Reconstruction of chaotic signals using symbolic data

• Published in: Physics letters. A Vol. 190; no. 5; pp. 393 - 398
• Main Authors: Tang, X.Z., Tracy, E.R., Boozer, A.D., deBrauw, A., Brown, Reggie
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 01.08.1994; Elsevier Science
• Subjects: Exact sciences and technology; Fluctuation phenomena, random processes, noise, and brownian motion; Nonlinear dynamics and nonlinear dynamical systems; Physics; Statistical physics, thermodynamics, and nonlinear dynamical systems; Signal reconstruction; Dynamical systems; Stochastic processes; Chaotic systems
• ISSN: 0375-9601; 1873-2429
• DOI: 10.1016/0375-9601(94)90721-8

We discuss the reconstruction of dynamical systems from noisy time-series. In particular, we consider the use of the symbol statistics (coarse-grained signal data) as the target for reconstruction. The statistics of symbol sequences is relatively insensitive to moderate amounts of measurement noise (σ(noise)/σ(signal) ≈ 10–20%), while larger amounts produce a substantial bias. We show that it is possible to produce robust reconstructions even when σ(noise)/σ(signal) ≈ O(1). Our study shows that even at such high noise levels the procedure is convergent: i.e. the accuracy of parameter estimates is limited only by the amount of data and computer time available.