Parameter estimation in chaotic noise

The problem of parameter estimation in chaotic noise is considered in this paper. Since a chaotic signal is inherently deterministic, a new complexity measure called the phase space volume (PSV) is introduced for estimation instead of using the conventional probabilistic measures. We show that the unknown parameters of a signal embedded in chaotic noise ran be obtained by minimizing the PSV (MPSV) of the output of an inverse filter of the received signal in a reconstructed phase space. Monte Carlo simulations are carried out to analyze the efficiency of the MPSV method for parameter estimation in chaotic noise. To illustrate the usefulness of the MPSV technique in solving real-life problems, the problem of sinusoidal frequency estimation in real radar clutter (unwanted radar backscatters) is considered. Modeling radar clutter as a chaotic process, we apply the MPSV technique to estimate the sinusoidal frequencies by estimating the coefficients of an autoregressive (AR) spectrum. The results show that the frequency estimates generated by the MPSV method are more accurate than those obtained by the standard least square (LS) technique.

[1]  H. Abarbanel,et al.  Noise reduction in chaotic time series using scaled probabilistic methods , 1991 .

[2]  Schreiber,et al.  Noise reduction in chaotic time-series data: A survey of common methods. , 1993, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[3]  Kevin Judd,et al.  Dangers of geometric filtering , 1993 .

[4]  K. Judd An improved estimator of dimension and some comments on providing confidence intervals , 1992 .

[5]  Alan V. Oppenheim,et al.  Synchronization of Lorenz-based chaotic circuits with applications to communications , 1993 .

[6]  S. K. Mullick,et al.  Attractor dimension, entropy and modelling of speech time series , 1990 .

[7]  James A. Yorke,et al.  Noise Reduction: Finding the Simplest Dynamical System Consistent with the Data , 1989 .

[8]  Clare D. McGillem,et al.  A chaotic direct-sequence spread-spectrum communication system , 1994, IEEE Trans. Commun..

[9]  H. Leung,et al.  Chaotic radar signal processing over the sea , 1993 .

[10]  Lyle Noakes,et al.  THE TAKENS EMBEDDING THEOREM , 1991 .

[11]  Don E. Johnson,et al.  ON THE EXISTENCE OF GAUSSIAN NOISE , 1991 .

[12]  Gottfried Mayer-Kress,et al.  APPLICATION OF DIMENSION ALGORITHMS TO EXPERIMENTAL CHAOS , 1987 .

[13]  D. Ruelle,et al.  Fundamental limitations for estimating dimensions and Lyapunov exponents in dynamical systems , 1992 .

[14]  C. Tannous,et al.  Strange attractors in multipath propagation , 1991, IEEE Trans. Commun..

[15]  Venkatesh Nagesha,et al.  Methods for chaotic signal estimation , 1995, IEEE Trans. Signal Process..

[16]  Don H. Johnson,et al.  On the existence of Gaussian noise (signal modelling) , 1991, [Proceedings] ICASSP 91: 1991 International Conference on Acoustics, Speech, and Signal Processing.

[17]  Stephen M. Hammel,et al.  A noise reduction method for chaotic systems , 1990 .

[18]  J. D. Farmer,et al.  Optimal shadowing and noise reduction , 1991 .