非高斯有色噪声中谐波恢复的累积量投影方法

本文研究非高斯有色噪声中的谐波恢复问题。首先建立了复数线性非高斯过程的高阶累积量投影定理。应用该定理，由含噪谐波信号的四阶累积量求得非高斯有色噪声的自相关，然后通过求解一个广义特征值问题对矢量空间进行预白化，最后结合噪声子空间方法ＭＵＳＩＣ恢复谐波信号参数。本文方法克服了以往的困难，成功地解决了对称分布非高斯噪声背景下和谐波信号中存在二次相位耦合时的谐波恢复问题。仿真实验验证了本文结论。     

基于遗传算法的二维谐波频率估计

针对高斯有色噪声背景下的二维谐波频率估计问题,本文利用二维四阶累积量对高斯噪声不敏感,却包含有二维谐波的频率与幅度信息,将该问题转化为一个多元函数的极值问题,然后提出了基于遗传算法的二维谐波信号参数估计算法.该算法可以直接估计出谐波的频率与振幅,并且不需要考虑频率的配对问题,使得估计过程得到了简化.仿真实验证明了算法的有效性.     

非高斯有色噪声中基于四阶累积量噪声建模的谐波恢复方法

本文提出一种在非高斯ＡＲＭＡ噪声中谐波恢复的高阶累积量方法，该方法首先通过Ｈｉｂｌｅｒｔ变换构造复数观测值，然后使用它的一种特殊的四阶累积量建立噪声过程ＡＲ参数，由此对观测值滤波，最后通过ＳＶＤ－ＴＬＳ方法估计谐波信号参数，本文方法克服了以往对非高斯噪声分布的非对称性假设，成功地解决了对称分布非高斯有色噪声中的谐波恢复问题，并且适用于于谐波信号存在二次相应耦合情形，仿真实验验证了文中结论。     

基于子空间旋转不变性的加性有色噪声中谐波频率的估计

噪声中的谐波恢复问题是信号处理领域的一个典型问题,在众多领域中有着广泛的应用。本文主要研究加性有色噪声中谐波频率的估计问题,提出了一种基于子空间旋转不变性的谐波频率的高分辨率估计方法。利用观测信号的自协方差函数构造了一个协方差矩阵,通过对协方差矩阵的特征值进行理论分析,结合子空间旋转不变性,得到了加性有色噪声中谐波的频率和协方差矩阵之间的一种内在联系。利用这个性质可以估计加性有色噪声中谐波的频率。本文方法对于有色噪声的模型无任何假设,而且对于噪声的分布也没有限制,对于高斯和非高斯有色噪声都适用。仿真实验验证了本文所提算法的有效性。      

乘性和加性噪声中二维谐波的参数估计

本文从循环平稳的观点出发来研究乘性和加性噪声中二维谐波的参数估计问题,利用循环累积量的性质证明了二维二阶循环累积量单一记录估计的统计性质.在此基础上,对于零均值乘性噪声中的二维谐波信号提出了基于二阶循环累积量的二维谐波分量个数和频率对的估计方法,并分别得到了估计的强收敛速度.仿真试验验证了所提方法的性能.     

四元数和超复数在二维二次非线性相位耦合分析中的应用

针对二维二次非线性相位耦合分析中的分维配对问题,本文首先对一般二维谐波信号模型进行变换,构造了符合四元数结构的新的信号模型.接着讨论了Hamilton四元数、三维超复数及"新四元数"在估计二维谐波频率中的可能性.最后根据上述模型利用特殊的三阶累积量切片分析了加性高斯有色噪声中二维二次非线性相位耦合及联合Hamilton四元数和超复数在二维二次非线性相位耦合中的应用前景.此方法避免了在复数模型的二维二次非线性相位耦合分析中构造复杂的增广矩阵,并从根本上解决了通过分维求取频率之后,频率配对中所有可能产生的错误频率对,以及有可能产生的两维频率估计精度的不平衡性.仿真实验验证了本文的理论.     

宽带非高斯信号的二维波达方向估计方法

该文提出了一种解决宽带非高斯信号二维波达方向估计的方法。该方法利用相干信号子空间方法把宽带的阵列频域数据四阶累积量聚焦到同一个参考频段下,然后利用基于信号空时特征结构的时空DOA 矩阵方法来进行二维DOA估计。理论上证明该方法在高斯噪声环境下对宽带非高斯信号都具有很好的估计性能,通过计算机仿真也验证了该方法的有效性。     

宽频段空间信号频率、二维到达角和极化联合估计

在空间欠采样的条件下,通过巧妙定义稀疏L型阵列的四阶累积量输出矩阵,利用高阶累计量的盲高斯及阵列扩展特性,实现了宽频段空间非高斯信号频率、到达角和极化估计的分离,给出了一个基于四阶累积量 ESPRIT和整数搜索解模糊的任意高斯噪声环境下多个独立空间信号频率、二维到达角和极化的联合估计算法,L型阵列由和坐标轴方向一致的偶极子对组成,数值模拟结果证实了该文方法的有效性。     

