Mission design and verification of multi-static SAR formation flying system for very-high-resolution strip-map imaging

다국어 초록 (Multilingual Abstract)

This study involved the development of a multi-static synthetic aperture radar (SAR) formation flying system capable of acquiring very-high-resolution (0.5~1 m) SAR images in strip-map mode with continuous SAR imaging using microscale SAR satellites with reasonable specifications. This required the specifications of the formation flying system, such as the number of satellites and the shape of the formation, to the determined such that very-high-resolution strip-map imaging (VHRSI) is possible. Moreover, autonomous relative orbit and attitude control algorithms for the operation of a multi-static SAR formation flying system are designed. Finally, SAR imaging simulations are conducted to verify that the multi-static SAR system delivers very-high-resolution SAR images.
Based on the spatial resolution theory of the SAR image, the synthetic aperture length that would result in submeter-level resolution is calculated. Subsequently, the baseline and the number of satellites in the multi-static SAR formation flying system are determined such that they correspond with the obtained synthetic aperture length for the strip map mode. This mode enables a large area to be observed owing to its continuous imaging capability. Implementation of the autonomous orbit and attitude control algorithms in the multi-satellite system for real-time in-flight operation is effective because it reduces the workload of ground station and increases the efficiency of mission operations. Therefore, an autonomous relative orbit control algorithm was designed to maintain the multi-static SAR formation for VHRSI using the relative orbital elements. Furthermore, an autonomous attitude control algorithm reflecting the concept of the optimal right ascension of the descending node (RADN) sector was developed to perform multi-static SAR imaging. Finally, the resolution enhancement of VHRSI was verified by multi-static SAR imaging simulation that reflects the orbit and attitude control errors due to the designed autonomous relative orbit and attitude control algorithms. The effects of navigation and attitude errors on multi-static SAR images were analyzed by conducting multi-static SAR imaging simulations that reflect the various navigation and pointing errors. This analysis establishes the requirements for the navigation and attitude error components for very-high-resolution imaging.
The multi-static SAR formation flying system for VHRSI comprises three satellites that are separated by 7.5 km from each other in the along-track direction. The autonomous relative orbit control simulation verifies that the relative position error is maintained within 45 m (3σ). Additionally, it was verified that the autonomous attitude control algorithm performs the attitude maneuvers required in each operation mode and maintains the pointing error within 0.0035˚ (3σ). The spatial resolution of the SAR images obtained by imaging simulations of the multi-static SAR formation flying system for VHRSI is 0.95 × 0.96 m, which meets the very-high resolution requirement. Furthermore, the navigation and posture error requirements for the images of this multi-static SAR system to meet the very-high-resolution condition are as follows: absolute orbit determination error ≤ 10 m, relative orbit determination error ≤ 1 m, –200 ≤ relative orbit control error ≤ +1500 m, and attitude control error ≤ 0.02 degrees.
To the best of my knowledge, this is the first multi-static SAR formation flying system for VHRSI to be presented. None of the SAR satellites currently in operation are able to produce very-high-resolution SAR images in strip-map mode, which enables continuous imaging with a wide swath width. Through this study, it became possible to design a multi-static SAR formation flying system that can perform very-high-resolution SAR imaging in the strip-map mode. Furthermore, an autonomous attitude control algorithm applying the optimal RADN sector concept was designed for efficient mission performance of multi-static SAR satellites. This autonomous attitude control algorithm can accurately control the attitude of multiple SAR satellites without many ground stations.
The multi-static SAR formation flying system can be applied to SAR satellites currently in operation by adding inexpensive receive-only SAR microsatellites. This would allow the multi-static SAR formation flying system for VHRSI to greatly increase the observation area for very-high-resolution imaging. Additionally, the autonomous attitude control algorithm developed in this study can be used for various Earth observation missions as well as multi-static SAR missions.

목차 (Table of Contents)

