The DOI matches its Crossref record; 41 of the 41 references it cites were found in a registry or an index.
Detection of signals in chaos
Abstract
In this paper, we present a new method for the detection of signals in "noise", which is based on the premise that the "noise" is chaotic with at least one positive Lyapunov exponent. The method is naturally rooted in nonlinear dynamical systems and relies on neural networks for its implementation. We first present an introductory review of chaos. The subject matter selected for this part of the paper is written with emphasis on experimental studies of chaos using a time series. Specifically, we discuss the issues involved in the reconstruction of chaotic dynamics, attractor dimensions, and Lyapunov exponents. We describe procedures for the estimation of the correlation dimension and the largest Lyapunov exponent. The need for an adequate data length is stressed. In the second part of the paper we apply the chaos-based method to a difficult task: the radar detection of a small target in sea clutter.>
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Citations
Cites
Multilayer feedforward networks are universal approximators
Hornik, K., Stinchcombe, M., & White, H. (1989) · Neural Networks · doi:10.1016/0893-6080(89)90020-8 · Cited by 21,728
Deterministic Nonperiodic Flow
Lorenz, E. N. (1963) · Journal of the Atmospheric Sciences · doi:10.1175/1520-0469(1963)020<0130:dnf>2.0.co;2 · Cited by 19,398
Detecting strange attractors in turbulence
Takens, F. (1981) · Lecture Notes in Mathematics · doi:10.1007/bfb0091924 · Cited by 10,459
Determining Lyapunov exponents from a time series
Wolf, A., Swift, J. B., Swinney, H. L., & Vastano, J. A. (1985) · Physica D: Nonlinear Phenomena · doi:10.1016/0167-2789(85)90011-9 · Cited by 9,499
Multilayer feedforward networks are universal approximators
HornikK., StinchcombeM., & WhiteH. (1989) · Neural Networks · doi:10.5555/70405.70408 · Cited by 9,081
Detection, Estimation, And Modulation Theory
Trees, H. L. V. (1968) · Cited by 5,969
Approximate entropy as a measure of system complexity.
Pincus, S. M. (1991) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.88.6.2297 · Cited by 5,811
Measuring the strangeness of strange attractors
Grassberger, P., & Procaccia, I. (1983) · Physica D: Nonlinear Phenomena · doi:10.1016/0167-2789(83)90298-1 · Cited by 5,650
Ergodic theory of chaos and strange attractors
Eckmann, J. P., & Ruelle, D. (1985) · Reviews of Modern Physics · doi:10.1103/revmodphys.57.617 · Cited by 4,941
Independent coordinates for strange attractors from mutual information
Fraser, A. M., & Swinney, H. L. (1986) · Physical Review A · doi:10.1103/physreva.33.1134 · Cited by 4,606
Metadata
- Authors
- Haykin, S., & Li, X. B.
- Venue
- Proceedings of the IEEE
- Published
- 1995
- Volume
- 83
- Issue
- 1
- Pages
- 95-122
- ISSN
- 0018-9219 (ISSN-L)
- OpenAlex
- W2146203966
- Cited by
- 299
- References
- 41
- FWCI
- 2.93
- Type
- journal article
- Language
- en
- Open access
- closed
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- Haykin, S., & Li, X. B. (1995). Detection of signals in chaos. Proceedings of the IEEE. https://doi.org/10.1109/5.362751
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Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
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