非高斯有色噪声中的正弦信号频率估计

本文研究非高斯ＡＲＭＡ有色噪声中的正弦信号频率估计问题。利用自相关函数和三阶累积量相结合，提出了一种先估计噪声模型ＡＲ参数，然后对观测值进行预滤波，最后估计信号模型参数的新方法，模拟实验结果表明，新方法具有良好的频率估计性能。     

四元数在多个频率对共用同一个频率下的二维谐波恢复

针对二维谐波频率估计中的分维配对问题,本文首先对一般二维谐波信号模型进行变换,构造了符合四元数结构的新的信号模型.接着讨论了Hamilton四元数、三维超复数在二维谐波频率估计中的可能性.同时利用Hua的思想,根据上述模型利用特殊的四阶累积量切片并构造增广矩阵分析了有多个频率对共享同一个频率时的二维谐波频率估计问题.     

Harmonic retrieval in colored non-Gaussian noise using cumulants

This paper addresses the harmonic retrieval problem in colored linear non-Gaussian noise of unknown covariance and unknown distribution. The assumptions made in the reported studies that the non-Gaussian noise is asymmetrically distributed and no quadratic phase coupling occurs are released. Using the elaborately defined fourth-order cumulants of the complex noisy observations, which are obtained by Hilbert transform, we can estimate either the correlation or the AR polynomial of the non-Gaussian noise via cumulant projections or ARMA modeling; then, the prewhitening or prefiltering techniques can be employed to retrieve harmonics, respectively. Simulation results are presented to demonstrate the effectiveness of the proposed algorithms     

A hybrid approach to harmonic retrieval in non-Gaussian ARMA noise

Addresses the harmonic retrieval problem in colored noise. As contrasted to the reported studies in which Gaussian noise was assumed, this paper focuses on additive non-Gaussian ARMA noise. Our approach is hybrid in the sense that third-order cumulants are first used to identify the AR part of the non-Gaussian noise process, and then correlation-based high-resolution methods are used for the filtered process to estimate the number of harmonics and their frequencies. Simulation examples are presented to demonstrate the high resolution of this approach     

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     

Nonlinear filtering methods for harmonic retrieval and model orderselection in Gaussian and non-Gaussian noise

This paper addresses the problem of high-resolution parameter estimation (harmonic retrieval) and model-order selection for superimposed sinusoids. The harmonic retrieval problem is analyzed using a nonlinear parameter estimation approach. Estimation is performed using several nonlinear estimators with signals embedded in white and colored Gaussian noise. Simulation results demonstrate that the nonlinear filters perform close to the Cramer-Rao bound. Model order selection is performed in Gaussian and non-Gaussian noise. The problem is formulated using a multiple hypothesis testing approach with assumed known a priori probabilities for each hypothesis. Parameter estimation is performed using the extended Kalman filter when the noise is Gaussian. The extended high-order filter (EHOF) is implemented in non-Gaussian noise. Simulation results demonstrate excellent performance in selecting the correct model order and estimating the signal parameters     

Adaptive frequency estimation of sinusoidal signals in colored non-Gaussian noises

This paper studies the problem of sinusoidal frequency estimation in colored non-Gaussian ARMA noises. A new adaptive approach is proposed by using the second-and third-order statistics of the measurements. Because of the simultaneous establishment of the signal and noise models, the new approach is applicable for tracking the frequencies at each time instant for stationary and nonstationary signal and/or noise cases. The effectiveness of the new approach is demonstrated by extensive computer simulations. As expected, the approach proposed in this paper outperforms the correlation-based approaches in suppressing the effects of the colored non-Gaussian ARMA noises.     

利用希尔伯特变换进行谐波恢复

非高斯有色噪声中具有相位耦合的谐波恢复问题是迄今为止没有得到很好解决的问题，本文基于希尔伯特变换和高阶累积量提出一种新方法：ＨＢＳＴＣＨ－ＳＶＤ－ＴＬＳ。仿真实验表明，该方法不仅次好地解决了非高斯有色噪声中的具有二次相位耦合的谐波恢复问题，而且具有广泛的适用性。     

Harmonic Signals Retrieval Approach Based on Blind Source Separation

A frequently encountered problem in signal processing is harmonic retrieval in additive colored Gaussian or non-Gaussian noise, especially when the frequencies of the harmonic signals are very close in space. The purpose of this paper is to develop an efficient Blind Source Separation (BSS) algorithm from linear mixtures of source signals, which enables to separate harmonic source signals using only one observed channel signal even if the frequencies of the harmonic signals are closely spaced. First, we establish the BSS based harmonic retrieval model in additive noise by using the only one observed channel, and analyze the fundamental principle by utilizing BSS method to retrieve harmonics. Then, we propose a BSS-based approach to the harmonic retrieval by resorting the concept of W-disjoint orthogonality in the over-complete BSS situation, and as a result, we get the separation algorithm using only one channel mixed signals. Simulation results show that the proposed separation algorithm-BSS-HR is able to separate the harmonic source signals.