• Contents i
• List of Figures iv
• List of Tables vii
• Abstract viii
• Chapter 1 Introduction 1
• 1.1 Research background 1
• 1.2 Objectives of research 7
• 1.3 Contributions 9
• 1.4 Outlines of dissertation 13
• Chapter 2 Methodology 14
• 2.1 Coordinate system 14
• 2.1.1 Earth-Centered Inertial (ECI) frame 14
• 2.1.2 Local orbital frame (RTN frame) 15
• 2.1.3 Body-fixed frame 16
• 2.2 Optimal RADN (RADNop) sector 17
• 2.2.1 Calculation of RADNop using the geometric method 17
• 2.2.2 Calculation of the precise RADNop using a numerical method 21
• 2.3 Resolution of SAR image 22
• 2.4 Operation modes of spaceborne SAR 28
• 2.4.1 Strip-map mode 25
• 2.4.2 Spot-light mode 26
• 2.4.3 Scan mode 27
• 2.5 Impulse response function (IRF) 28
• 2.6 Polar format algorithm (PFA) 29
• Chapter 3 Preliminary design of a multi-static SAR formation for VHRSI 33
• 3.1 Top-level requirements of multi-static SAR system 33
• 3.2 Resolution enhancement strategy using multiple SAR satellites 34
• 3.3 Formation design of multi-static SAR satellites for VHRSI 36
• Chapter 4 Design of the autonomous relative orbit control algorithm 40
• 4.1 Objectives of the autonomous relative orbit control 40
• 4.2 Performance analysis of a COTS thruster 41
• 4.3 Relative orbit control to maintain along-track formation 43
• 4.3.1 Calculation of the mean relative orbital elements (step 1,2,3 in Figure 4.2) 44
• 4.3.2 Calculation of the control value of relative eccentricity and inclination (∆δe and ∆δi) for desired relative orbit motion (step 4 in Figure 4.2) 46
• 4.3.3 Calculations of the control value of the relative semi-major axis (∆δa) to maintain the desired relative mean argument of latitude δu (step 5, 6 in Figure 4.2) 49
• 4.3.4 Calculation of control parameters ∆vT,uMT,∆vN,uMN (step 6 in Figure 4.2) 50
• 4.4 Relative orbit control simulations for formation maintenance 52
• Chapter 5 Design of the autonomous attitude control algorithm 63
• 5.1 Objectives of autonomous attitude control 63
• 5.2 Concept of the optimal RADN (RADNop) sectors 64
• 5.3 Attitude control strategy for multi-static SAR imaging 67
• 5.4 Design of the attitude control algorithm 68
• 5.5 Modeling of the four-axis reaction wheel with a pyramid structure 70
• 5.6 Numerical simulations of the autonomous attitude control 73
• Chapter 6 Multi-static SAR image analysis 80
• 6.1 Objectives of multi-static SAR image analysis 80
• 6.2 SAR image analysis of the preliminary designed multi-static SAR system 82
• 6.2.1 Case of the designed orbit path (without errors) 83
• 6.2.2 Case of the perturbed orbit path (with errors) 85
• 6.2.3 Analysis of imaged target separation phenomenon 86
• 6.2.4 Perturbed orbit case with phase-correction algorithm applied 88
• 6.3 Design change for multi-static SAR formation to satisfy spatial resolution requirement 89
• 6.4 Analysis of the navigation and beam pointing errors effects on multi-static SAR image 93
• 6.4.1 SAR image analysis according to relative orbit determination error 94
• 6.4.2 SAR image analysis according to relative orbit control error 95
• 6.4.3 SAR image analysis according to the absolute orbit determination and attitude control errors 96
• 6.5 Performance verification of the multi-static SAR system for VHRSI through near-multi-target imaging simulation 97
• Chapter 7 Conclusions 99
• 7.1 Summary 99
• 7.2 Discussion 103
• 7.3 Future works 104
• References 106
• 국문 요약 112

참고문헌 (Reference)

1. Reaction wheel performance, NEWSPACE SYSTEMS. com, Available online https://www. newspacesystems. com/wp-content/uploads/2022/07/NewSpace-Reaction-Wheel_V11.2. pdf/accessed on, , 2022

2. Navigation and control of the TanDEM-X formation, D’Amico, S., Kahle, R., Ardaens, J. S., Montenbruck, O., 56, 341–357. https://doi. org/10.1007/BF03256557, , 2008

3. Overview of the TECSAR satellite hardware and mosaic mode, Naftaly, U., Levy-Nathansohn, R., 5, 423–426. https://doi. org/10.1109/LGRS.2008.915926, , 2008

4. An adaptive ship detection scheme for spaceborne SAR imagery, Leng, X., Zhou, S., Xing, X., Zou, H., Ji, K., 16, 1345. https://doi. org/10.3390/s16091345, , 2016

5. Review article SAR interferometry-issues, techniques, applications, Van Genderen J. L., Gens, R., 17, 1803–1835. https://doi. org/10.1080/01431169608948741, , 1996

6. Azimuth migration-corrected phase gradient autofocus for bistatic SAR polar format imaging, Miao, Y., Wu, J., Yang, J., 18, 697–701. https://doi: 10.1109/LGRS.2020.2984909, , 2020

7. Small-satellite synthetic aperture radar for continuous global biospheric monitoring: A review, Balasubramanian, S., de Weck, O., Kim, S., Paek, S. W., 12, 2546. https://doi. org/10.3390/rs12162546, , 2020

8. Thermal design and analysis of unfurlable CFRP skin based parabolic reflector for spaceborne SAR antenna, Kim, S. Y., Yi, D. W., Oh, H. U., Yun, J. H., Park, T. Y., Lee, J. E., Jung, H. Y., 22, 433–444. https://doi. org/10.1007/s42405-020-00301-7., , 2021