Applications of cumulants to array processing. II. Non-Gaussiannoise suppression

The main motivation of using higher order statistics in signal processing applications has been their insensitivity to additive colored Gaussian noise. The main objection to those methods is their possible vulnerability to non-Gaussian noise. The authors investigate the effects of non-Gaussian ambient noise on cumulant-based direction-finding systems using the interpretation for the information provided by cumulants for array processing applications described in Dogan and Mendek. they first demonstrate the suppression of uncorrelated non-Gaussian noise that has spatially varying statistics. Then, they indicate methods to suppress spatially colored non-Gaussian noise using cumulants and an additional sensor whose measurement noise component is independent of the noise components of the original array measurements. They also indicate the noise suppression properties of the virtual-ESPRIT algorithm proposed in Dogan and Mendel. In addition, they propose a method that combines second- and fourth-order statistics together in order to suppress spatially colored non-Gaussian noise. Finally, they also illustrate how to suppress spatially colored non-Gaussian noise when the additional sensor measurement is not available. Simulations are presented to verify the results     

基于四阶累积量特征分解的空间谱估计测向方法

传统的空间谱估计测向方法大都是在二阶统计基础上提出的。而高阶累积量(cumulant)及其对应的高阶谱具有更加丰富的信息,而且对任何谱特性的高斯噪声都有很好的抑制能力。本文研究了基于四阶累积量特征结构分析的谱估计测向方法。从累积量的基本定义和性质出发,导出了基于特征分解的测向算法,并给出了模拟实验和测向系统外场实验结果。实验结果显示,基于四阶累积量方法的性能优于传统谱估计测向方法,特别是对于未知谱特性的色高斯噪声的情况。     

时空欠采样宽频段信号频率和二维角估计方法

本文提出了一种时空欠采样宽频段(2~18GHz)信号频率、方位角和仰角三维参数估计方法.该方法采用均匀圆阵和阵元延时,可在时间欠采样条件下实现频率无模糊估计;在空间欠采样条件下,用整数搜索法实现方位角和仰角无模糊估计,且频率、方位角和仰角估计可自动配对.该方法不仅可用于二阶统计量阵元空间和DFT波束空间,而且还可用于四阶累积量,可在高斯白或色噪声背景下,估计非高斯信源的参数.在DFT波束空间、阵元数相同和最大孔径相当时,该方法方位角和仰角估计的方差比L阵方法的方差小1~2个数量级.仿真实验表明了算法的有效性.     

New approaches without postprocessing to FIR system identificationusing selected order cumulants

In this paper, we address the problem of identifying the parameters of the nonminimum-phase FIR system from the cumulants of noisy output samples. The system is driven by an unobservable, zero-mean, independent and identically distributed (i.i.d) non-Gaussian signal. The measurement noise may be white Gaussian, colored MA, ARMA Gaussian processes, or even real. For this problem, two novel methods are proposed. The methods are designed by using higher order cumulants with the following advantages. (i) Flexibility: method 1 employs two arbitrary adjacent order cumulants of output, whereas method 2 uses three cumulants of output: two cumulants with arbitrary orders and the other one with an order equal to the summation of the two orders minus one. Because of this flexibility, we can select cumulants with appropriate orders to accommodate different applications. (ii) Linearity: both the formulations in method 1 and method 2 are linear with respect to the unknowns, unlike the existing cumulant-based algorithms. The post-processing is thus avoided. Extensive experiments with ARMA Gaussian and three real noises show that the new algorithms, especially algorithm 1, perform the FIR system identification with higher efficiency and better accuracy as compared with the related algorithms in the literature     

基于累量的方向估计与阵列校正

本文提出了一种基于最大非冗余四阶累量集合的方向估计阵列校正方法，该方法利用了四阶累量阵的所有非冗余信息，并具有对加性高斯噪声不敏感，比传统协方差方法有较强的分辩性能和容差性能的特点。     

房间环境下基于四阶累积量的语音时延估计

主要研究了利用四阶累积量在房间环境下的语音信号时延估计。根据模拟实验环境和实际实验环境下的仿真结果,分别比较了在高斯白噪声情况下与有色高斯噪声情况下基于二阶统计量的广义互相关法和基于四阶累积量的时延估计法性能,验证了四阶累积量法的有效性。仿真结果表明四阶累积量法具有很好的鲁棒性。     

