Preface ........................................................ xi
Contributors List ............................................ xiii
1. Introduction ................................................. 1
Simon Haykin
Experimental Radar Facilities ................................ 2
Organization of the Book ..................................... 5
Part I Radar Spectral Analysis
2. Angle-of-Arrival Estimation in the Presence of Multipath .... 11
Anastasios Drosopoulos and Simon Haykin
2.1 Introduction ............................................ 11
2.2 The Low-Angle Tracking Radar Problem .................... 13
2.3 Spectrum Estimation Background .......................... 14
2.3.1 The Fundamental Equation of Spectrum Estimation ... 17
2.4 Thomson's Multi-Taper Method ............................ 18
2.4.1 Prolate Spheroidal Wavefunctions and Sequences .... 19
2.5 Test Dataset and a Comparison of Some Popular Spectrum
Estimation Procedures ................................... 23
2.5.1 Classical Spectrum Estimation ..................... 26
2.5.2 MUSIC and MFBLP ................................... 27
2.6 Multi-taper Spectrum Estimation ......................... 28
2.6.1 The Adaptive Spectrum ............................. 28
2.6.2 The Composite Spectrum ............................ 32
2.6.3 Computing the Crude, Adaptive, and Composite
Spectra ........................................... 33
2.7 F-Test for the Line Components .......................... 35
2.7.1 Brief Outline of the F-Test ....................... 35
2.7.2 The Point Regression Single-Line F-Test ........... 37
2.7.3 The Integral Regression Single-Line F-Test ........ 39
2.7.4 The Point Regression Double-Line F-Test ........... 42
2.7.5 The Integral Regression Double-Line F-Test ........ 46
2.7.6 Line Component Extraction ......................... 47
2.7.7 Prewhitening ...................................... 54
2.7.8 Multiple Snapshots ................................ 57
2.7.9 Multiple Snapshot, Single-Line, Point-Regression
F-Tests ........................................... 57
2.7.10 Multiple-Snapshot, Double-Line Point-Regression
F-Tests .......................................... 59
2.8 Experimental Data Description for a Low-Angle Tracking
Radar Study ............................................. 60
2.9 Angle-of-Arrival (AOA) Estimation ....................... 63
2.10 Diffuse Multipath Spectrum Estimation .................. 78
2.11 Discussion ............................................. 85
References .................................................. 88
3. Time-Frequency Analysis of Sea Clutter ...................... 91
David J. Thomson and Simon Haykin
3.1 Introduction ............................................ 91
3.2 An Overview of Nonstationary Behavior and
Time-Frequency Analysis ................................. 92
3.3 Theoretical Background on Nonstationarity ............... 94
3.3.1 Multi-taper Estimates ............................. 97
3.3.2 Spectrum Estimation as an Inverse Problem ......... 98
3.4 High-Resolution Multi-taper Spectrograms ................ 99
3.4.1 Nonstationary Quadratic-Inverse Theory ........... 101
3.4.2 Multi-taper Estimates of the Loeve Spectrum ...... 103
3.5 Spectrum Analysis of Radar Signals ..................... 104
3.6 Discussion ............................................. 111
3.6.1 Target Detection Rooted in Learning .............. 112
References ................................................. 113
Part II Dynamic Models
4. Dynamics of Sea Clutter .................................... 119
Simon Haykin, Rembrandt Bakker, and Brian Currie
4.1 Introduction ........................................... 119
4.2 Statistical Nature of Sea Clutter:
Classical Approach ..................................... 123
4.2.1 Background ....................................... 123
4.2.2 Current Models ................................... 126
4.3 Is There a Radar Clutter Attractor? .................... 130
4.3.1 Nonlinear Dynamics ............................... 130
4.3.2 Chaotic Invariants ............................... 132
4.3.3 Inconclusive Experimental Results on
the Chaotic Invariants of Sea Clutter ............ 133
4.3.4 Dynamic Reconstruction ........................... 134
4.3.5 Chaos, a Self-Fulfilling Prophecy? ............... 137
4.4 Hybrid AM/FM Model of Sea Clutter ...................... 139
4.4.1 Radar Return Plots ............................... 139
4.4.2 Rayleigh Fading .................................. 139
4.4.3 Time-Doppler Spectra ............................. 142
4.4.4 Evidence for Amplitude Modulation, Frequency
Modulation, and More ............................. 144
4.4.5 Modeling Sea Clutter as a Nonstationary Complex
Autoregressive Process ........................... 146
4.5 Discussion ............................................. 150
4.5.1 Nonlinear Dynamics of Sea Clutter ................ 150
4.5.2 Autoregressive Modeling of Sea Clutter ........... 150
4.5.3 State-Space Theory ............................... 151
4.5.4 Nonlinear Dynamical Approach Versus Classical
Statistical Approach ............................. 152
4.5.5 Stochastic Chaos ................................. 153
References ................................................. 155
Appendix A Specifications of the Three Sea-Clutter Sets
Used in This Chapter ........................... 157
5. Sea-Clutter Nonstationarity: The Influence of Long Waves ... 159
Maria Greco and Fulvio Gini
5.1 Introduction ........................................... 159
5.2 Radar and Data Description ............................. 163
5.3 Statistical Data Analyses .............................. 164
5.4 Modulation of Long Waves: Hybrid AM/FM Model ........... 169
5.5 Nonstationary AR Model ................................. 179
5.6 Parametric Analysis of Texture Process ................. 181
5.7 Discussion ............................................. 188
5.7.1 Autoregressive Modeling of Sea Clutter ........... 189
5.7.2 Cyclostationarity of Sea Clutter ................. 189
References ................................................. 189
6. Two New Strategies for Target Detection in Sea Clutter ..... 193
Rembrandt Bakker, Brian Currie, and Simon Haykin
6.1 Introduction ........................................... 193
6.2 Bayesian Direct Filtering Procedure .................... 195
6.2.1 Single-Target Scenario ........................... 195
6.2.2 Conditioning on Past and Future Measurements ..... 196
6.3 Operational Details .................................... 197
6.3.1 Experimental Data ................................ 197
6.3.2 Statistics of Sea Clutter ........................ 197
6.3.3 Statistics of Target Returns ..................... 199
6.3.4 Motion Model of the Target ....................... 200
6.4 Experimental Results on the Bayesian Direct Filter ..... 200
6.5 Additional Notes on the Bayesian Direct Filter ......... 204
6.6 Correlation Anomally Detection Strategy ................ 205
6.7 Experimental Comparison of the Bayesian Direct Filter
and Correlation Anomaly Receiver ....................... 206
6.7.1 Target-to-interference Ratio ..................... 207
6.7.2 Receiver Comparison .............................. 207
6.8 Discussion ............................................. 217
6.8.1 Further Research ................................. 218
References ................................................. 219
Index ......................................................... 221
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