A Fast, Three-Dimensional, Indirect Geolocation Method Using IAGM and DSM Data without GCPs for Spaceborne SAR Images
Abstract
:1. Introduction
2. The Geolocation Theory
2.1. The Coordinate System and Transformation Formula
2.2. The RD Model for SAR Images
2.2.1. The Earth Model Equation
2.2.2. The SAR Doppler Equation
2.2.3. The SAR Range Equation
2.2.4. The RD Model
2.3. Iterative Analytical Geolocation Method (IAGM)
- (a)
- Calculate the geocentric latitude and longitude of the sub-satellite point :
- (b)
- In the local coordinate system, the vectors , , and in the ECR coordinate system can be transformed to , , and [16]:
- (c)
- Calculate the angle from the Doppler equation.
- (d)
- Calculate the geocentric latitude and longitude for the ground point by using the angle and the angle [16].
- Get , , and according to the above method.
- Use Equation (14) to calculate the angle .
- According to the steps from (a) to (d), the position vector can be obtained.
- Calculate the value . If , then stop the iteration and get the final result . Otherwise, let and re-execute step 2.
2.4. Atmospheric Propagation Delay for Microwaves
2.4.1. The Ionospheric Delay
2.4.2. The Tropospheric Delay
2.4.3. Real Data for the Ionosphere and Troposphere
3. A Fast, Three-Dimensional, Indirect Geolocation Method
- (a)
- Calculate the slopes of the latitude and the longitude between the first azimuth time and the last azimuth time at the nearest and furthest slant ranges, respectively.Then, the average values for the slopes of latitude and the longitude are given by:
- (b)
- Calculate the distance between C1 and C3:
- (c)
- As point ’s projection point is , the positions of and are and , respectively. The rectangular space coordinates of point and point are and , respectively. Then calculate the distance between C1 and .
- (d)
- Estimate point on the straight line C1C3, whose geodetic coordinate is given by:
- (e)
- From the ratio relationship, the azimuth time of point can be derived:
- (f)
- Obtain point ’s precise azimuth time . Calculate the Doppler frequency at the estimated azimuth time by Equations (9)–(11).
- (g)
- Calculate the slant range of point .
4. Experiments and Analyses
4.1. Geolocation Results
4.2. Computational Efficiency and Accuracy
5. Discussion
6. Conclusions
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
References
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Parameter Name | Value | Units |
---|---|---|
Image size | − | |
Azimuth spacing | 0.8705 | m |
Range spacing | 0.4547 | m |
Slant range to the first pixel | 706,315.7084 | m |
Pulse repetition frequency | 3720.4126 | Hz |
Radar frequency | 9649.998153 | MHz |
The number of orbit state vectors | 12 | − |
Date of acquisition(UTC) | 20 December 2018 | − |
Acquisition mode | Spotlight | − |
Producttype | SSC_HS_S | − |
Descending/Ascending | Ascending | − |
Look direction | Right | − |
Check Points | N (m) | E (m) | H (m) | Spatial (m) |
---|---|---|---|---|
