Noise level estimation of time series using coarse grained entropy

TL;DR

This paper introduces a novel method for estimating noise levels in time series data using coarse grained correlation entropy, effective even at high noise levels, and applicable to various noise types and systems.

Contribution

The paper develops a new approach based on the dependence of $K_2( ext{ε})$ on noise standard deviation, valid for different noise distributions and dynamical systems.

Findings

Method accurately estimates noise in chaotic systems

Effective for high noise levels and various noise distributions

Validated on electronic circuit and simulated systems

Abstract

We present a method of noise level estimation that is valid even for high noise levels. The method makes use of the functional dependence of coarse grained correlation entropy $K_2(\eps)$ on the threshold parameter $\eps$. We show that the function $K_2(\eps)$ depends in a characteristic way on the noise standard deviation $\sigma$. It follows that observing $K_2(\eps)$ one can estimate the noise level $\sigma$. Although the theory has been developed for the gaussian noise added to the observed variable we have checked numerically that the method is also valid for the uniform noise distribution and for the case of Langevine equation corresponding to the dynamical noise. We have verified the validity of our method by applying it to estimate the noise level in several chaotic systems and in the Chua electronic circuit contaminated by noise.