Space Based Radar: Theory & Applications Book

Preface     ix
List of Abbreviations     xiii
Introduction     1
Overview     3
The Radar Equation     7
Notations and Matrix Identities     9
Eigenvalues and Eigenvectors     10
Hermitian Matrices     12
Singular Value Decomposition (SVD)     16
Schur, Kronecker, and Khatri-Rao Products     17
Matrix Inversion Lemmas     25
Line Spectra and Singular Covariance Matrices     26
References     28
The Conics     31
What Is a Conic?     31
Ellipse     33
Parabola     39
Hyperbola     40
The Solar System     44
Spherical Triangles     46
References     50
Two Body Orbital Motion and Kepler's Laws     51
Orbital Mechanics     51
The Motion of the Center of Mass     52
Equations of Relative Motion     54
Kepler's Laws     57
Synchronous and Polar Orbits     60
Satellite Velocity     61
Kepler's Equation     67
Euler's Equation and the Identification of Comets     71
Lambert's Equation for Elliptic Orbits     74
References     76
Space Based Radar-Kinematics     77
Radar-Earth Geometry     77
Maximum Range on Earth     81
Mainbeam Footprint Size     83
Packing of Mainbeam Footprints     86
Range Foldover Phenomenon     90
Mainbeam Foldover     90
Total Range Foldover     94
Doppler Shift     97
Crab Angle and Crab Magnitude: Modeling Earth's Rotation for SBR     101
Range Foldover and Crab Phenomenon     118
Ground Range from Latitude and Longitude Coordinates     121
Nonsphericity of Earth and the Grazing Angle Correction Factor     123
Doppler Effect     130
Oblate Spheroidal Earth and Crab Angle Correction     134
References     137
Space-Time Adaptive Processing     139
Spatial Array Processing     139
Why Use an Array?     140
Maximization of Output SNR     148
Space-Time Adaptive Processing     153
Side-Looking Airborne Radar     155
Minimum Detectable Velocity (MDV)     162
Sample Matrix Inversion (SMI)     162
Sample Matrix with Digonal Loading (SMIDL)     165
Eigen-Structure Based STAP     165
Brennan's Rule     166
Eigencanceler Methods     167
Hung-Turner Projection (HTP)     171
Subaperture Smoothing Methods     173
Subarray Smoothing     177
Subaperture Smoothing Methods for STAP     183
Subarray Method     183
Subpulse Method     184
Subarry-Subpluse Method     184
Array Tapering and Covariance Matrix Tapering     188
Diagonal Loading as Tapering     192
Convex Projection Techniques     194
Convex Sets     195
Toeplitz Property     196
Positive-Definite Property     197
Methods of Alternating Projections     198
Relaxed Projection Operators     200
Factor Time-Space Approach     201
Joint-Domain Localized Approach     205
Uniform Array Sidelobe Levels     208
References     213
STAP for SBR     215
SBR Data Modeling     216
Mainbeam and Sidelobe Clutter     218
Ideal Clutter Spectrum     223
Minimum Detectable Velocity (MDV)     232
MDV with Earth's Rotation and Range Foldover     234
Range Foldover Minimization Using Orthogonal Pulsing     246
Scatter Return Modeling     255
Terrain Modeling     256
ICM Modeling     261
MDV with Terrain Modeling and Wind Effect     268
Effect of Wind on Doppler     270
General Theory of Wind Damping Effect on Doppler     275
Joint Effect of Terrain, Wind, Range Foldover, and Earth's Rotation on Performance     280
STAP Algorithms for SBR     283
Matrix Inversion Identity     296
Output SINR Derivation     297
Spectral Factorization     298
Rational System Representation     303
References     307
Performance Analysis Using Cramer-Rao Bounds     309
Cramer-Rao Bounds for Multiparameter Case     309
Cramer-Rao Bounds for Target Doppler and Power in Airborne and SBR Cases     320
Simulation Results     331
References     338
Waveform Diversity     341
Matched Filter Receivers     344
Matched Filter Receivers in White Noise     346
Matched Filter Receivers in Colored Noise     353
Chirp and Pulse Compression      358
Joint Transmitter-Receiver Design in Noise     364
Joint Time Bandwidth Optimization     376
Transform of a Chirp Signal     385
References     391
Advanced Topics     393
An Infinitesimal Body Around Two Finite Bodies     394
Particular Solutions of the Three-Body Problem     401
Stability of the Particular Solutions     405
Stability of Linear Solutions     409
Stability of Equilateral Solutions     412
Hill Sphere     417
References     420
Index     421