随机幅度多项式相位信号的时延估计方法

研究了一类非平稳信号具有随机幅度的多项式相位信号的时延估计问题。充分利用信号的高阶循环平稳性，提出了一种基于信号高阶循环矩的时延估计方法。该方法容易实现，估计精度能有效地抑制加性平稳非高斯和任何高斯噪声。试验结果证明了提出方法的正确性。     

Harmonics in multiplicative and additive noise: parameterestimation using cyclic statistics

The problem of concern here is parameter estimation of harmonics in the presence of multiplicative and additive noise. Cyclic statistics are employed to estimate the frequencies and phases, after which the time series is demodulated and cumulants of the noise processes are estimated. The latter are then supplied to linear or nonlinear cumulant-based algorithms to identify ARMA model parameters for the noises. Cyclic statistics and higher order spectra-based approaches are shown to yield the same frequency estimates. Simulation examples illustrate the algorithms     

Estimation of frequency-delay of arrival (FDOA) using fourth-orderstatistics in unknown correlated Gaussian noise sources

A new family of nonparametric and parametric methods based on fourth-order statistics for the estimation of the frequency-delay of arrival (FDOA) between two sensor signal measurements, corrupted by correlated Gaussian noise sources in an unknown way, is presented. The new family of FDOA estimation methods utilizes the fourth-order cumulants or 1-D Fourier transforms of sliced fourth-order cumulants of the two signal measurements. It is demonstrated that the new family of FDOA estimation methods suppresses the effect due to correlated Gaussian measurement noises and outperforms existing second-order statistics-based FDOA estimation methods using either cross-ambiguity function or MUSIC algorithm. Various simulation results are presented for different types of signals, different lengths of data, and different signal-to-noise ratios     

Applications of cumulants to array processing .I. Apertureextension and array calibration

An interpretation for the use of cumulants in narrowband array processing problems is proposed. It is shown how fourth-order cumulants of multichannel observations increase the directional information compared with second-order statistics. Based on the interpretation, it is shown how cumulants can be used to increase the effective aperture of an arbitrary antenna array. The amount of partial information necessary to jointly calibrate an arbitrary array and estimate the directions of far-field sources is also investigated. It is proven that the presence of a doublet and use of fourth-order cumulants is sufficient to accomplish this task. The proposed approach is computationally efficient and more general than covariance-based algorithms that have addressed the calibration problem under constraints. A class of beamforming techniques is proposed to recover the source waveforms. Proposed estimation procedures are based on cumulants, which bring insensitivity to the spatial correlation structure of additive Gaussian measurement noise. Simulations are provided to illustrate the use of the proposed algorithms     

Cumulant-based approach to harmonic retrieval and related problems

A frequently encountered problem in signal processing is that of estimating the frequencies and amplitudes of harmonics observed in additive colored Gaussian noise. In practice, the observed signals are contaminated with spatially and temporally colored noise of unknown power spectral density. A cumulant-based approach to these problems is proposed. The cumulants of complex processes are defined, and it is shown that specific 1-D slices of the fourth-order cumulant of the noisy signal for the direction of arrival (DOA) and retrieval of harmonics in noise (RHN) problems are identical to the autocorrelation of a related noiseless signal. Hence correlation-based high-resolution methods may be used with fourth-order cumulants as well. The effectiveness of the proposed methods is demonstrated through standard simulation examples     

基于四阶累积量的DOA估计方法

从一个统一的角度来研究基于高阶累积量的高分辨阵列信号处理方法,用四阶累积量构造了一个较通用的累积量矩阵,该矩阵符合MUSIC算法的结构,从而可进行DOA(Direction ofArrival)估计。对于这种方法在阵列信号处理中的应用,通过计算机仿真与基于二阶矩的MU-SIC算法进行了较全面的比较。仿真结果表明,该方法在高斯噪声中具有良好的统计性能,是实现高分辨方位估计的有效方法。     

Statistical characterization of sample fourth-order cumulants of anoisy complex sinusoidal process

The paper deals with the statistical characterization of sample estimates of the fourth-order cumulants of a random process consisting of multiple complex sinusoids and additive colored Gaussian noise. In particular, it presents necessary and sufficient conditions for strong consistency of the sample cumulants of arbitrary orders, and derives expressions for the asymptotic covariance of the sample estimates of the fourth-order cumulants. It is shown that the fourth-order cumulant C_4y (τ₁,...,τ₄) can be written as a function of a single argument τ=τ₃+τ₄ -τ₁-τ₂, which implies large flexibility in estimating the cumulant. It is recommended that the estimate be based upon lags such that τ₁ is distant from τ₂ and τ₃ is distant from τ₄, and/or as a linear combination of such terms. The asymptotic variance of a cumulant-based frequency estimator is shown to have the form c₂·SNR^-2+c₃·SNR^-3 +c₄·SNR^-4, where the coefficient c ₂ may possibly vanish. The theory is illustrated via numerical examples. The results of this paper will be useful in analyzing the performance of various cumulant-based frequency estimation algorithms     

