Application of the Non-Hermitian Singular Spectrum Analysis to the exponential retrieval problem

TL;DR

This paper introduces a stable non-Hermitian singular spectrum analysis method for exponential retrieval, utilizing SVD of lag-covariance matrices and generalized eigenvalue problems to improve accuracy and noise robustness.

Contribution

The paper presents a novel approach combining non-Hermitian singular spectrum analysis with phase portrait analysis for exponential signal retrieval, enhancing stability and noise discrimination.

Findings

Method outperforms existing techniques in noisy environments

Effective in distinguishing signal from noise using phase portraits

Comparable or superior accuracy demonstrated on simulated data

Abstract

We present a new approach to solve the exponential retrieval problem. We derive a stable technique, based on the singular value decomposition (SVD) of lag-covariance and crosscovariance matrices consisting of covariance coefficients computed for index translated copies of an initial time series. For these matrices a generalized eigenvalue problem is solved. The initial signal is mapped into the basis of the generalized eigenvectors and phase portraits are consequently analyzed. Pattern recognition techniques could be applied to distinguish phase portraits related to the exponentials and noise. Each frequency is evaluated by unwrapping phases of the corresponding portrait, detecting potential wrapping events and estimation of the phase slope. Efficiency of the proposed and existing methods is compared on the set of examples, including the white Gaussian and auto-regressive model noise.