### A Primer for Applied Mathematicians and Physicists

### A Primer for Applied Mathematicians and Physicists

#### Get Citation

Radar-based imaging of aircraft targets is a topic that continues to attract a lot of attention, particularly since these imaging methods have been recognized to be the foundation of any successful all-weather non-cooperative target identification technique. Traditional books in this area look at the topic from a radar engineering point of view. Consequently, the basic issues associated with model error and image interpretation are usually not addressed in any substantive fashion. Moreover, applied mathematicians frequently find it difficult to read the radar engineering literature because it is jargon-laden and device specific, meaning that the skills most applicable to the problem's solution are rarely applied.

Enabling an understanding of the subject and its current mathematical research issues, Radar Imaging of Airborne Targets: A Primer for Applied Mathematicians and Physicists presents the issues and techniques associated with radar imaging from a mathematical point of view rather than from an instrumentation perspective. The book concentrates on scattering issues, the inverse scattering problem, and the approximations that are usually made by practical algorithm developers. The author also explains the consequences of these approximations to the resultant radar image and its interpretation, and examines methods for reducing model-based error.

PREFACE

INTRODUCTION

Brief History of Radar

Contemporary Issues in Radar Imaging

Overview

RADAR FUNDAMENTALS

Radar Signals

Radiation Condition

The Radar Equation

Atmospheric Windows

Radar Data

The Ambiguity Function

Radar Measurement Systems

SCATTERING MODELS

The Magnetic Field Integral Equation for a Perfect Conductor

The Weak Scatterer and High-Frequency Limits

Dielectric Scatterers

The (Approximate) Radar Scattering Model

ONE-DIMENSIONAL IMAGING

Range Profiles

Ill-Posed Problems and Regularization

Resolution Improvement Methods

Bayesian Methods

Model-Based Resolution Improvement

TWO-DIMENSIONAL IMAGING

The Basic Imaging Equation

Data Errors

Resolution Improvement

Signal Diversity Radar

MODEL ERRORS AND THEIR EFFECTS

Template-Based ATR

Unresolved Scatterers and Scintillation

Non-Weak and Dispersive Scatterers

Corrective PSF

Ducts and Cavities

THREE-DIMENSIONAL IMAGING

Angle Tracking, Scintillation and Glint

Angle-of-Arrival Imaging

High-Frequency Zeros

Statistical Methods

OTHER METHODS

Resonant-Frequency Poles

Polarization

Target Structure-Induced Modulations

Wide Band Radar

Future Efforts

APPENDIX: ILL-POSED PROBLEMS

Compactness of a Set and Compact Operators

Singular Value Decomposition

Least-Squares Solutions and Ill-Posedness

BIBLIOGRAPHY

INDEX

Each chapter contains References.

Radar-based imaging of aircraft targets is a topic that continues to attract a lot of attention, particularly since these imaging methods have been recognized to be the foundation of any successful all-weather non-cooperative target identification technique. Traditional books in this area look at the topic from a radar engineering point of view. Consequently, the basic issues associated with model error and image interpretation are usually not addressed in any substantive fashion. Moreover, applied mathematicians frequently find it difficult to read the radar engineering literature because it is jargon-laden and device specific, meaning that the skills most applicable to the problem's solution are rarely applied.

Enabling an understanding of the subject and its current mathematical research issues, Radar Imaging of Airborne Targets: A Primer for Applied Mathematicians and Physicists presents the issues and techniques associated with radar imaging from a mathematical point of view rather than from an instrumentation perspective. The book concentrates on scattering issues, the inverse scattering problem, and the approximations that are usually made by practical algorithm developers. The author also explains the consequences of these approximations to the resultant radar image and its interpretation, and examines methods for reducing model-based error.

