【作者】 窦慧晶；

【导师】 王树勋；

【作者基本信息】 吉林大学 ， 通信与信息系统， 2005， 博士

【摘要】 本文对二维谐波参量估计和非线性耦合这一信号处理领域的核心问题进行了研究。总结了谐波参量估计及非线性耦合问题的研究现状,介绍了各种主要的分析方法。在此基础上,针对不同的噪声背景提出了相应的算法,尤其对相关乘性噪声背景下的谐波参量估计和非线性耦合问题进行了深入的研究。在加性噪声背景下,文中通过对二维信号相关矩阵进行分析,得出相关阵大特征值对应的各特征矢量是由信号矢量线性相加构成的结论,并在此基础上提出两种二维谐波参量估计的方法――基于二维信号相关阵信号子空间的正交矢量法和基于二维信号相关阵特征向量的二维ESPRIT 方法。对于二维三次非线性相位耦合问题,提出了四阶累积量切片谱方法。在相关乘性噪声背景下,针对信号具有循环平稳性的特点,利用循环统计量对一维、二维谐波参量估计及非线性耦合问题进行了分析。文中提出了互可混的概念,表明了它所描述的各元素之间在时间上的近似不相关性,以此来描述噪声间的相关性。噪声互可混的假设与以往的理论是相容的,并且基于噪声互可混假设的观测信号模型更具一般性。在互可混理论的基础上,对相关乘性噪声背景下的谐波参量估计问题,提出了二维六阶时间平均矩谱切片的方法,一维和二维四阶时间平均矩谱方法。对相关乘性噪声背景下三次非线性耦合问题,提出了一维和二维四阶时间平均矩谱方法。更多还原

【Abstract】 The parameter estimation of harmonics has taken on a much more significant role in modern signal processing. The parameter estimation of two-dimensional (2-D) harmonics has received a lot of attention in recent years and has widespread applications, ranging from radar, sonar, geophysics, radio communications and medical imaging.This dissertation studies the harmonics parameter estimation via higher-order statistics, cyclic statistics and matrix theory.And brings forwoard an advantageous approach to estimating harmonics parameter and nonlinear coupling in various noises, such as independent additive noise, independent multiplicative noise, correlative additive noise and correlative multiplicative noise. The innovative pursuits in the dissertation can be summarized as the following three aspects. Firstly, the concept of 2-D cross-mixing of stochastic process is proposed. Its physical signification and characteristics are presented. It is illuminated that cross-mixing may describe the relationship among several noises. In comparison to the model based on self-mixing and independent noise,the model based on the cross-mixing assumption has more universality, and the cross-mixing concept is compatible with previous theory. This pursuit builds theoretical basis for the study on the 2-D harmonics parameter estimation and nonlinear coupling analysis in the complex noise. Secondly, a special 2-D slice of the sixth-order and fourth-order time-average moment spectrum is addressed to estimate harmonics frequencies in the presence of correlative multiplicative and additive noise of zero mean, which solves the problem of 2-D harmonics parameter estimation in correlative noise for the first time. Finally, a special fourth-order time-average moment spectrum approach is proposed to estimate one-dimensional (1-D) and two-dimensional cubic nonlinear coupling powerfully. It can be applied to obtain the coupled and coupling frequencies in the noise that any mean multiplicative and additive noises are mutually independent, the multiplicative noises are correlative. In the meantime, this method needn’t constrain the distribution and the color of noises. This dissertation consists of eight chapters. In chapter one, researches and trend of 1-D and 2-D harmonics parameter estimation and nonlinear coupling harmonic estimation are summarized. Main methods of 2-D harmonics parameter estimation and the key problems are introduced and discussed. The significance and practicality about the content of this dissertation are elucidated. In chapter two, relative base knowledge about matrix algebra is introduced. The definitions and properties of higher order moment, higher order cumulant, higher order spectra and cyclostationary are described, which are the theoretic bases of this dissertation. In chapter three, the problem of 2-D harmonics parameter estimation in independent additive noise is studied. Based on the fact that, on the one hand, the spectral estimation methods based on signal subspace possess higher statistical stability and are much less sensitive to SNR and the length of data set than those ones based on noise subspace, but their resolution are lower. On the other hand, those methods based on noise subspace have higher resolution, but high sensitivity to noise and the length of data set. Using the signal subspace and the noise subspace of the correlation matrix synthetically, two kinds of methods are presented to estimate the 2-D harmonic parameter. One is an orthogonal vector spectral estimation method based on autocorrelation matrix signal subspace. The other one is the 2-D ESPRIT method based on autocorrelation matrix eigenvector. Both methods possess high stability and high resolution. In chapter four, utilizing the characteristics that the higher order cumulant of colored or white Gaussian noise is zero, the problem of 2-D cubic nonlinear phase coupling estimation in independent additive noise is considered, specialfourth-order cumulants are defined and the slice spectrum of fourth-order cumulant approach is proposed to extract the coupled and coupling frequency components in Gaussian noise. The 2-D fourth-order cumulant spectrum can be drawn easily in the three dimensional domain by choosing the slice spectrum. This method is very convenient, flexible, fast and practical. In chapter five, the parameter estimation of 2-D harmonics is addressed in the presence of correlative multiplicative and additive noise. The concept of 2-D cross-mixing of stochastic process is proposed. It can depict the correlative relationship of noise. Its physical signification and characteristics are presented. In comparison to the model based on self-mixing and independent noise,the model based on the cross-mixing assumption has more universality, and the cross-mixing concept is compatible with previous theory. This pursuit builds theoretical basis for the study on the 2-D harmonics parameter estimation and nonlinear coupling analysis in the complex noise. On the basis of cross-mixing assumption, the 2-D cyclic mean is adopted to estimate harmonic frequencies in nonzero mean multiplicative noise and a special 2-D slice of the sixth-order time-average moment spectra is defined to estimate frequency in zero mean multiplicative and additive noise. This method needn’t constrain the distribution and color of noises. This method is proven in the paper. In chapter six, based of cross-mixing assumption, a special fourth-order time-average moment spectra approach is presented to analyze the problem of 1-D and 2-D harmonic parameter estimation in correlative noise. The computational burden of the method described in chapter five is larger. The fourth-order time-average moment spectra approach overcomes the shortage of 1-D and 2-D slice of the sixth-order time-average moment spectra and has much less computation burden and good result. In chapter seven, the problem of cubic nonlinear coupling is studied in the noise that any mean multiplicative and additive noises are mutually independent; the multiplicative noises are correlative. On the base of cross-mixing assumption, a special fourth-order time-average moment spectrum approach is proposed. The更多还原