Smooth projective noise reduction for nonlinear time series
Date of Original Version
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. © The Society for Experimental Mechanics, Inc. 2013.
Conference Proceedings of the Society for Experimental Mechanics Series
Chelidze, David. "Smooth projective noise reduction for nonlinear time series." Conference Proceedings of the Society for Experimental Mechanics Series 1, (2013): 77-83. doi:10.1007/978-1-4614-6570-6_6.