阶段具有恒虚警特性。Monte Carlo仿真结果验证了该方法的有效性。     

基于特征值能量的盲信号检测方法

针对低信噪比下电子侦察机接收到的多分量信号的盲检测问题,提出了一种基于特征值能量的盲信号检测算法.该算法首先计算归一化特征值,然后进行信号子空间维数估计,构建检验统计量表达式,进而研究了扰动分布,从而确定给定虚警概率下的检测门限,实现信号的盲检测.理论分析和仿真结果表明,该算法对多分量信号尤其是时频重叠的多分量信号适应...     

改进白化的MDL快速独立分量分析算法

采用主分量分析法(PCA)进行的白化处理,可能会错误估计信号子空间维数,且未考虑噪声影响。提出了一种基于最小描述长度(MDL)准则信源个数估计改进白化的盲分离算法。通过信源个数估计确定信号子空间的维数,区分信号与噪声子空间,并估计噪声平均方差,对信号特征值进行修正,进而减小噪声影响,提高算法分离性能。仿真表明,在信噪比高于5 dB时,MDL估计正确估计概率趋近于1,改进白化的MDL快速独立分量分析(FastICA)算法比经典FastICA算法分离性能有较为明显的提高。     

四阶累积量稀疏表示的DOA估计方法

针对现有稀疏重构DOA估计算法不能抑制噪声项以及在高斯色噪声背景下不再适用的问题,本文提出了基于四阶累积量稀疏重构的DOA估计方法。首先,利用接收数据的四阶累积量构建了稀疏表示模型,该模型抑制了噪声项;其次对四阶累计量矩阵进行奇异值分解,化简了稀疏表示模型,通过奇异值分解,不仅减小了数据规模,而且进一步抑制了噪声。对于稀疏表示模型的求解,先利用信号子空间与噪声子空间的正交特性选取权值矢量,然后利用加权l1范数法对模型求解实现DOA估计。理论分析和仿真实验表明本文算法在高斯白噪声和色噪声背景下均适用;能够处理非相干和相干信号,且在低信噪比条件下,对相干信号有更高的估计精度;较之同类的稀疏重构算法,本文算法具有较低的算法复杂度和更高的角度分辨力。      

雷达脉冲信号检测及参数估计新方法

基于信号包络的信号检测是从信号与噪声能量差异的角度来区分两者,因此在信噪比较低的情况下包络检测效果不好。针对这个问题,提出利用信号的特征值——奇异谱斜率来区分信号和噪声,并从脉冲宽度角度来检测信号。在低信噪比环境中该方法可以有效地检测脉冲信号的有无,而在较高信噪比时该方法可以估计脉冲信号的到达时间和脉冲宽度。仿真试验证明了新方法在信号检测和参数估计方面的优越性。     

前后向线性预测全最小二乘方法实现高分辨空间谱估计方法研究

本文利用全最小二乘方法,对空间阵元前、后向线性预测方程的增广矩阵进行奇异值分解,建立信号、噪声子空间,在误差增广矩阵F范数最小的准则下,证明了预测方程系数矢量的增阶形式刚好位于噪声子空间内。信号子空间的扰动分析表明,这种方法优于修正的空间平滑方法。理论与模拟结果证明这种方法可以实现低信噪比、相干信号源的良好分辨。     

On updating signal subspaces

The authors develop an algorithm for adaptively estimating the noise subspace of a data matrix, as is required in signal processing applications employing the `signal subspace' approach. The noise subspace is estimated using a rank-revealing QR factorization instead of the more expensive singular value or eigenvalue decompositions. Using incremental condition estimation to monitor the smallest singular values of triangular matrices, the authors can update the rank-revealing triangular factorization inexpensively when new rows are added and old rows are deleted. Experiments demonstrate that the new approach usually requires O(n²) work to update an n×n matrix, and that it accurately tracks the noise subspace     

基于奇异值分解的空域海杂波抑制算法

为实现对高频地波雷达(high frequency surface wave radar,HFSWR)一阶海杂波谱中目标的检测,提出了基于奇异值分解(singular value decomposition,SVD)的空域海杂波抑制算法(简称空域SVD算法).空域SVD算法是利用海杂波较强的相关性,将邻近距离单元作为参...     

