Efficient noncausal noise reduction for deterministic time series

We present a simple noncausal noise reduction algorithm for time series tha t consist of noisy measurements of the state vectors of a deterministic (ch aotic) nonlinear system. The underlying dynamical system is assumed to be k nown and to operate in discrete time. The noise reduction algorithm is an i terative scheme for finding exact deterministic orbits close to the measure d noisy orbits. Furthermore, we discuss cases where the solution is not the original orbit but homoclinic to it. (C) 2001 American Institute of Physic s.