An Efficient Imaging Algorithm for GNSS-R Bi-Static SAR
Abstract
:1. Introduction
- The complex expression for range history: The range history is due to the motion of both the GNSS satellite and the receiving platform, which makes it extremely difficult to obtain a precise analytical solution to the stationary phase point of the Doppler phase.
- The translational variant Doppler history: Unlike mono-static SAR, the Doppler history of the echo signal of GNSS-R BSAR is translationally variant since the trajectories of the transmitter and the receiver are non-parallel and their velocities are also different. This means that imaging becomes a two-dimensional spatially varying filtering process.
2. Materials and Methods
2.1. Modelling and Analysis
- The spatially varying Doppler centroid: It is formed by the linear component of the residual transmitter range and represented by the spatially varying delay time tdk. This means the equivalent squint angle is also spatially varying.
- The translational variant Doppler FM rate: It is formed by the constant component of the residual transmitter range and represented by the shifting factor Rshiftk. The shifting factor Rshiftk indicates that the echo data for targets with the same minimum receiver range (thus the same Doppler FM rate) will not appear in the same range cell. In other words, the signals that appear in the same range cell have a different Doppler FM rate.
- The scene space in which the echo data are received.
- The echo space in which the echo data are stored and processed.
2.2. Imaging Methods
2.2.1. Bulk Compensation and Range Compression
2.2.2. Residual RCMC
- The scaling operation is not applied to the range frequency axis, but to the range time axis, and thus in some sense, it is more appropriate to name the modified algorithm the range scaling algorithm rather than the frequency scaling algorithm.
- The scaling of the range time needs four multiplications rather than three as in the frequency scaling algorithm.
- The scaling factors should all be adapted to the new application.
2.2.3. Azimuth Phase Perturbation
- The constant component πat03: It changes the phase of the signal according to the position of the target, which can be ignored when only the amplitude of the image is concerned. Here:
- The first order component 3πat02(t − t0): It adds a small spatially varying Doppler shift to the signal. This shift is a quadratic function of the azimuth time t, which can be incorporated into the Doppler shift caused by the residual transmitter range, i.e.,
- The second order compound 3πat0(t − t0) 2: It equalizes the Doppler FM rate along the range cell.
- The third order compound πa(t − t0)3: It is a cubic phase modulation, which is the same for all targets. It is far smaller than the phase modulation caused by the receiver motion, which can be ignored during the derivation of the azimuth stationary phase point of the signal.
2.2.4. Azimuth Compensation
3. Results
3.1. Simulation Results
3.2. Experimental Results
4. Discussion
5. Conclusions
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
References
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x | y | z | |
---|---|---|---|
Satellite position (km) | −5908 | −12,714 | 16,112 |
Satellite velocity (m/s) | −2475 | −1198 | −1310 |
Receiver position (m) | 0 | 0 | 6000 |
Receiver velocity (m/s) | 60 | 0 | 0 |
Satellite/Signal | GPS L5 |
---|---|
Carrier frequency | 1176.45 MHz |
Signal bandwidth | 10.23 MHz |
Sample rate | 40 MHz |
Integration time | 10 s |
Target | Range | Azimuth | ||||
---|---|---|---|---|---|---|
Resolution (m) | PSLR (dB) | ISLR (dB) | Resolution (m) | PSLR (dB) | ISLR (dB) | |
1 | 17.1 | −32.92 | −14.53 | 9.9 | −12.97 | −10.50 |
7 | 16.7 | −34.76 | −13.47 | 9.7 | −13.24 | −10.83 |
13 | 16.5 | −34.68 | −13.45 | 9.6 | −13.27 | −10.90 |
19 | 16.6 | −35.04 | −13.47 | 9.8 | −13.21 | −10.89 |
25 | 16.9 | −33.85 | −13.65 | 10.1 | −12.90 | −10.59 |
Theoretical | 16.5 | −35.00 | −13.45 | 9.6 | −13.26 | −10.90 |
Satellite used | GPS PRN30 |
Signal used | L5 C/A code |
Satellite elevation | 55.7° |
Satellite azimuth | 268.6° |
Carrier frequency | 1176.45 MHz |
Sample rate | 62 MHz |
Signal bandwidth | 10 MHz |
Equivalent PRF | 1000 Hz |
Doppler bandwidth | 151 Hz |
x | y | z | ||
---|---|---|---|---|
Satellite position (km) | start | −11,822 | −300 | 17,341 |
middle | −11,799 | − 735 | 17,341 | |
end | −11,778 | −1172 | 17,332 | |
Satellite velocity (m/s) | start | 173 | −3001 | −2 |
middle | 137 | −2962 | −31 | |
end | 129 | −2998 | −101 |
Na | Nr | Nx | Ny | Nkel |
---|---|---|---|---|
3e5 | 1024 | 500 | 500 | 8 |
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Zhou, X.-k.; Chen, J.; Wang, P.-b.; Zeng, H.-c.; Fang, Y.; Men, Z.-r.; Liu, W. An Efficient Imaging Algorithm for GNSS-R Bi-Static SAR. Remote Sens. 2019, 11, 2945. https://doi.org/10.3390/rs11242945
Zhou X-k, Chen J, Wang P-b, Zeng H-c, Fang Y, Men Z-r, Liu W. An Efficient Imaging Algorithm for GNSS-R Bi-Static SAR. Remote Sensing. 2019; 11(24):2945. https://doi.org/10.3390/rs11242945
Chicago/Turabian StyleZhou, Xin-kai, Jie Chen, Peng-bo Wang, Hong-cheng Zeng, Yue Fang, Zhi-rong Men, and Wei Liu. 2019. "An Efficient Imaging Algorithm for GNSS-R Bi-Static SAR" Remote Sensing 11, no. 24: 2945. https://doi.org/10.3390/rs11242945
APA StyleZhou, X. -k., Chen, J., Wang, P. -b., Zeng, H. -c., Fang, Y., Men, Z. -r., & Liu, W. (2019). An Efficient Imaging Algorithm for GNSS-R Bi-Static SAR. Remote Sensing, 11(24), 2945. https://doi.org/10.3390/rs11242945