 | Doring B.J. Traceable radiometric calibration of synthetic aperture radars: Diss. … Dr.-Ing. / Deutsches Zentrum für Luft- und Raumfahrt, Institut für Hochfrequenztechnik und Radarsysteme, Oberpfaffenhofen. - Köln: DLR, 2016. - viii, 200 p.: ill., tab. - (Forschungsbericht; 2016-13). - Res. also Germ. - Bibliogr.: p. 187-200. - ISSN 1434-8454
Шифр: (Pr 1120/2016-13) 02
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1 Introduction ............................................... 1
1.1 State of the Art in Radiometric SAR Calibration ............ 2
1.2 Problem Statement .......................................... 4
1.3 Contributions and Thesis Structure ......................... 5
2 Fundamentals of SAR and Calibration ........................ 7
2.1 Synthetic Aperture Radar Principles ........................ 7
2.1.1 Image Formation for Point Targets ................... 7
2.1.2 Imaging Geometries ................................. 10
2.1.3 The Range-Doppler Algorithm ........................ 11
2.1.4 Distributed Targets ................................ 13
2.2 Measurement, Calibration, and Traceability Principles ..... 14
2.2.1 Measurements and Measurement Quantities ........... 14
2.2.2 The Guide to the Evaluation of Uncertainty in
Measurement ....................................... 15
2.2.3 Calibration ....................................... 19
2.2.4 Metrological Traceability ......................... 20
2.3 Fundamentals of Radiometric SAR Calibration ............... 21
2.3.1 Influences on Radiometric Measurements and
General Calibration Approach ....................... 21
2.3.2 Terminology in SAR Calibration ..................... 24
2.3.3 The Integral Method for Radiometrically
Calibrating Distributed Targets .................... 24
2.4 Typical SAR Calibration Point Targets and Properties ...... 28
2.4.1 Point Target Properties ............................ 29
2.4.2 Trihedral Corner Reflectors ........................ 30
2.4.3 Transponders ....................................... 33
2.4.4 Other Passive Calibration Point Targets ............ 37
3 Novel Definition of the Radiometric Measurement Quantity .. 45
3.1 Introduction .............................................. 45
3.2 Review of the Current Definition .......................... 46
3.3 Problems Arising from the Current Definition .............. 47
3.3.1 Pulse Compression in the Complex Domain ............ 47
3.3.2 Integration Intervals and Weighted Means:
Qualitative Examples ............................... 48
3.4 Novel Definition of the Radiometric Measurement Quantity .. 51
3.5 Implications of Proposed Terminology for Calibration ...... 52
3.6 Discussion of Novel Quantity .............................. 54
3.7 Conclusions ............................................... 55
4 Novel Method for Relating Point Target Properties to
ERCS ...................................................... 57
4.1 Motivation and Principle .................................. 57
4.2 Implementation of the Point Target SAR Simulator .......... 60
4.3 Quantitative Analyses: Link Between Target Properties
and ERCS .................................................. 61
4.3.1 RCS Dependence on Frequency and Angle:
Calibration Transponder ............................ 61
4.3.2 Frequency-Dependent Phase Response: Ionosphere ..... 67
4.4 Discussion ................................................ 69
4.5 Conclusions ............................................... 69
5 The SAR Passband Problem: Analytical Model and Practical
Solutions ................................................. 71
5.1 Introduction and Example .................................. 71
5.2 Apodization Functions in SAR Processing ................... 74
5.3 Modeling Passband Effects with Central Moments ............ 75
5.3.1 Derivation of the Governing Equation ............... 77
5.3.2 Modeling with Central Moments: One-Dimensional
Case ............................................... 78
5.3.3 Extension to the Two-Dimensional Case .............. 80
5.4 Quantitative Examples and Verification .................... 82
5.5 Resolving the Passband Problem ............................ 89
5.5.1 Accepting Higher Radiometric Uncertainties ......... 89
5.5.2 Introducing Standardized Passbands ................. 89
5.5.3 Conversion Between Different Scales ................ 90
5.6 Conclusions ............................................... 91
6 The Three-Transponder Method .............................. 93
6.1 Introduction .............................................. 93
6.2 Existing Approaches for Measuring the Transponder RCS ..... 94
6.2.1 Measuring the Loop Gain ............................ 94
6.2.2 The Substitution Method ............................ 95
6.2.3 The Transponder as a Radar Instrument .............. 96
6.3 The Three-Transponder Method Principle .................... 97
6.3.1 The Three Antenna Method .......................... 98
6.3.2 Prerequisites on Transponder Design ................ 99
6.3.3 System of Linear Equations ......................... 99
6.3.4 Random Variables, 3TM Equations, and GUM .......... 101
6.3.5 The Maximum-Likelihood versus the James-Stein
Estimator ......................................... 104
6.4 Demonstration Measurement Campaign with DLR's C-Band
Transponders ............................................. 110
6.4.1 Measurement Setup ................................. 110
6.4.2 Measurement Data Analysis ......................... 113
6.4.3 Uncertainty Analysis and Results .................. 119
6.4.4 Discussion of Measurement Results ................. 123
6.5 Method Extension for an Inherent Plausibility Check ...... 124
6.5.1 Description of the 3TM Method Extension ........... 124
6.5.2 Formulation of Hypothesis Test - Gaussian
Distributions ..................................... 125
6.5.3 Derivation of Hypothesis Rejection Conditions ..... 127
6.5.4 Practical Implications and Conclusions ............ 129
6.6 Discussions of the Three-Transponder Method .............. 129
6.6.1 Advantages ........................................ 129
6.6.2 Limitations ....................................... 130
6.6.3 Open Points ....................................... 130
6.7 Conclusions .............................................. 131
7 Derivation of Calibration Parameters Through
Hierarchical Bayesian Data Analysis ...................... 133
7.1 Introduction ............................................. 133
7.2 Methodology for Radiometric Parameter Estimation from
SAR Data Through Bayesian Statistics ..................... 135
7.2.1 Hierarchical Models ............................... 135
7.2.2 Summary of Method ................................. 137
7.3 Case Study: Measurement Campaign Goal and Setup .......... 138
7.3.1 Introduction and Goal ............................. 138
7.3.2 Campaign Setup and Reference Targets .............. 138
7.4 Case Study: Data Analysis and Results .................... 139
7.4.1 Overview .......................................... 140
7.4.2 Energy Estimation for Point Targets from SAR
Images ............................................ 140
7.4.3 Bayesian Statistics and Hierarchical Model
Fitting ........................................... 141
7.4.4 Posterior Predictive Checks: Model Verification ... 149
7.4.5 Plausibility Check with Classical Statistics ...... 149
7.5 Discussion of Hierarchical Bayesian Data Analysis for
Radiometric Calibration .................................. 150
7.6 Conclusions ......................................... 151
8 Conclusions and Outlook ................................... 153
A Pseudo Code for the Method of Point Target SAR
Simulation ............................................... 157
В Functions of Random Variables ............................ 161
B.l Moments of Functions of Random Variables ................. 161
B.2 Sum and Subtraction of Two Random Variables .............. 164
B.4 Multiplication of Random Variables ....................... 167
С Introduction to Bayesian Statistics and to the Markov
Chain Monte Carlo Method ................................. 169
C.l Bayesian Statistics ...................................... 169
C.2 Bayesian Computations and Markov Chain Monte Carlo
Methods .................................................. 170
Glossary ...................................................... 173
Acronyms ...................................................... 175
Notation ...................................................... 179
Symbols and Notational Conventions ............................ 179
Greek Letters ................................................. 179
Roman Letters ................................................. 181
Bibliography .................................................. 187
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