Preface ......................................................... x
1 Introduction ................................................. 1
1.1 Doppler Effect .......................................... 2
1.2 Relativistic Doppler Effect and Time Dilation ........... 4
1.3 Doppler Effect Observed in Radar ........................ 7
1.4 Estimation and Analysis of Doppler Frequency Shifts .... 10
1.5 Cramer-Rao Bound of the Doppler Frequency Estimation ... 17
1.6 The Micro-Doppler Effect ............................... 18
1.7 Micro-Doppler Effect Observed in Radar ................. 20
1.8 Estimation and Analysis of Micro-Doppler Frequency
Shifts ................................................. 20
1.8.1 Instantaneous Frequency Analysis ................ 21
1.8.2 Joint Time-Frequency Analysis ................... 23
1.9 The Micro-Doppler Signature of Objects ................. 26
References .................................................. 28
Appendix 1A ................................................. 32
MATLAB Source Codes ......................................... 32
2 Basics of the Micro-Doppler Effect in Radar ................. 35
2.1 Rigid Body Motion ...................................... 35
2.1.1 Euler Angles .................................... 36
2.1.2 Quaternion ...................................... 42
2.1.3 Equations of Motion ............................. 44
2.2 Nonrigid Body Motion ................................... 47
2.3 Electromagnetic Scattering from a Body with Motion ..... 50
2.3.1 Radar Cross Section of a Target ................. 50
2.3.2 RCS Prediction Methods .......................... 53
2.3.3 EM Scattering from a Body with Motion ........... 54
2.4 Basic Mathematics for Calculating the Micro-Doppler
Effect ................................................. 56
2.4.1 Micro-Doppler Induced by a Target with Micro
Motion .......................................... 56
2.4.2 Vibration-Induced Micro-Doppler Shift ........... 60
2.4.3 Rotation-Induced Micro-Doppler Shift ............ 63
2.4.4 Coning Motion-Induced Micro-Doppler Shift ....... 66
2.5 Bistatic Micro-Doppler Effect .......................... 71
2.6 Multistatic Micro-Doppler Effect ....................... 77
2.7 Cramer-Rao Bound of the Micro-Doppler Estimation ....... 79
References .................................................. 79
Appendix 2A ................................................. 81
Appendix 2B ................................................. 83
MATLAB Source Codes ......................................... 83
3 The Micro-Doppler Effect of the Rigid Body Motion ........... 93
3.1 Pendulum Oscillation ................................... 94
3.1.1 Modeling Nonlinear Motion Dynamic of a
Pendulum ........................................ 95
3.1.2 Modeling RCS of a Pendulum ..................... 101
3.1.3 Radar Backscattering from an Oscillating
Pendulum ....................................... 102
3.1.4 Micro-Doppler Signatures Generated by an
Oscillating Pendulum ........................... 105
3.2 Helicopter Rotor Blades ............................... 105
3.2.1 Mathematic Model of Rotating Rotor Blades ...... 107
3.2.2 RCS Model of Rotating Rotor Blades ............. 112
3.2.3 PO Facet Prediction Model ...................... 114
3.2.4 Radar Backscattering from Rotor Blades ......... 116
3.2.5 Micro-Doppler Signatures of Rotor Blades ....... 120
3.2.4 Required Minimum PRF ........................... 123
3.2.5 Analysis and Interpretation of the Micro-
Doppler Signature of Rotor Blades .............. 123
3.3 Spinning Symmetric Top ................................ 127
3.3.1 Force-Free Rotation of a Symmetric Top ......... 130
3.3.2 Torque-Induced Rotation of a Symmetric Top ..... 132
3.3.3 RCS Model of a Symmetric Top ................... 133
3.3.4 Radar Backscattering from a Symmetric Top ...... 135
3.3.5 Micro-Doppler Signatures Generated by a
Precession Top ................................. 136
3.3.6 Analysis and Interpretation of the Micro-
Doppler Signature of a Precession Top .......... 136
3.4 Wind Turbines ......................................... 139
3.4.1 Micro-Doppler Signatures of Wind Turbines ...... 140
3.4.2 Analysis and Interpretation of the Micro-
Doppler Signature of Wind Turbines ............. 140
References ................................................. 141
Appendix 3А ................................................ 143
MATLAB Source Codes ........................................ 143
4 The Micro-Doppler Effect of the Nonrigid Body Motion ....... 157
4.1 Human Body Articulated Motion ......................... 159
4.1.1 Human Walking .................................. 159
4.1.2 Description of the Periodic Motion of Human
Walking ........................................ 161
4.1.3 Simulation of Human Movements .................. 162
4.1.4 Human Body Segment Parameters .................. 162
4.1.5 Human Walking Model Derived from Empirical
Mathematical Parameterizations ................. 164
4.1.6 Capturing Human Motion Kinematic Parameters .... 177
4.1.7 Three-Dimensional Kinematic Data Collection .... 182
4.1.8 Characteristics of Angular Kinematics Using
the Angle-Cyclogram Pattern .................... 184
4.1.9 Radar Backscattering from a Walking Human ...... 184
4.1.10 Human Movement Data Processing ................. 187
4.1.11 Human Movement-Induced Radar Micro-Doppler
Signatures ..................................... 189
4.2 Bird Wing Flapping .................................... 194
4.2.1 Bird Wing Flapping Kinematics .................. 195
4.2.2 Doppler Observations of the Bird Wing
Flapping ....................................... 198
4.2.3 Simulation of the Bird Wing Flapping ........... 199
4.3 Quadrupedal Animal Motion ............................. 202
4.3.1 Modeling of Quadrupedal Locomotion ............. 204
4.3.2 Micro-Doppler Signatures of Quadrupedal
Locomotion ..................................... 205
4.3.3 Summary ........................................ 205
References ................................................. 207
Appendix 4A ................................................ 209
MATLAB Source Codes ........................................ 209
Appendix 4B ................................................ 238
MATLAB Source Codes ........................................ 238
5 Analysis and Interpretation of Micro-Doppler Signatures .... 247
5.1 Biological Motion Perception .......................... 248
5.2 Decomposition of Biological Motion .................... 250
5.2.1 Statistics-Based Decomposition ................. 251
5.2.2 Decomposition of Micro-Doppler Signatures in
the Joint Time-Frequency Domain ................ 251
5.2.3 Physical Component-Based Decomposition ......... 252
5.3 Extraction of Features from Micro-Doppler
Signatures ............................................ 256
5.4 Estimation of Kinematic Parameters from Micro-
Doppler Signatures .................................... 257
5.5 Identifying Human Movements ........................... 262
5.5.1 Features Used for Identifying Human Movements .. 263
5.5.2 Anomalous Human Behavior ....................... 264
5.5.3 Summary ........................................ 266
References ................................................. 267
6 Summary, Challenges, and Perspectives ...................... 271
6.1 Summary ............................................... 271
6.2 Challenges ............................................ 272
6.2.1 Decomposing Micro-Doppler Signatures ........... 273
6.2.2 Feature Extraction and Target Identification
Based on Micro-Doppler Signatures .............. 273
6.3 Perspectives .......................................... 275
6.3.1 Multistatic Micro-Doppler Analysis ............. 275
6.3.2 Micro-Doppler Signature-Based Classification ... 276
6.3.3 Aural Methods for Micro-Doppler-Based
Discrimination ................................. 276
6.3.4 Through-the-Wall Micro-Doppler Signatures ...... 277
References ................................................. 278
About the Author .............................................. 281
Index ......................................................... 283
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