 | Kim Jun Su. Development of ionosphere estimation techniques for the correction of SAR data / Deutsches Zentrum für Luft- und Raumfahrt, Institut für Hochfrequenztechnik und Radarsysteme, Oberpfaffenhofen. - Köln: DLR, Bibliotheks- und Informationswesen, 2013. - xvii, 126, 5 p.: ill. - (Forschungsbericht; 2014-08). - Ref.: p.121-126. - ISSN 1434-8454
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Development of Ionosphere Estimation Techniques for the
Correction of SAR Data .......................................... i
Abstract ...................................................... iii
Zusammenfassung ................................................ iv
Acknowledgements ................................................ v
List of Tables ................................................. xi
List of Figures .............................................. xiii
List of Symbols and Acronyms ................................. xvii
Roman Symbols ................................................ xvii
Roman Symbol with Arial Font for Geometric Notation ........... xix
Greek Symbols ................................................. xix
Pre-defined functions, operators and distributions ............. xx
Fields ........................................................ xxi
Acronyms ...................................................... xxi
1 Introduction ................................................. 1
1.1 Background and Motivation ............................... 1
1.2 State of Art ............................................ 2
1.3 Objectives .............................................. 3
1.4 Synopsis ................................................ 4
2 SAR and InSAR ................................................ 5
2.1 Imaging Geometry ........................................ 5
2.2 Range Focusing .......................................... 6
2.2.1 Chirp Signal ..................................... 6
2.2.2 Convolution & Resolution ......................... 8
2.2.3 Sampling Rate .................................... 9
2.3 Azimuth Focusing ....................................... 10
2.3.1 Doppler Effect .................................. 10
2.3.2 Resolution and PRF .............................. 10
2.3.3 Modes of SAR Acquisition ........................ 11
2.4 SAR Interferometry ..................................... 11
2.4.1 Geometry of SAR Interferometry .................. 11
2.4.2 InSAR in the Frequency Domain ................... 13
2.4.3 Decorrelation ................................... 14
3 Polarimetry ................................................. 17
3.1 Transverse Wave ........................................ 17
3.2 Description of Polarimetry ............................. 18
3.2.1 Wave Polarimetry ................................ 18
3.2.2 Scattering Matrix ............................... 19
3.2.3 Basis and Transformations ....................... 20
3.2.4 Scattering Vector ............................... 21
3.2.5 Coherency/Covariance Matrix ..................... 22
3.3 Polarimetrie SAR Interferometry ........................ 23
4 Ionosphere .................................................. 25
4.1 Overview ............................................... 25
4.2 Variation of the Background Ionosphere ................. 26
4.2.1 Spatial Distribution ............................ 26
4.2.2 Temporal Pattern ................................ 28
4.3 Scintillation .......................................... 28
4.4 Magnetic Field ......................................... 29
4.5 Orbit .................................................. 29
5 Ionospheric Effects on SAR Images ........................... 31
5.1 Appleton-Hartree Equation .............................. 31
5.1.1 Equation of Motion .............................. 31
5.1.2 Index of Refraction ............................. 34
5.1.3 Eigenpolarisations .............................. 35
5.1.4 Characteristics of an Ionospheric Wave .......... 36
5.2 Attenuation ............................................ 37
5.3 Dispersion ............................................. 38
5.3.1 Phase and Group Velocities ...................... 38
5.3.2 Phase Advance ................................... 39
5.3.3 Group Delay ..................................... 39
5.3.4 Range Defocusing ................................ 40
5.3.5 Cross-Track TEC Gradient ........................ 40
5.4 Birefringence .......................................... 41
5.4.1 Faraday Rotation ................................ 41
5.4.2 Power Imbalance ................................. 43
5.4.3 Pol-InSAR ....................................... 43
5.5 Inhomogeneity .......................................... 44
5.5.1 Azimuth Shift ................................... 44
5.5.2 Scintillation ................................... 45
5.5.3 Ray-bending ..................................... 46
6 Data-level Correction Approaches ............................ 47
6.1 Correction of Faraday Rotation ......................... 47
6.1.1 Mathematical Background ......................... 47
6.1.2 Faraday Rotation Estimators ..................... 48
6.1.3 Performance Metrics and Analysis ................ 49
6.1.4 Faraday Rotation Estimation Performance ......... 51
6.1.5 Correction Results .............................. 56
6.1.6 Conclusions ..................................... 58
6.2 Correction of Interferometric Azimuth Shift ............ 59
6.2.1 Background ...................................... 59
6.2.2 Dataset ......................................... 60
6.2.3 Shift Estimation ................................ 61
6.2.4 Results of correction ........................... 63
6.2.5 Discussion and Conclusion ....................... 65
6.3 Interferometric Phase Correction Using Differential
FR ..................................................... 66
6.3.1 Faraday Rotation and Interferometric Phase ...... 66
6.3.2 Number of Looks ................................. 66
6.3.3 Correction of Interferometric Phase ............. 69
7 Correction of Scintillation ................................. 73
7.1 Scintillation Correction ............................... 73
7.1.1 P-band Airborne Data ............................ 73
7.1.2 Ionospheric Phase Screen ........................ 74
7.1.3 Ionospheric Disturbances ........................ 76
7.2 Correction Methodology ................................. 79
7.2.1 Faraday Rotation Estimation ..................... 79
7.2.2 Noise Modelling ................................. 80
7.2.3 TEC and Scintillation Phase Estimation .......... 83
7.2.4 Compensation with Partial Decompression ......... 83
7.2.5 Correlation Map ................................. 84
7.2.6 Effect of Ionospheric Altitude .................. 84
7.3 Results & Performance Analysis ......................... 85
7.3.1 Impact of the Number of Looks ................... 87
7.3.2 Impact of SNR ................................... 88
7.3.3 Impact of the Geomagnetic Latitude .............. 88
7.3.4 Standard Deviation of Correlations .............. 89
7.3.5 Conclusion ...................................... 90
7.4 Test with L-band Data .................................. 90
7.5 Discussion ............................................. 91
7.5.1 Estimation Window ............................... 91
7.5.2 Correction Criteria ............................. 93
8 Combined Estimator .......................................... 95
8.1 Model .................................................. 95
8.1.1 Differential Faraday Rotation ................... 96
8.1.2 Azimuth Shift ................................... 97
8.1.3 Equation Formation .............................. 97
8.2 Data & Model Covariance Matrices ....................... 98
8.2.1 Covariance of the Differential Faraday
Rotations ....................................... 98
8.2.2 Covariance of the Azimuth Shift Estimates ...... 100
8.2.3 Model Covariance Matrix ........................ 101
8.2.4 Building the 2-D TEC Map Equation .............. 101
8.3 Model-Level Correction ................................ 102
8.4 Results ............................................... 103
8.4.1 Coherence Improvement .......................... 104
8.4.2 Residual Interferometric Phase ................. 105
8.5 Discussion ............................................ 107
8.5.1 Balancing Data Covariance Matrices ............. 107
8.5.2 Epsilon Parameter .............................. 109
8.5.3 Ionospheric Altitude ........................... 109
8.6 Conclusion ............................................ 111
9 Altitude Estimation ........................................ 113
9.1 Simple Parallax ....................................... 113
9.2 Adaptive Focusing ..................................... 114
10 Conclusion ................................................. 117
10.1 Summary ............................................... 117
10.2 Contributions ......................................... 118
10.3 Future Work ........................................... 119
Reference ..................................................... 121
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