NOISE REDUCTION BY GRADIENT DESCENT

Abstract

The problem of reducing noise in a time series from a nonlinear dynamical system can be formulated as a nonlinear minimisation process. This paper demonstrates that this can be easily solved using a steepest descent method without any of the stability problems that have been associated with using a Newton method [Hammel, 1990; Farmer & Sidorowich, 1991]. The optimisation function to be minimised is also shown not to contain any local minima if the trajectory is always hyperbolic. So that in this case this method will converge eventually to a purely deterministic trajectory. Finally this method is compared with a recently proposed algorithm [Schreiber & Grassberger, 1991], which can be viewed as an alternative gradient descent method.