Chaotic behaviour and non-linear prediction of airborne radar sea clutter data

The potential to model sea clutter radar returns using chaos theory is examined. Chaotic systems display qualitative similarities to sea clutter returns such as broad flat spectra, boundedness and irregular temporal behaviour. In this report several key parameters of chaotic systems, namely correlation dimension, Lyapunov spectrum and Lyapunov dimension are calculated from real sea clutter returns and found to be consistent with a chaotic interpretation. The airborne high resolution data (less than one metre) produces a correlation coefficient with an average value of 4.63 and an embedding dimension of 6-7. Lyapunov dimensions are consistent with correlation values. A local linear technique and a radial basis function (RBF) are used to construct a one step non-linear predictor. A mean square error (MSE) of approximately 0.0032 between the predicted and normalized (i.e. maximum +/-1 range) real time series is measured.

[1]  J. Nazuno.  Haykin, Simon. Neural networks: A comprehensive foundation, Prentice Hall, Inc. Segunda Edición, 1999 , 2000 .

[2]  H. Abarbanel,et al.  Determining embedding dimension for phase-space reconstruction using a geometrical construction. , 1992, Physical review. A, Atomic, molecular, and optical physics.

[3]  Simon Haykin,et al.  Detection of signals in chaos , 1995, Proc. IEEE.

[4]  James Theiler,et al.  Testing for nonlinearity in time series: the method of surrogate data , 1992 .

[5]  Simon Haykin,et al.  Neural Networks: A Comprehensive Foundation , 1998 .

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

[7]  Takens,et al.  Estimation of the dimension of a noisy attractor. , 1994, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[8]  S. Haykin.  Radar clutter attractor: implications for physics, signal processing and control , 1999 .

[9]  Recognizing chaos in radar images , 1994 .

[10]  D. Ruelle,et al.  Recurrence Plots of Dynamical Systems , 1987 .

[11]  H. Leung,et al.  Applying chaos to radar detection in an ocean environment: an experimental study , 1995 .

[12]  S. Haykin,et al.  Chaotic dynamics of sea clutter. , 1999, Chaos.

[13]  L. Chua,et al.  Chaos: A tutorial for engineers , 1987, Proceedings of the IEEE.

[14]  D. Broomhead,et al.  Robust estimation of tangent maps and Liapunov spectra , 1996 .

[15]  S. Haykin,et al.  Is there a radar clutter attractor , 1990 .