Multi-Parameters Estimation Of Harmonics And Vector-sensor Array Based On Quaternion

The dissertation is part of the research item"Research and application of quaternion in parameters estimation of two dimensional harmonics", which are sponsored by the National Natural Science Foundation of China.The Signal & Information Processing has already been one of disciplines that developing rapidly in the Information Science field in the latest ten years. Parameter estimation is an important component of Signal & Information Processing, and has received a lot of attention in recent years. Parameter estimation, as an important method of signal analysis, has extensive application and significant value, and its application relates to a lot of military affairs and civil fields, such as radar, sonar, navigation, communication, geologic prospecting and biomedicine. The parameter estimation of harmonics has taken on a much more significant role in modern signal processing. The parameters which are cared about in harmonics signal estimation are frequency, amplitude and initial phase of harmonic signal.Array signal processing, called as the space-field signal processing, is a very important content of modern signal processing. Recently, the vector-sensor array processing has become a new branch of array signal processing, and has the wide application prospect in communication, radar, sonar, electronic warfare, radioastronomy, seismic prospecting, medical system etc,. In vector-sensor array parameter estimation, direction of arrival (DOA), frequency and polarization parameters need to be estimated.Quaternion was first introduced into math by Hamilton in 1843. Since the quaternion multiplication isn't commutative, study on quaternion is much more complicated than in real and complex field, which is the right reason that the theory of quaternion and quaternion matrix is developed slowly in a long time. But in recent two decades years, the research on quaternion and quaternion matrix theory has already become a hotspot, especially in algebra field of China. In addition, because of the development of robot technology, body flying control and computer, quaternion is applied into practice. One goal of the study on quaternion for many scientists is to find the way to resolve the problem in interspace geometry via quaternion the same as in plane geometry via complex number. Harmonics parameter estimation and vector -sensor array parameter estimation can be also regarded as interspace geometry problems.The purpose of applying quaternion into harmonics and vector–sensor array parameter estimation is to make use of the characteristic of quaternion, that is, quaternion is able to express more information. First, the quaternion models of both harmonics and vector-sensor array signal are constructed, many parameters of them are contained in the model, and then harmonics and vector-sensor array multi-parameters are estimated via solving quaternion problem.This dissertation consists of six chapters.In chapter one, current researches and trend of one-dimensional (1-D) & two-dimensional (2-D) harmonics and vector-sensor array parameter estimation are summarized, and the application of quaternion in signal processing is also introduced. In addition, the existing problems in harmonics and vector-sensor arrayparameter estimation are presented. Finally, the study work of this dissertation is determined.In chapter two, basic knowledge concerned about matrix algebra is introduced. The definitions and properties of high-order moment, high-order cumulant, high-order spectra, quaternion and quaternion matrix are described, which will be used later.In chapter three, the problem of two-component vector-sensor array multi-parameters estimation is researched based on quaternion. Firtst, the theoy of right eigrnvalue decomposition of quaternion matrix is introduced in detail, and Toeplitz matrix of quaternion dual correlation function is constructed; which can not only express two-component vector-sensor array parameters, but also constrian MA noise; then the orthogonal signal subspace and noise subspace can be obtained using right eigrnvalue decomposition of quaternion matrix; fianally, vector-sensor array multi-parameters are estimated by quaternion MUSIC algorithm. The simulation results illustrate the method can effectively estimate DOA and polarization parameter of vector-sensor array in MA noise.In chapter four, the problem of 1-D harmonic multi-parameters estimation based on quaternion is researched. A new quaternion model of 1-D harmonic is presented, which contains every signal parameter, such as amplitude, frequency and initial phase; Toeplitz matrix of quaternion auto-correlation function is constructed, and multi-parameters are estimated by quaternion MUSIC algorithm. The simulation results illustrate the method can estimate signal parameters effectively under lower signal-to-noise ratio (SNR).In chapter five, the problem of 2-D harmonic parameter estimation in non-Gaussian colored noise is researched. The 2-D cumulant projection theorem of complex linear non-Gaussian process is presented; the noise auto-correlationestimation is obtained based on this theorem by constructing a high-order cumulant of the complex noisy harmonic; then a generalized eigen-value problem is solved to prewhiten the noise space; finally 2-D MUSIC is employed to retrieve the 2-D harmonic frequencies. This method can effectively extract frequencies from colored non-Gaussian noise moded as AR, MA or ARMA, even though the noise is symmetrically-distributed or there exists quadratic phase coupling. Theory and algorithm are illustrated by simulation experiments.In chapter six, a brief summary of the dissertation is given. The suggestion for future researches related to multi-parameters estimation of harmonics and vector-sensor array based on quaternion is put forward.The innovative work of this dissertation includes three aspects.①The concept of dual correlation function is proposed, and multi-parameters of two-component vector-sensor array in MA noise are estimated by right eigrnvalue decomposition of quaternion matrix and quaternion MUSIC algorithm.②A new quaternion model of 1-D harmonic is presented, and 1-D harmonic multi-parameters are estimated using quaternion MUSIC algorithm. Compared with classical MUSIC algorithm, the method of the dissertation is still effective under lower SNR.③The 2-D cumulant projection theorem of complex linear non-Gaussian process is established, and the method of 2-D harmonic parameter estimation in non-Gaussian colored noise is proposed. This method can effectively extract frequencies from colored non-Gaussian noise moded as AR, MA or ARMA, even though the noise is symmetrically-distributed or there exists quadratic phase coupling.