Space Based Radar

Space Based Radar

Authors: S Pillai, Ke Yong Li and Braham Himed

Published: December 2007

eISBN: 9780071595926 0071595929 | ISBN: 9780071497565

Contents

Preface

List of Abbreviations

1 Introduction

1.1 Overview

1.2 The Radar Equation

1.3 Notations and Matrix Identities

1.3.1 Eigenvalues and Eigenvectors

1.3.2 Hermitian Matrices

1.3.3 Singular Value Decomposition (SVD)

1.3.4 Schur, Kronecker, and Khatri-Rao Products

1.3.5 Matrix Inversion Lemmas

Appendix 1-A: Line Spectra and Singular Covariance Matrices

References

2 The Conics

2.1 What Is a Conic?

2.1.1 Ellipse

2.1.2 Parabola

2.1.3 Hyperbola

2.2 The Solar System

Appendix 2-A: Spherical Triangles

References

3 Two Body Orbital Motion and Kepler’s Laws

3.1 Orbital Mechanics

3.1.1 The Motion of the Center of Mass

3.1.2 Equations of Relative Motion

3.2 Kepler’s Laws

3.3 Synchronous and Polar Orbits

3.4 Satellite Velocity

Appendix 3-A: Kepler’s Equation

Appendix 3-B: Euler’s Equation and the Identification of Comets

Appendix 3-C: Lambert’s Equation for Elliptic Orbits

References

4 Space Based Radar—Kinematics

4.1 Radar-Earth Geometry

4.2 Maximum Range on Earth

4.3 Mainbeam Footprint Size

4.4 Packing of Mainbeam Footprints

4.5 Range Foldover Phenomenon

4.5.1 Mainbeam Foldover

4.5.2 Total Range Foldover

4.6 Doppler Shift

4.7 Crab Angle and Crab Magnitude: Modeling Earth’s Rotation for SBR

4.7.1 Range Foldover and Crab Phenomenon

Appendix 4-A: Ground Range from Latitude and Longitude Coordinates

Appendix 4-B: Nonsphericity of Earth and the Grazing Angle Correction Factor

Appendix 4-C: Doppler Effect

Appendix 4-D: Oblate Spheroidal Earth and Crab Angle Correction

References

5 Space-Time Adaptive Processing

5.1 Spatial Array Processing

5.1.1 Why Use an Array?

5.1.2 Maximization of Output SNR

5.2 Space-Time Adaptive Processing

5.3 Side-Looking Airborne Radar

5.3.1 Minimum Detectable Velocity (MDV)

5.3.2 Sample Matrix Inversion (SMI)

5.3.3 Sample Matrix with Diagonal Loading (SMIDL)

5.4 Eigen-Structure Based STAP

5.4.1 Brennan’s Rule

5.4.2 Eigencanceler Methods

5.4.3 Hung-Turner Projection (HTP)

5.5 Subaperture Smoothing Methods

5.5.1 Subarray Smoothing

5.6 Subaperture Smoothing Methods for STAP

5.6.1 Subarray Method

5.6.2 Subpulse Method

5.6.3 Subarry-Subpluse Method

5.7 Array Tapering and Covariance Matrix Tapering

5.7.1 Diagonal Loading as Tapering

5.8 Convex Projection Techniques

5.8.1 Convex Sets

5.8.2 Toeplitz Property

5.8.3 Positive-Definite Property

5.8.4 Methods of Alternating Projections

5.8.5 Relaxed Projection Operators

5.9 Factor Time-Space Approach

5.10 Joint-Domain Localized Approach

Appendix 5-A: Uniform Array Sidelobe Levels

References

6 STAP for SBR

6.1 SBR Data Modeling

6.1.1 Mainbeam and Sidelobe Clutter

6.1.2 Ideal Clutter Spectrum

6.2 Minimum Detectable Velocity (MDV)

6.3 MDV with Earth’s Rotation and Range Foldover

6.4 Range Foldover Minimization Using Orthogonal Pulsing

6.5 Scatter Return Modeling

6.5.1 Terrain Modeling

6.5.2 ICM Modeling

6.6 MDV with Terrain Modeling and Wind Effect

6.6.1 Effect of Wind on Doppler

6.6.2 General Theory of Wind Damping Effect on Doppler

6.7 Joint Effect of Terrain, Wind, Range Foldover, and Earth’s Rotation on Performance

6.8 STAP Algorithms for SBR

Appendix 6-A: Matrix Inversion Identity

Appendix 6-B: Output SINR Derivation

Appendix 6-C: Spectral Factorization

Appendix 6-D: Rational System Representation

References

7 Performance Analysis Using Cramer-Rao Bounds

7.1 Cramer-Rao Bounds for Multiparameter Case

7.2 Cramer-Rao Bounds for Target Doppler and Power in Airborne and SBR Cases

7.3 Simulation Results

References

8 Waveform Diversity

8.1 Matched Filter Receivers

8.1.1 Matched Filter Receivers in White Noise

8.1.2 Matched Filter Receivers in Colored Noise

8.2 Chirp and Pulse Compression

8.3 Joint Transmitter–Receiver Design in Noise

8.4 Joint Time Bandwidth Optimization

Appendix 8-A: Transform of a Chirp Signal

References

9 Advanced Topics

9.1 An Infinitesimal Body Around Two Finite Bodies

9.1.1 Particular Solutions of the Three-Body Problem

9.1.2 Stability of the Particular Solutions

9.1.3 Stability of Linear Solutions

9.1.4 Stability of Equilateral Solutions

Appendix 9-A: Hill Sphere

References

Index