Denoising signals corrupted by chaotic noise

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 R d and { s i } a sequence in R d 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.