基于四阶累积量的最大似然测向方法研究

论述了最大似然（ML）算法测向以及四阶累积量阵列扩展的基本原理，在此基础上给出了一种基于最大似然算法和四阶累积量的DOA估计新方法。与普通的基于二阶矩的最大似然算法相比，本方法具有对阵列进行四阶扩展的能力，可以解决信号源数大于阵元数时的测向问题，并且由于四阶累积量自身的盲高斯性，还可以有效抑制高斯色噪声。     

基于四阶累积量和奇异值分解的参数型多径时延估计

在背景相关噪声的情况下,提出了一种基于四阶累积量和奇异值分解（SVD）的参数型时延估计方法。分析表明该方法能够准确进行多径传输情况下的时延估计,有效抑制相关高斯噪声的影响。最后采用Matlab进行仿真验证。     

一种基于四阶累积量的约束自适应多径时延估计

在存在多径信号和空间相关性未知的背景高斯噪声情况下,不考虑多径信号传输的传统时延估计方法的性能会受到影响,甚至恶化。针对此问题,提出了一种基于四阶累积量的约束自适应多径时延估计算法,并对该算法的多径时延估计性能进行了收敛性能分析。该算法能够有效抑制空间相关性未知噪声的影响,在低信噪比的情况下能够直接、准确地进行自适应多径时延估计,克服了传统算法不能直接估计非整数倍采样间隔时延的缺点。计算机仿真试验验证了新算法的有效性。     

Estimation and detection in non-Gaussian noise using higher orderstatistics

One of the primary applications of higher order statistics has been for detection and estimation of nonGaussian signals in Gaussian noise of unknown covariance. This is motivated by the fact that higher order cumulants of Gaussian processes vanish. We study the opposite problem, namely, detection and estimation in nonGaussian noise. We estimate cumulants of nonGaussian processes in the presence of unknown deterministic and/or Gaussian signals, which allows either parametric or nonparametric estimation of the covariance of the nonGaussian noise. Our approach is to augment existing second-order detection methods using cumulants. We propose solutions for detection of deterministic signals based on matched filters and the generalized likelihood ratio test which incorporate cumulants, where the resulting solutions are valid under either detection hypotheses. This allows for single record detection and obviates the need for noise-only training records. The problem of estimating signal strength in the presence of nonGaussian noise of unknown covariance is also considered, and a cumulant-based solution is proposed which uses a single data record. Examples are used throughout to illustrate our proposed methods     

基于累积量的杂波多卜勒频率估计

利用相关函数ｒＹ（１）估计杂波多卜勒频率是一种工程上易于实现且常用的频率估计方法。在双模杂波情况下，这种频率估计方法在其在偏性而性能严重下降。本文在一种常见的双模杂波模型假设下，研究了一种基于四阶累积ｋ４ｙ（１）的非高斯杂波多卜勒频率的无偏估计方法，该方法利用ｋ４（１）所对应的所有非冗余四阶累积量元素的加权和，从而明显降低了估计方差。     

Maximum likelihood localization of sources in noise modeled as astable process

This paper introduces a new class of robust beamformers which perform optimally over a wide range of non-Gaussian additive noise environments. The maximum likelihood approach is used to estimate the bearing of multiple sources from a set of snapshots when the additive interference is impulsive in nature. The analysis is based on the assumption that the additive noise can be modeled as a complex symmetric α-stable (SαS) process. Transform-based approximations of the likelihood estimation are used for the general SαS class of distributions while the exact probability density function is used for the Cauchy case. It is shown that the Cauchy beamformer greatly outperforms the Gaussian beamformer in a wide variety of non-Gaussian noise environments, and performs comparably to the Gaussian beamformer when the additive noise is Gaussian. The Cramer-Rao bound for the estimation error variance is derived for the Cauchy case, and the robustness of the SαS beamformers in a wide range of impulsive interference environments is demonstrated via simulation experiments     

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。