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Denoising signals corrupted by chaotic noise. (English) Zbl 1222.94023

Summary: 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 \(\mathbb{R}^{d}\) and \({s_{i}}\) a sequence in \(\mathbb{R}^{d}\) 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 \(n\to \infty \) for typical asymptotic behaviors of orbits.

MSC:

94A12 Signal theory (characterization, reconstruction, filtering, etc.)
37N35 Dynamical systems in control
62G07 Density estimation
65T60 Numerical methods for wavelets
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