自适应奇异值分解瞬变信号检测研究

该文介绍了奇异值分解检测信号的原理,研究了井下电磁脉冲数据传输中接收到的瞬变信号和噪声的奇异值分布特性,提出了相邻奇异值增量的概念,并根据瞬变信号和噪声相邻奇异值增量的不同,区分信号与噪声。在此基础上,提出了自适应选择主奇异值个数的奇异值分解检测瞬变信号的方法,并给出该方法检测瞬变信号的具体流程。仿真结果表明,与传统奇异值分解相比,该方法检测微弱瞬变信号更准确。     

GSVD-based optimal filtering for single and multimicrophone speech enhancement

A generalized singular value decomposition (GSVD) based algorithm is proposed for enhancing multimicrophone speech signals degraded by additive colored noise. This GSVD-based multimicrophone algorithm can be considered to be an extension of the single-microphone signal subspace algorithms for enhancing noisy speech signals and amounts to a specific optimal filtering problem when the desired response signal cannot be observed. The optimal filter can be written as a function of the generalized singular vectors and singular values of a speech and noise data matrix. A number of symmetry properties are derived for the single-microphone and multimicrophone optimal filter, which are valid for the white noise case as well as for the colored noise case. In addition, the averaging step of some single-microphone signal subspace algorithms is examined, leading to the conclusion that this averaging operation is unnecessary and even suboptimal. For simple situations, where we consider localized sources and no multipath propagation, the GSVD-based optimal filtering technique exhibits the spatial directivity pattern of a beamformer. When comparing the noise reduction performance for realistic situations, simulations show that the GSVD-based optimal filtering technique has a better performance than standard fixed and adaptive beamforming techniques for all reverberation times and that it is more robust to deviations from the nominal situation, as, e.g., encountered in uncalibrated microphone arrays.     

A geometrical interpretation of signal detection and estimation (Corresp.)

By introducing an appropriate representation of the observation, detection problems may be interpreted in terms of estimation. The case of the detection of a deterministic signal in Gaussian noise is associated with two orthogonal subspaces: the first is the signal subspace which is generally one dimensional and the second is called a reference noise alone (RNA) space because it contains only the noise component and no signal. The detection problem can then be solved in the signal subspace, while the use of the RNA space is reduced to the estimation of the noise in the signal subspace. This decomposition leads to a very simple interpretation of singular detection, even in the non-Gaussian case, in terms of perfect estimation. The method is also extended to multiple signal detection problems and to some special cases of detection of random signals.     

Subspace tracking with adaptive threshold rank estimation

In frequency and direction of arrival (DOA) tracking problems, singular value decomposition (SVD) can be used to track the signal subspace. Typically, for a problem sizen, only a few, sayr dominant eigencomponents need to be tracked, wherern. In this paper we show how to modify the Jacobi-type SVD to track only ther-dimensional signal subspace by forcing the (n-r)-dimensional noise subspace to be spherical. Therby, the computational complexity is brought down fromO(n²) toO(nr) per update. In addition to tracking the subspace itself, we demonstrate how to exploit the structure of the Jacobi-type SVD to estimate the signal subspace dimension via a simple adptive threshold comparison technique. Most available computationally efficient subspace tracking algorithms rely on off-line estimation of the signal subspace dimension, which acts as a bottleneck in real-time parallel implementations. The noise averaged Jacobi-type SVD updating algorithm presented in this paper is capable of simultaneously tracking the signal subspace and its dimension, while preserving both the low computational cost ofO(nr) and the parallel structure of the method, as demonstrated in a systolic implementation. Furthermore, the algorithm tracks all signal singular values. Their squares are estimates of the powers in the orthogonal modes of the signal. Thus, applications of the algorithm are not limited to only DOA and frequency tracking where information about the powers of signal components is not exploited.     

