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

¹ The 28 th Research Institute, China Electronics Technology Group Corporation, Nanjing, China
² Southeast University, School of instrument science and engineering, Key laboratory of micro-inertial instrument and advanced navigation technology, Ministry of education, Nanjing, China

^a Corresponding author: ytzzw126@126.com

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.