Range-Doppler-Time Tensor Processing for Deep-Space Satellite Characterization Using Narrowband Radar †
Abstract
:1. Introduction
- Development of a novel RDT tensor processing technique for deep-space satellite characterization
- Quantitative performance assessment of the RDT tensor processing technique considering the impact of key parameters on characterization performance
- Demonstration of extensions to the RDT tensor framework, including tensor denoising using the Higher-Order Singular Value Decomposition (HOSVD) to produce enhanced sensitivity images
2. Background on Radar Characterization of Space Objects
2.1. Radar Imaging Geometry
2.2. Radar-Return Signal Model
2.3. Compact-Range Satellite Model Case Study
2.4. Standard Radar-Characterization Processing
2.4.1. Range–Time Intensity (RTI)
2.4.2. Range–Doppler Map (RDM)
2.4.3. Inverse Synthetic Aperture Radar (ISAR) Imaging
2.4.4. Doppler–Time Intensity (DTI)
3. 3D Range-Doppler-time (RDT) Tensor Technique
3.1. Mathematical Description
3.2. Range and Doppler Superpulses
3.3. Compressed Trajectory Representation and Rank-Reducing Transform
3.4. Power-Sum Image Reconstruction
3.4.1. Relation to Doppler Tomography
3.4.2. Relation to Bandwidth Enhanced Non-Coherent Imaging (BENI)
4. Performance Assessment of RDT Tensor Processing
4.1. Influence of Rotation-Rate Estimate
4.2. Influence of Integration Time
4.3. Transient Features
4.4. Resolvability of Features
4.5. Dynamic Motion: Precession and Non-Uniform Rotation
4.6. Unfavorable Imaging Geometries
5. Extensions to the RDT Tensor Technique
5.1. Rotational-Rate Estimation
5.2. RDT Tensor Denoising Using Higher-Order Singular Value Decomposition (HOSVD)
6. Conclusions
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
Abbreviations
BENI | Bandwidth Enhanced Non-Coherent Imaging |
BWE | BandWidth Extrapolation |
DTI | Doppler-Time Intensity |
GEO | Geosynchronous Earth Orbit |
HOSVD | Higher-Order Singular Value Decomposition |
ISAR | Inverse Synthetic Aperture Radar |
LECP | Local Extended Coherent Processing |
LEO | Low Earth Orbit |
LOS | Line-Of-Sight |
MEO | Medium Earth Orbit |
RDM | Range–Doppler Map |
RDT | range-Doppler-time Tensor |
RTI | Range–Time Intensity |
SDA | Space Domain Awareness |
SVD | Singular Value Decomposition |
Appendix A. Notation and Terminology
Appendix A.1. Derivation of ISAR Imaging Expression
Angular velocity vector (rad/s) | |
Radar position relative to target center of mass (m) | |
3D scatterer (scattering element) position (m) | |
Complex-valued radar scattering reflectivity density | |
3D volumetric support of target | |
Radar line-of-sight unit vector | |
Cross-range axis unit vector | |
Tumble period (s) | |
Rotation rate (rad/s) | |
Tumble angle between line of sight and angular velocity (rad) | |
Relative range of scatterer at (m) | |
Range rate of scatterer at (m/s) | |
Phase history data of the received signal | |
Transmission frequency (Hz) | |
Baseband frequency (Hz) | |
Carrier frequency (Hz) | |
Wavelength (m) | |
B | Bandwidth (Hz) |
T | Integration interval (s) |
Integration angle (rad) | |
Center of k-th Doppler-processing interval (s) | |
Range resolution (m) | |
Doppler resolution (m/s) | |
Range–Time Intensity (RTI) | |
Range–Doppler Map (RDM) | |
Doppler–Time Intensity (DTI) | |
3D range-Doppler-time (RDT) tensor (continuous time) | |
3D range-Doppler-time (RDT) tensor (discrete time) | |
Range superpulses | |
Doppler superpulses | |
Rank-reduced RDT tensor | |
Power-sum image | |
Doppler tomography image | |
BENI image | |
Position of scatterer in RDT space (m, m/s) | |
Transformed position after rank-reducing transform (m, m) | |
Rank-reducing transform matrix |
Appendix A.2. Derivation of Slant-Plane Image
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Serrano, A.; Capper, J.; Morrison, R.L., Jr.; Abouzahra, M.D. Range-Doppler-Time Tensor Processing for Deep-Space Satellite Characterization Using Narrowband Radar. Remote Sens. 2024, 16, 1374. https://doi.org/10.3390/rs16081374
Serrano A, Capper J, Morrison RL Jr., Abouzahra MD. Range-Doppler-Time Tensor Processing for Deep-Space Satellite Characterization Using Narrowband Radar. Remote Sensing. 2024; 16(8):1374. https://doi.org/10.3390/rs16081374
Chicago/Turabian StyleSerrano, Alexander, Jack Capper, Robert L. Morrison, Jr., and Mohamed D. Abouzahra. 2024. "Range-Doppler-Time Tensor Processing for Deep-Space Satellite Characterization Using Narrowband Radar" Remote Sensing 16, no. 8: 1374. https://doi.org/10.3390/rs16081374