Parameter Estimation Of Two-dimensional Harmonics In Complex Noise

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...