Noise reduction by recycling dynamically coupled time series

Abstract

We say that several scalar time series are dynamically coupled if they record the values of measurements of the state variables of the same smooth dynamical system. We show that much of the information lost due to measurement noise in a target time series can be recovered with a noise reduction algorithm by crossing the time series with another time series with which it is dynamically coupled. The method is particularly useful for reduction of measurement noise in short length time series with high uncertainties.

Algorithm for noise reduction for strongly contaminated chaotic oscillators based on the local projection approach and 2D wavelet filtering

“…Over the past two decades, a number of important algorithms have been developed for noise reduction of chaotic signals. A comprehensive overview of these algorithms can be found in [1,2]. All noise reduction methods for chaotic time series may be classified as model-based or model-free.…”

Error Covariance Matrix Estimation of Noisy and Dynamically Coupled Time Series

“…Our method is effective when all the scalar time series are the time ordered values of real functions (observables) of the state variables of the same smooth dynamical system. When this property holds we say that these time series are dynamically coupled [38] (see Ref. [39] for other approaches to coupled systems in the setting of noisy time series).…”