非高斯有色噪声背景下二维谐波频率估计的累积量投影方法

针对非高斯有色噪声中的二维谐波频率估计问题,该文提出了复数线性非高斯过程的二维累积量投影定理。应用该定理并巧妙地构造观测信号的高阶累积量求得非高斯噪声的自相关,并通过求解一个广义特征值对噪声空间进行预白化,然后结合高分辨率的子空间方法二维MUSIC估计得到二维谐波参量。该文方法解决了非高斯有色噪声中的二维谐波频率估计问题,特别地当非高斯噪声为对称分布和谐波信号中存在二次相位耦合时该文方法同样有效。仿真实验验证了该文结论。     

非高斯ARMA噪声中谐波恢复的杂交ESPRIT方法

本文研究非高斯ＡＲＭＡ噪声中的谐波恢复问题，提出了一种基于二阶和三阶统计量的杂交ＥＳＰＲＩＴ方法，该方法先估计噪声过程的ＡＲ部分参数，然后对观测值进行预滤波，最后估计谐波信号参量。模拟实验还验证了该方法的有效性和高分辨率。     

基于广义协方差矩阵的乘性和加性噪声中的谐波恢复

针对非零均值乘性噪声中的谐波恢复问题,本文提出一种基于广义协方差矩阵的乘性噪声中谐波个数和频率的估计方法。首先定义一类广义协方差并构造广义协方差矩阵,通过对广义协方差矩阵进行特征值理论分析,得到了非零均值乘性噪声中谐波分量个数与协方差矩阵特征值之间的内在联系,这个性质可以用来估计谐波分量个数。而且利用子空间旋转不变性技术,可以从协方差矩阵中估计出谐波的频率。本文所提方法对于乘性和加性噪声的颜色和分布均无任何假设,可以应用于任意分布和任意颜色的乘性和加性噪声中的谐波恢复。仿真实验表明,本文所提谐波恢复方法具有很高的频率分辨率。      

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。      

零均值独立复杂噪声背景下二维谐波估计的时间平均矩方法

对于零均值独立乘性噪声背景下二维谐波的三次非线性耦合估计问题,由于缺乏理论支持及有效的计算方法,至今尚无有效的解决办法.本文首先分析了不同的噪声模型对谐波耦合分析所产生的影响,通过对原始采样数据进行平方预处理,改变了采样信号的信噪模型,利用新模型下噪声的统计特性及噪声间的相关特性,通过定义一种特殊四阶时间平均矩,首次解决了零均值独立噪声背景下谐波频率的二维三次非线性耦合问题.数学推导了该特殊四阶时间平均矩的矩多谱,理论证明了相应估计子渐进无偏性和一致性.理论分析和试验结果表明,该方法用于二维谐波的三次耦合分析时,不再需要对噪声的统计特性及噪声间的相关特性作任何限制.     

乘性和加性噪声中二维谐波频率估计

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。本文主要研究零均值乘性和加性噪声并存下的二维谐波信号频率估计问题,提出了一种基于数据矩阵的奇异值分解和子空间的旋转不变性的零均值乘性和加性噪声中的谐波频率的估计方法。乘性噪声为零均值情形下传统的估计方法往往难以直接应用或估计失效。本文利用谐波模型信号特征,通过对观测信号进行平方运算构造了一个数据矩阵。通过对数据矩阵的特征值进行理论分析,结合子空间旋转不变性,得到了零均值乘性和加性噪声中的谐波频率和数据矩阵之间的一种内在关系。这个性质可以用于零均值乘性和加性噪声并存下的二维谐波信号频率估计,并且所得的二维频率能自动配对。仿真实验验证了本文所提算法的有效性。      

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.     

分形差分高斯噪声中正弦波频率估计

本文提出了分形噪声中的谐波恢复问题，针对分形差分高斯噪声中正弦波频率估计，提出了一种偏差补偿线性最小二乘与极大似然估计相结合的组合算法。模拟实验结果表明，该方法不仅具有高的分辨率，而且能有效地抑制分形差分高斯噪声的影响。     

有色噪声中谐波频率的频域非线性预滤波估计方法

基于谐波信号表现为频域中的 异常点 这一思路,利用滑动中值滤波器滤除数据异常点的能力,本文提出了未知有色噪声背景下谐波信号频率的一种高分辨估计方法.其突出特点是对噪声分布的强普适性,且算法实现简单.仿真结果验证了该方法的性能.     

