基于四阶累积量的相干信号子空间DOA估计

A. Bassias
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引用次数: 2

摘要

本文利用了四阶累积域对加性高斯噪声源的抑制作用。因此,我们研究了将相干信号子空间方法的变换矩阵与空间四阶累积矩阵相结合,在未知协方差的空间相关高斯噪声中估计非高斯宽带信号的到达方向的效果。与CSS方法使用的空间协方差矩阵不同,这里使用变换矩阵来对齐四阶累积矩阵的信号子空间,使其在阵列输出的每个快照被分解的时间频率处与信号子空间在中心频率处对齐。仿真结果表明,在基于空间协方差的估计存在较大偏差和较大波动的情况下,新方法可以有效地抑制噪声和分解信号。在未知相关矩阵的空间相关高斯噪声中,利用一组传感器估计非高斯宽带信号的到达角问题。是解决。这是在实践中经常遇到的一种情况,即观察到信号作为随机过程偏离高斯,并且噪声相关矩阵不是空间白色,这是基于信号子空间的方法为了给出合理的估计所要求的。相干信号子空间(CSS)方法[13]已被开发用于估计由一组传感器接收的宽带信号的到达方向。本文考察了将CSS方法的变换矩阵与四阶累积矩阵相结合的效果。这是由高斯过程的已知性质引起的,即所有大于2阶的累积谱都等于;en,[2]。因此,通过使用阵列数据的四阶累积量,任何破坏非高斯信号的加性高斯噪声将(原则上)被抑制。本文介绍了空间相关高斯噪声条件下窄带信号的阵列处理方法。在那里,处理是在时域进行的,而在这里,所有的处理都是在频域进行的。下面对CSS方法进行简要回顾,并对新方法进行详细说明。通过模拟对其性能进行了评估,并进行了简短的讨论,给出了评论和观察结果。在存在噪声的情况下,由M个宽带源产生的波场在时间和空间上由已知任意几何形状的N (N>M)水听器的被动阵列进行采样。源信号的特征是在观测区间To上的零均值、非高斯平稳随机过程,带宽限制在带宽B可能与中心频率o具有相同数量级的公共频带内。源信号矢量s(t)定义为其中t表示矢量或矩阵的转置。请注意,在本文中,粗体字中的小写字母表示向量,而粗体字中的大写字母表示矩阵。在第i个水听器处接收到的信号xi(t)可以表示为,其中aim为第i个水听器对第m个源的振幅响应,Ti为第i个水听器与参考水听器之间的传播时差,ni(t)为第i个水听器处的加性噪声。通过快速傅里叶变换。所以,本质上。对输出信号的每个频率分量采样K次,得到数据集xk(fj), j=1,…J;k = l,…, K.来自Eqn。(2), xi(fj)由
本文章由计算机程序翻译,如有差异,请以英文原文为准。
DOA Estimation Using Coherent Signal - Subspace Method Based On Fourth - Order Cumulants
In this paper the advantage provided by the fourth order cumulant domain is exploited, that is the suppression of additive Gaussian noise sources. Thus we examine the effect of combining the transformation matrices of the Coherent Signal Subspace Method with spatial fourth order cumulant matrices for the estimation of the direction of arrival of non Gaussian wideband signals in spatially correlated, Gaussian noise of unknown covariance. Instead of spatial covariance matrices which are used by the CSS Method, the transformation matices are used here in order to align the Signal Subspaces of the fourth order cumulant matrices at the temporal frequencies in which each snapshot of the array outputs is decomposed, with the Signal Subspace at center frequency. It is shown with simulations that the new method can suppress noise and resolve signals in cases where the spatial covariance based methods do not but the estimates present higher bias and strong fluctuation. INTRODUCTION The problem of estimating the angles of arrival of non Gaussian wideband signals in spatially correlated Gaussian noises of unknown correlation matrix, using an array of !.ensorS. is addressed. This is a situation that is often encountered in practice where a deviation of the signals as stochastic processes from being Gaussian is observed and the noise correlation matrix is not spatially white as is required by the signal subspace based methods in order to give reasonable estimates. The Coherent Signal Subspace (CSS) method [ 13 has been developed for the estimation of diredon of arrival of wideband signals received by an anay of sensors. Here, the effect of combining the Transformation matrices of the CSS methods with fourth order cumulant matrices is examined. This is motivated by the known property of Gaussian processes that all cumulant spectra of order greater than two are identical to ;en, [2]. So, by using the fourth order cumulants of the array data, any additive Gaussian noises corrupting non Gaussian signals will (in principle) be suppressed. Array processing methods for narrowband signals in spatially correlated Gaussian noise have been introduced in [3]. There, the processing is performed in the time domain ithile, all the processing here is performed in the 'rcquency domain. In the following, the CSS method is reviewed briefly and the new method is explained in detail. Its performance is assessed with simulations and a short discussion with comments and observations is provided. PROBLEM FORMULATION A wavefield generated by M wideband sources in the presence of noise is sampled temporally and spatially by a passive array of N (N>M) hydrophones with a known arbitrary geometry. The source signals are characterized as zero mean, non Gaussian stationary stochastic processes over the observation interval To, bandlimited to a common frequency band with bandwidth B which may be of the same order of magnitude as the center frequency fo. The source signal vector s(t) is defined as where T denotes transpose of a vector or a matrix. Note that throughout this paper, small letters in bold print will indicate vectors while capital letters in bold print will indicate matrices. The signal xi(t), received at the i-th hydrophone, can be expressed as where aim is the amplitude response of the i-th hydrophone to the m-th source, Ti, is the propagation time difference between the i-th hydrophone and the reference hydrophone and ni(t) is the additive noise at the i-th hydrophone. The observation interval To is divided into K nonoverlapping snapshot intervals T, and for each of these intervals the array output signals Xi(t) are decomposed into J frequency components xi(fj), j=1, ... J. via Fast Fourier Transform 0. So, essentially. we sample K times each frequency component of the output signals, thus obtaining the data set xk(fj), j=1, ... J; k=l, ..., K. From Eqn. (2), xi(fj) will be given by
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