Denoising signals corrupted by chaotic noise

Abstract

We consider the problem of signal estimation where the observed time series is modeled as y_i=x_i+s_i with {x_i} being an orbit of a chaotic self-map on a compact subset of and {s_i} a sequence in converging to zero. This model is motivated by experimental results in the literature where the ocean ambient noise and the ocean clutter are found to be chaotic. Making use of observations up to time n, we propose an estimate of s_i for i<n and show that it approaches s_i as n→ ∞ for typical asymptotic behaviors of orbits.