Dynamics-aware noise reduction in time Series

Abstract Filtering methods tailored to noisy observables from deterministic dynamical systems go beyond traditional noise reduction techniques by leveraging the system’s inherent dynamics to distinguish the true signal from noise. The methods explored in this work were tested on challenging, discretely sampled chaotic observables deliberately contaminated with Gaussian white noise. Indicators used to measure the efficiency of noise reduction included an improved ability to estimate the fractal dimension of the underlying system. Strategies based on local approximation or prediction of dynamics in reconstructed state spaces reduced noise by up to an order of magnitude, even when the signal was corrupted by noise levels as high as 100%. The prediction-based noise suppression method proposed in this work was inspired by an idea originally introduced by Farmer and Sidorowich in the late 1980s.