On noise reduction methods for chaotic data.

@article{citeulike:81493, abstract = {Recently proposed noise reduction methods for nonlinear chaotic time sequences with additive noise are analyzed and generalized. All these methods have in common that they work iteratively, and that in each step of the iteration the noise is suppressed by requiring locally linear relations among the delay coordinates, i.e., by moving the delay vectors towards some smooth manifold. The different methods can be compared unambiguously in the case of strictly hyperbolic systems corrupted by measurement noise of infinitesimally low level. It was found that all proposed methods converge in this ideal case, but not equally fast. Different problems arise if the system is not hyperbolic, and at higher noise levels. A new scheme which seems to avoid most of these problems is proposed and tested, and seems to give the best noise reduction so far. Moreover, large improvements are possible within the new scheme and the previous schemes if their parameters are not kept fixed during the iteration, and if corrections are included which take into account the curvature of the attracting manifold. Finally, the fact that comparison with simple low-pass filters tends to overestimate the relative achievements of these nonlinear noise reduction schemes is stressed, and it is suggested that they should be compared to Wiener-type filters.}, address = {Physics Department, University of Wuppertal, Gauss-Strasse 20, D-5600 Wuppertal 1, Germany.}, author = {Grassberger, Peter and Hegger, Rainer and Kantz, Holger and Schaffrath, Carsten and Schreiber, Thomas }, citeulike-article-id = {81493}, doi = {http://dx.doi.org/10.1063/1.165979}, issn = {1054-1500}, journal = {Chaos}, keywords = {stats, time\_series}, month = {April}, number = {2}, pages = {127--141}, posted-at = {2005-01-21 15:53:33}, priority = {0}, title = {On noise reduction methods for chaotic data.}, url = {http://dx.doi.org/10.1063/1.165979}, volume = {3}, year = {1993} }

TY - JOUR ID - citeulike:81493 L3 - citeulike-article-id:81493 TI - On noise reduction methods for chaotic data. JF - Chaos VL - 3 IS - 2 SP - 127 EP - 141 AD - Physics Department, University of Wuppertal, Gauss-Strasse 20, D-5600 Wuppertal 1, Germany. SN - 1054-1500 N2 - Recently proposed noise reduction methods for nonlinear chaotic time sequences with additive noise are analyzed and generalized. All these methods have in common that they work iteratively, and that in each step of the iteration the noise is suppressed by requiring locally linear relations among the delay coordinates, i.e., by moving the delay vectors towards some smooth manifold. The different methods can be compared unambiguously in the case of strictly hyperbolic systems corrupted by measurement noise of infinitesimally low level. It was found that all proposed methods converge in this ideal case, but not equally fast. Different problems arise if the system is not hyperbolic, and at higher noise levels. A new scheme which seems to avoid most of these problems is proposed and tested, and seems to give the best noise reduction so far. Moreover, large improvements are possible within the new scheme and the previous schemes if their parameters are not kept fixed during the iteration, and if corrections are included which take into account the curvature of the attracting manifold. Finally, the fact that comparison with simple low-pass filters tends to overestimate the relative achievements of these nonlinear noise reduction schemes is stressed, and it is suggested that they should be compared to Wiener-type filters. KW - stats KW - time_series AU - Grassberger, Peter AU - Hegger, Rainer AU - Kantz, Holger AU - Schaffrath, Carsten AU - Schreiber, Thomas PY - 1993/04// UR - http://dx.doi.org/10.1063/1.165979 ER -