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Chaotic Dynamics of Sea Clutter [Kietas viršelis]

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Radar backscattering from an ocean surface, commonly called sea clutter, has been traditionally viewed as the sample function of a stochastic process. Expanding on a paper published in CHAOS in December 1997, the authors (McMaster University) offer experimental results that demonstrate that sea clutter is in reality chaotic. The book also presents the elements of a rigorous procedure for determining whether an experimental time series is chaotic or not, as well as an overview of the pertinent aspects of chaos theory. Intended for radar engineers and scientists working on the characterization of sea clutter, and researchers probing into the chaotic nature of experimental time series. Annotation c. Book News, Inc., Portland, OR (booknews.com)

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.
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