PREFACE

INTRODUCTION

Brief History of Radar

Contemporary Issues in Radar Imaging

Overview

RADAR FUNDAMENTALS

Radar Signals

Radiation Condition

The Radar Equation

Atmospheric Windows

Radar Data

The Ambiguity Function

Radar Measurement Systems

SCATTERING MODELS

The Magnetic Field Integral Equation for a Perfect Conductor

The Weak Scatterer and High-Frequency Limits

Dielectric Scatterers

The (Approximate) Radar Scattering Model

ONE-DIMENSIONAL IMAGING

Range Profiles

Ill-Posed Problems and Regularization

Resolution Improvement Methods

Bayesian Methods

Model-Based Resolution Improvement

TWO-DIMENSIONAL IMAGING

The Basic Imaging Equation

Data Errors

Resolution Improvement

Signal Diversity Radar

MODEL ERRORS AND THEIR EFFECTS

Template-Based ATR

Unresolved Scatterers and Scintillation

Non-Weak and Dispersive Scatterers

Corrective PSF

Ducts and Cavities

THREE-DIMENSIONAL IMAGING

Angle Tracking, Scintillation and Glint

Angle-of-Arrival Imaging

High-Frequency Zeros

Statistical Methods

OTHER METHODS

Resonant-Frequency Poles

Polarization

Target Structure-Induced Modulations

Wide Band Radar

Future Efforts

APPENDIX: ILL-POSED PROBLEMS

Compactness of a Set and Compact Operators

Singular Value Decomposition

Least-Squares Solutions and Ill-Posedness

BIBLIOGRAPHY

INDEX

Each chapter contains References.

Radar-based imaging of aircraft targets is a topic that continues to attract a lot of attention, particularly since these imaging methods have been recognized to be the foundation of any successful all-weather non-cooperative target identification technique. Traditional books in this area look at the topic from a radar engineering point of view. Consequently, the basic issues associated with model error and image interpretation are usually not addressed in any substantive fashion. Moreover, applied mathematicians frequently find it difficult to read the radar engineering literature because it is jargon-laden and device specific, meaning that the skills most applicable to the problem's solution are rarely applied.

Enabling an understanding of the subject and its current mathematical research issues, Radar Imaging of Airborne Targets: A Primer for Applied Mathematicians and Physicists presents the issues and techniques associated with radar imaging from a mathematical point of view rather than from an instrumentation perspective. The book concentrates on scattering issues, the inverse scattering problem, and the approximations that are usually made by practical algorithm developers. The author also explains the consequences of these approximations to the resultant radar image and its interpretation, and examines methods for reducing model-based error.

PREFACE

INTRODUCTION

Brief History of Radar

Contemporary Issues in Radar Imaging

Overview

RADAR FUNDAMENTALS

Radar Signals

Radiation Condition

The Radar Equation

Atmospheric Windows

Radar Data

The Ambiguity Function

Radar Measurement Systems

SCATTERING MODELS

The Magnetic Field Integral Equation for a Perfect Conductor

The Weak Scatterer and High-Frequency Limits

Dielectric Scatterers

The (Approximate) Radar Scattering Model

ONE-DIMENSIONAL IMAGING

Range Profiles

Ill-Posed Problems and Regularization

Resolution Improvement Methods

Bayesian Methods

Model-Based Resolution Improvement

TWO-DIMENSIONAL IMAGING

The Basic Imaging Equation

Data Errors

Resolution Improvement

Signal Diversity Radar

MODEL ERRORS AND THEIR EFFECTS

Template-Based ATR

Unresolved Scatterers and Scintillation

Non-Weak and Dispersive Scatterers

Corrective PSF

Ducts and Cavities

THREE-DIMENSIONAL IMAGING

Angle Tracking, Scintillation and Glint

Angle-of-Arrival Imaging

High-Frequency Zeros

Statistical Methods

OTHER METHODS

Resonant-Frequency Poles

Polarization

Target Structure-Induced Modulations

Wide Band Radar

Future Efforts

APPENDIX: ILL-POSED PROBLEMS

Compactness of a Set and Compact Operators

Singular Value Decomposition

Least-Squares Solutions and Ill-Posedness

BIBLIOGRAPHY

INDEX

Each chapter contains References.

