Smooth Projective Noise Reduction for Nonlinear Time Series

摘要

Many nonlinear or chaotic time series exhibit an innate broad spectrum, which makes noise reduction difficult. Locally projective noise reduction using proper orthogonal decomposition (POD) is one of the most effective tools. It works for both map-like and continuously sampled time series. However, it only looks at geometrical or topological properties of data and does not take into account temporal characteristics of time series. Here we present a new noise reduction method using smooth orthogonal decomposition (SOD) of bundles of locally reconstructed trajectory strands, which imposes temporal smoothness on the filtered time series. It is shown that SOD based noise reduction significantly outperforms the POD based method for the continuously sampled noisy time series.