P1-M1 | 1.0942 | 3.9758 | −1.1020 | 4.2684 |
P1-M2 | 0.4080 | −0.2308 | −0.5400 | 0.7151 |
P2-M1 | 0.2842 | 4.1319 | −1.2079 | 4.3143 |
P2-M2 | −0.4020 | −0.0747 | −0.8236 | 0.9195 |
P3-M1 | −0.0664 | 3.5610 | −1.4886 | 3.8602 |
P3-M2 | −0.0664 | −0.6456 | −0.4571 | 0.7938 |
P4-M1 | 0.6374 | 5.2201 | −0.6411 | 5.2978 |
P4-M2 | 0.6374 | −0.0382 | −0.8710 | 1.0800 |
P5-M1 | −0.0816 | 5.3240 | −0.2730 | 5.3316 |
P5-M2 | −0.7678 | −0.4600 | −1.3277 | 1.6012 |
P6-M1 | −0.1002 | 3.6949 | −0.6922 | 3.7605 |
P6-M2 | −0.7864 | −0.5117 | −0.3195 | 0.9912 |
P7-M1 | 0.0063 | 4.3063 | −0.2809 | 4.3155 |
P7-M2 | −0.6799 | 0.0998 | −0.2821 | 0.7429 |
P8-M1 | 0.1632 | 5.7325 | 1.1457 | 5.8481 |
P8-M2 | −0.5230 | 1.0001 | 0.7717 | 1.3672 |
Check Points | N (m) | E (m) | H (m) | Spatial (m) |
---|---|---|---|---|
P1-M1 | 0.1944 | 3.7567 | −0.7724 | 3.8402 |
P1-M2 | −0.4918 | −0.9774 | −0.9034 | 1.4189 |
P2-M1 | −0.0275 | 4.2506 | −1.0030 | 4.3674 |
P2-M2 | −0.7137 | −0.4836 | −1.1060 | 1.4023 |
P3-M1 | 0.2397 | 4.7571 | −0.5951 | 4.8002 |
P3-M2 | −0.4465 | 0.0229 | −0.1541 | 0.4729 |
P4-M1 | 0.2034 | 4.3313 | −0.5728 | 4.3737 |
P4-M2 | −0.4828 | −0.9289 | −0.8107 | 1.3240 |
P5-M1 | 0.3324 | 4.6884 | −0.7787 | 4.7642 |
P5-M2 | −0.3538 | −0.0458 | −0.5379 | 0.6455 |
P6-M1 | 0.2901 | 4.3786 | −1.1601 | 4.5390 |
P6-M2 | −0.3961 | −0.8816 | −1.3881 | 1.6915 |
P7-M1 | −0.0604 | 3.4302 | 0.0244 | 3.4308 |
P7-M2 | −0.7466 | −1.3040 | 0.1605 | 1.5111 |
P8-M1 | 0.6558 | 4.3651 | −0.8153 | 4.4888 |
P8-M2 | −0.0304 | −0.3691 | −0.9421 | 1.0123 |
P9-M1 | 0.5451 | 4.2038 | −0.5918 | 4.2801 |
P9-M2 | −0.1411 | −0.5304 | −0.7880 | 0.9603 |
P10-M1 | 0.1747 | 4.2544 | −1.0270 | 4.3801 |
P10-M2 | −0.5115 | −0.4798 | −0.8043 | 1.0671 |
P11-M1 | 0.0195 | 4.6897 | −0.2976 | 4.6992 |
P11-M2 | −0.6667 | −0.0445 | −0.1763 | 0.6911 |
SN | Scale | Traditional | Proposed |
---|---|---|---|
i | 1024 × 1024 | 59.15 s | 4.69 s |
ii | 2048 × 2048 | 232.82 s | 18.58 s |
SN | Scale | Traditional | Proposed |
---|---|---|---|
i | 1024 × 1024 | 1.026 m | 1.026 m |
ii | 2048 × 2048 | 1.108 m | 1.108 m |
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Liu, M.; Xiao, P. A Fast, Three-Dimensional, Indirect Geolocation Method Using IAGM and DSM Data without GCPs for Spaceborne SAR Images. Sensors 2019, 19, 5062. https://doi.org/10.3390/s19235062
Liu M, Xiao P. A Fast, Three-Dimensional, Indirect Geolocation Method Using IAGM and DSM Data without GCPs for Spaceborne SAR Images. Sensors. 2019; 19(23):5062. https://doi.org/10.3390/s19235062
Chicago/Turabian StyleLiu, Min, and Peng Xiao. 2019. "A Fast, Three-Dimensional, Indirect Geolocation Method Using IAGM and DSM Data without GCPs for Spaceborne SAR Images" Sensors 19, no. 23: 5062. https://doi.org/10.3390/s19235062
APA StyleLiu, M., & Xiao, P. (2019). A Fast, Three-Dimensional, Indirect Geolocation Method Using IAGM and DSM Data without GCPs for Spaceborne SAR Images. Sensors, 19(23), 5062. https://doi.org/10.3390/s19235062