Optimal constrained representation and filtering of signals

A random signal is observed in independent random noise. We are addressing the problem of finding the optimum signal estimate that is constrained to lie in a given linear subspace. The optimality is defined in the sense of weighted mean square error. In the second step, we find the optimum linear subspace of given dimensionality. It is shown to be the linear manifold spanned by the eigenvectors of the simultaneous diagonalization of the signal and noise covariance, that correspond to the largest eigenvalues. The result is valid for both discrete and continuous time. For large observation time and stationary signals, it is shown that the constrained optimal estimate is determined by the two spectral densities and a weighted Fourier Transform of the noise observations. The above result applies to both discrete time and continuous time signals.The Wiener filter emerges as a special case of the constrained filtering estimate, when the linear subspace is enlarged to coincide with the total measurement space.     

A resampling method for estimating the signal subspace of spatio-temporal EEG/MEG data

Source localization using spatio-temporal electroencephalography (EEG) and magnetoencephalography (MEG) data is usually performed by means of signal subspace methods. The first step of these methods is the estimation of a set of vectors that spans a subspace containing as well as possible the signal of interest. This estimation is usually performed by means of a singular value decomposition (SVD) of the data matrix: The rank of the signal subspace (denoted by r) is estimated from a plot in which the singular values are plotted against their rank order, and the signal subspace itself is estimated by the first r singular vectors. The main problem with this method is that it is strongly affected by spatial covariance in the noise. Therefore, two methods are proposed that are much less affected by this spatial covariance, and old and a new method. The old method involves prewhitening of the data matrix, making use of an estimate of the spatial noise covariance matrix. The new method is based on the matrix product of two average data matrices, resulting from a random partition of a set of stochastically independent replications of the spatio-temporal data matrix. The estimated signal subspace is obtained by first filtering out the asymmetric and negative definite components of this matrix product and then retaining the eigenvectors that correspond to the r largest eigenvalues of this filtered data matrix. The main advantages of the partition-based eigen decomposition over prewhited SVD is that 1) it does not require an estimate of the spatial noise covariance matrix and 2b) that it allows one to make use of a resampling distribution (the so-called partitioning distribution) as a natural quantification of the uncertainty in the estimated rank. The performance of three methods (SVD with and without prewhitening, and the partition-based method) is compared in a simulation study. From this study, it could be concluded that prewhited SVD and the partition-based eigen decomposition perform equally well when the amplitude time series are constant, but that the partition-based method performs better when the amplitude time series are variable.     

一种宽带相干信源的无网格超分辨DOA估计方法

由于无网格（grid-less）稀疏重构方法的波达方向（direction of arrival,DOA）估计数学模型为单快拍形式,因此该方法只有在噪声电平趋近于零时才具有优越的性能.为了提高grid-less方法在信噪比（signal-to-noise ratio,SNR）较低时宽带相干信源的估计性能,提出了一种多快拍grid-less DOA估计方法.首先,对多快拍阵列观测矢量实施奇异值分解（singular value decomposition,SVD）获得观测矩阵的时域信号子空间,通过观测矩阵到时域信号子空间的投影实现观测矩阵的降噪;然后,为了不增加多快拍计算复杂度,将降噪后观测矩阵的列向量加权累加处理得到单快拍形式;最后,从理论上证明了本文提出的GL-SVD方法求解的模型是凸的,能够实现宽带信号DOA的精确重构.仿真结果表明,该方法在低SNR以及宽带相干信源情况下的估计精度都高于L₁范数最小化奇异值分解（L₁-norm minimum singular value decomposition,L₁-SVD）和离格稀疏贝叶斯推断奇异值分解（off-grid sparse Bayesian inference singular value decomposition,OGSBI-SVD）,且在较小角度间隔的情况下具有更高的估计概率和分辨率.