一种可用于声目标特征提取的超分辨率混合谱估计算法

本文研究了一种估计有色噪声中多组谐波信号参数的去耦参数估计算法。其中提出了一种基于FFT的谐波组迭代清除算法来估计谐波信号的参数,并根据谐波图的值来确定谐波信号的个数。该算法不仅计算简单并可获得较高的频率分辩率,而且对信号模型具有较强的鲁棒性。     

NEW APPROACH TO HARMONIC RETRIEVAL IN NOISE

This paper addresses the harmonic retrieval problem in non-Gaussian ARMA noise. A hybrid ESPRIT approach using second-and third-order statistics is proposed. First, third-order statistics are used to identify the AR part of the non-Gaussian noise process, then the noisy measurements are filtered by AR polynomial, finally, the harmonic signal parameters are estimated. Simulation examples show the effectiveness and high resolution of the new approach.     

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     

非高斯相关噪声中高斯信号的时延估计

高阶统计量在信号处理中成功的应用例子之一是估计高斯相关噪声中非高斯信号的时延参数.本文则研究非高斯相关噪声中高斯信号的时延估计问题,提出了一种解决该问题的混合方法.该方法先计算观测值的三阶累积量,然后利用累积投影公式计算观测噪声的二阶统计量,最后利用互相关方法确定信号时延参数.仿真结果验证了该方法的有效性.     

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.     

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。     

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     

AR modelling of skewed signals using third-order cumulants

Algorithms for selecting the order and estimating the parameters of an AR process, which is driven by noise having an underlying non-Gaussian distribution, from the observed noisy time series are presented. The order selection algorithm makes use of the growing memory covariance predictive least-squares (GMCPLS) criterion together with diagonal slices of the third-order cumulant plane. A triangular region of the third-order cumulant plane is used to estimate the model parameters. Extensive simulation results are presented and based on these trends, one of which has been verified using real data obtained from a rotating machine, recommendations are made on the efficacy of methods for AR order selection and parameter estimation problems     

基于分数低阶统计量的双谱及其估计方法

稳定分布可更好地描述实际中所遇到的具有显著脉冲特性的随机噪声.为了更好地抑制信号背景中的非高斯噪声,本文提出了基于分数低阶的双谱定义,并给出在分数低阶有色噪声背景下双谱非参数和参数模型的估计方法.仿真结果表明,同传统的双谱估计相比较,非参数法分数低阶双谱估计能有效的识别信号,保留了信号的幅度和相位信息,但存在较大的估计方差.基于AR模型的分数低阶双谱估计具有最大的谱平坦度,能够有效地抑制噪声,具有良好的韧性.     

Fast computation of the exact FIM for deterministic signals incolored noise

A fast algorithm for computing the exact finite-sample Fisher information matrix (FIM) for the parameters of a deterministic signal observed in Gaussian AR noise is derived. In the case of a harmonic signal with random phases, closed-form expressions for the finite-sample posterior Cramer-Rao bound (PCRB) are established. It is shown that the fast algorithm is also useful for computing the conditional CRB when the additive noise is a non-Gaussian AR process. It is seen that the asymptotic CRB may deviate significantly from the exact CRB even when the data length is moderate, whereas the PCRB, which is easy to compute, provides a better approximation. Theoretical results are illustrated via numerical evaluation of the different lower bounds     

Causal AR modeling using a linear combination of cumulant slices

We address the problem of estimating the parameters of a pure AR causal model excited with non-Gaussian, ergodic, unobservable process. Output samples may be corrupted with colored Gaussian noise. Other types of noise are allowed provided that they have a set of mth order statistics whose value is zero, if the same set of statistics are different from zero for the signal. It is shown that each sample of the impulse response of the AR system that generates the process may be expressed as a linear combination of cumulant slices of any order, thus providing a new framework to combine cumulants of different orders. The resulting algorithm is shown to be well behaved and to provide consistent estimates while reducing the complexity significantly with respect to other approaches.