An hybrid noise reduction method for state-space reconstruction

A method for separating observational noise from the motion of a high-dimensional deterministic system is described. The method is based on a combination of smoothing and decoding stages. The former are intended to perform a coarse rejection of the smallest space and time scales and to provide a consistent set of neighbors for learning the dynamics. The learning is done by first embedding the smoothed data in a state-space of sufficiently high dimension and then estimating the reconstruction function on that space. If there are enough data available for the estimation one can expect this function to encode every important excursion in the attractor, and thus one can use it in a later stage to decode structured motion from the high-pass time series. In case of insufficient data there might not be this possibility, since some state-space transitions may be missing in the smoothed time series as well as in the noisy one. In these cases, the reconstruction function must be estimated from a memorized clean reference. The method will work as long as this reference reproduces to a certain degree of approximation the current environmental conditions in the absence of noise.<>