PREFACE

INTRODUCTION

Brief History of Radar

Contemporary Issues in Radar Imaging

Overview

RADAR FUNDAMENTALS

Radar Signals

Radiation Condition

The Radar Equation

Atmospheric Windows

Radar Data

The Ambiguity Function

Radar Measurement Systems

SCATTERING MODELS

The Magnetic Field Integral Equation for a Perfect Conductor

The Weak Scatterer and High-Frequency Limits

Dielectric Scatterers

The (Approximate) Radar Scattering Model

ONE-DIMENSIONAL IMAGING

Range Profiles

Ill-Posed Problems and Regularization

Resolution Improvement Methods

Bayesian Methods

Model-Based Resolution Improvement

TWO-DIMENSIONAL IMAGING

The Basic Imaging Equation

Data Errors

Resolution Improvement

Signal Diversity Radar

MODEL ERRORS AND THEIR EFFECTS

Template-Based ATR

Unresolved Scatterers and Scintillation

Non-Weak and Dispersive Scatterers

Corrective PSF

Ducts and Cavities

THREE-DIMENSIONAL IMAGING

Angle Tracking, Scintillation and Glint

Angle-of-Arrival Imaging

High-Frequency Zeros

Statistical Methods

OTHER METHODS

Resonant-Frequency Poles

Polarization

Target Structure-Induced Modulations

Wide Band Radar

Future Efforts

APPENDIX: ILL-POSED PROBLEMS

Compactness of a Set and Compact Operators

Singular Value Decomposition

Least-Squares Solutions and Ill-Posedness

BIBLIOGRAPHY

INDEX

Each chapter contains References.

PREFACE

INTRODUCTION

Brief History of Radar

Contemporary Issues in Radar Imaging

Overview

RADAR FUNDAMENTALS

Radar Signals

Radiation Condition

The Radar Equation

Atmospheric Windows

Radar Data

The Ambiguity Function

Radar Measurement Systems

SCATTERING MODELS

The Magnetic Field Integral Equation for a Perfect Conductor

The Weak Scatterer and High-Frequency Limits

Dielectric Scatterers

The (Approximate) Radar Scattering Model

ONE-DIMENSIONAL IMAGING

Range Profiles

Ill-Posed Problems and Regularization

Resolution Improvement Methods

Bayesian Methods

Model-Based Resolution Improvement

TWO-DIMENSIONAL IMAGING

The Basic Imaging Equation

Data Errors

Resolution Improvement

Signal Diversity Radar

MODEL ERRORS AND THEIR EFFECTS

Template-Based ATR

Unresolved Scatterers and Scintillation

Non-Weak and Dispersive Scatterers

Corrective PSF

Ducts and Cavities

THREE-DIMENSIONAL IMAGING

Angle Tracking, Scintillation and Glint

Angle-of-Arrival Imaging

High-Frequency Zeros

Statistical Methods

OTHER METHODS

Resonant-Frequency Poles

Polarization

Target Structure-Induced Modulations

Wide Band Radar

Future Efforts

APPENDIX: ILL-POSED PROBLEMS

Compactness of a Set and Compact Operators

Singular Value Decomposition

Least-Squares Solutions and Ill-Posedness

BIBLIOGRAPHY

INDEX

Each chapter contains References.

PREFACE

INTRODUCTION

Brief History of Radar

Contemporary Issues in Radar Imaging

Overview

RADAR FUNDAMENTALS

Radar Signals

Radiation Condition

The Radar Equation

Atmospheric Windows

Radar Data

The Ambiguity Function

Radar Measurement Systems

SCATTERING MODELS

The Magnetic Field Integral Equation for a Perfect Conductor

The Weak Scatterer and High-Frequency Limits

Dielectric Scatterers

The (Approximate) Radar Scattering Model

ONE-DIMENSIONAL IMAGING

Range Profiles

Ill-Posed Problems and Regularization

Resolution Improvement Methods

Bayesian Methods

Model-Based Resolution Improvement

TWO-DIMENSIONAL IMAGING

The Basic Imaging Equation

Data Errors

Resolution Improvement

Signal Diversity Radar

MODEL ERRORS AND THEIR EFFECTS

Template-Based ATR

Unresolved Scatterers and Scintillation

Non-Weak and Dispersive Scatterers

Corrective PSF

Ducts and Cavities

THREE-DIMENSIONAL IMAGING

Angle Tracking, Scintillation and Glint

Angle-of-Arrival Imaging

High-Frequency Zeros

Statistical Methods

OTHER METHODS

Resonant-Frequency Poles

Polarization

Target Structure-Induced Modulations

Wide Band Radar

Future Efforts

APPENDIX: ILL-POSED PROBLEMS

Compactness of a Set and Compact Operators

Singular Value Decomposition

Least-Squares Solutions and Ill-Posedness

BIBLIOGRAPHY

INDEX

Each chapter contains References.