Two Dimensional Harmonics Retrieval in Zero-Mean Independent Multiplicative and Additive Noises

Zheng-Wei Zhang,Zhong Chen,Li-Hui Wang

doi:10.1051/itmconf/20160702003

Abstract

For some theoretical problems and computational inefficiency, the problem of estimating the frequencies of two dimensional harmonics in zero-mean independent multiplicative and additive noises is not resolved completely. Existing methods based on cyclic statistics assume that the noise is non-Gaussian, and that the shape of the noise’s distribution is not symmetrical. A novel approach which imposes no constraints on the distribution or the color of noises is developed. It relies on fourth-order special cumulant or moment slices. The fourth-order moment spectrum is shown to have computational advantages over existing method. As a byproduct, the variance of the noises can also be estimated directly from the spectrum. Finally we give as an illustrative example a complete experiment to corroborate the theoretical results. The results of this experiment do show preliminarily that the new method is valid and efficient for the problem of harmonics retrieval in zero-mean independent multiplicative and additive noises.

Highlights

Estimating harmonics with multiplicative noises using higher order spectra or cyclic statistics has been drawing a great deal of attention
Dwyer [1] estimated the frequencies of one-dimensional harmonic in the presence of Gaussian multiplicative and additive noises based on the spectrum of a special fourth-order cumulant
The method in literature [7] is designed specially for harmonics retrieval problem in zero-mean independent noises, whereas it requires the multiplicative noises in Eq (1) are nonsymmetrical or non-Gaussian

Summary

Introduction

Estimating harmonics with multiplicative noises using higher order spectra or cyclic statistics has been drawing a great deal of attention. Kareem [4] provided a measure of the multiplicative nonlinear interactions of frequency components and offers physical insight into the nature and characteristics of nonlinear fluctuations Baars [5] reduced essentially to spectral Linear Stochastic Estimation when only first-order terms are considered, and is presented in the context of stochastic estimation as spectral Higher-Order Stochastic Estimation All these methods assume different noise background. A novel method to estimate harmonics in zero-mean independent multiplicative and additive noises is developed based on higher order spectra using only a single record of data. This method only requires that the noises are mixing and stationary, and imposes no constraints on the distribution or color of the noises

Base Problem Statements

Harmonics Retrieval Algorithm

T1 2T2

Simulation Results

Conclusions