Chaotic Dynamics of Sea Clutter

by Simon Haykin (McMaster University); Sadasivan Puthusserypady (McMaster University)

• ISBN13: 9780471252429
• ISBN10: 0471252425
• Format: Hardcover
• Copyright: 1999-01-01
• Publisher: Wiley-Interscience

Summary

Chaotic dynamics of sea clutter boasts important applications in a number of fields, including weather radar systems, which are intensely studied at major universities. This book presents a detailed account of chaotic dynamics of sea clutter, using real-life sea clutter data rather than simulated data, and drawing on eight years of research by one of the most highly regarded researchers in this area.

Table of Contents

Preface	ix
Overview	1	(6)
Introduction	1	(4)
Objectives of the Book	5	(1)
List of Abbreviations	5	(2)
Sea Clutter	7	(6)
Introduction	7	(2)
Sea Clutter at Low Grazing Angles	9	(2)
Compound K-Distributions	11	(2)
Radar and Database	13	(12)
Introduction	13	(1)
IPIX Radar	14	(3)
System Features and Capabilities	15	(2)
Field Experiments	17	(8)
Chaotic Dynamics of a Physical Time Series	25	(22)
Introduction	25	(3)
Some Basic Definitions	28	(18)
Attractors	28	(3)
Basin of Attraction	31	(1)
Sink (Map)	32	(1)
Limit Cycle	32	(1)
Strange Attractor	32	(1)
Manifold	32	(1)
Fractal Dimension	32	(3)
Lyapunov Spectrum	35	(6)
Lyapunov (Kaplan--Yorke) Dimension	41	(2)
Kolmogorov Entropy (KE)	43	(2)
Relationship between the Kolmogorov Entropy and Lyapunov Exponents	45	(1)
Embedding Dimension (dE)	45	(1)
Embedding Delay (τ)	45	(1)
Criteria for Assessing the Chaotic Dynamics of an Experimental Time Series	46	(1)
Preprocessing of the Radar Data	47	(20)
Introduction	47	(1)
Amplitude and Phase Corrections (I--Q Calibration)	48	(4)
Effect of Miscalibration	50	(2)
Filtering	52	(4)
Three-Point Smoothing	52	(2)
FIR Filtering	54	(2)
Results of Preprocessing of the Signals	56	(2)
Continuity and Differentiability Tests on Filtered Data	58	(1)
Continuity	59	(2)
Definition	59	(1)
Test of Continuity	60	(1)
Differentiability	61	(3)
Definition	61	(1)
Test of Differentiability	62	(2)
Results of Continuity and Differentiability Tests	64	(3)
Tests of Stationarity and Nonlinearity	67	(12)
Introduction	67	(1)
Test of Stationarity	68	(3)
Recurrence Plots	68	(3)
Tests of Nonlinearity	71	(3)
WSF Method	72	(1)
SIPD Method	73	(1)
SCD Method	73	(1)
Results of Nonlinearity Tests	74	(5)
Some Facts About Chaotic Processes	79	(12)
Introduction	79	(2)
Sensitive Dependence on Initial Conditions	81	(4)
Nonlinear Dynamical Systems	85	(3)
What Is Phase Space?	88	(1)
Why a Chaotic Approach?	89	(2)
Reconstruction of Embedding Space	91	(30)
Introduction	91	(1)
Measurements and State Representation	91	(15)
Embedding	93	(10)
Differentiable Embedding	103	(3)
Phase-Space Reconstruction	106	(2)
Estimation of Embedding Parameters	108	(5)
Embedding Delay	108	(2)
Global Embedding Dimension (dE)	110	(1)
Local Embedding Dimension (dL)	111	(2)
Results of Estimation of Embedding Parameters	113	(8)
Comparison of dE for Sea Clutter, Tides, and Correlated Noise	114	(7)
Estimation of Chaotic Invariants	121	(46)
Introduction	121	(1)
Estimation of Correlation Dimension	121	(9)
Maximum-Likelihood Estimate of the Correlation Dimension	124	(2)
Results of Case Studies	126	(4)
Lyapunov Exponents	130	(17)
Estimation of the Lyapunov Exponents	132	(1)
Results of Case Studies	133	(14)
Horizon of Predictability (HP)	147	(4)
Lyapunov Dimension	151	(5)
Results of Case Studies	152	(4)
Kolmogorov Entropy	156	(11)
How to Estimate the Kolmogorov Entropy	157	(2)
Maximum-Likelihood Estimation of the Entropy	159	(2)
Results of Case Studies	161	(6)
Chaotic Study of Simulated Sea Clutter Data	167	(24)
Introduction	167	(1)
Overview of the Simulation Model	167	(11)
Sea Surface Dynamics	168	(5)
Sea Surface Scattering	173	(5)
Radar Model	178	(1)
Comparison Conditions and Criteria	178	(1)
Comparison Criteria	178	(1)
Determining Measurements Conditions and Simulation Parameters	178	(1)
Comparison of Measurement and Simulation Results	179	(1)
Results of Chaotic Characterization	179	(12)
Summary of Experimental Results and Conclusions	191	(4)
Supporting Physical Evidence	193	(1)
Dynamic Reconstruction	194	(1)
Appendix	195	(6)
A.1 Estimation of Chaotic Invariants from Measurements of a Single Variable	195	(6)
A.1.1 Results	196	(5)
Bibliography	201	(12)
Index	213