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Poster Session 1
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On Modeling of The SAR-Image Squint Parameter
4. Experimentation And Analysis
4.1 Airborne Chaochou SAR-Image
The airborne SAR-image over a 5.0 km*14.0 km area near the Chaochou town, Figure 3 on the last page, was a result of the Canadian CV-580 GlobeSAR campaign in Taiwan, near the end of October, 1993 (INTERA, 1994).
The nominal flying height was 7.1 km above a mean sea level, with the airplane cruising at ~120 m/s (240 knots). A ground range resolution was ~4.0 m; an azimuth resolution was ~4.0 m, too.
Ground control/check point coordinates (X i,Y i,Z i) were digitized/interpolated from the available 1:5000 topographic photo-maps. The corresponding image point line/pixel coordinates were measured, using the ERDAS/Imagine software utilities. All the coordinates were independently measured by three operators. The averaged coordinate measurements were accepted and prepared in an input data file. In our radargrammetric processing, the measurements were treated as being independent and identically distributed.
4.2 Significant Parameters
For the monoscopic Chaochou SAR-image, its space resection deals with the determination of radar antenna's orientation parameters. With regard to the range/Doppler and the trajectory modeling equations (1-4), significant polynomial coefficients can be identified by following the stage-by-stage significance testing and the optimality assessment algorithm, in terms of Eq. (10-11). The results are given in Table 1, according to which the optimal set of parameters produced at the second stage will have been selected.
4.3 Planimetric Accuracy
When the SAR-image orientation parameters are made available, they can be used for each image point to determine its planimetric ground coordinates
(X i,Y i) where the Z i-coordinate is assumed to be known. This point-by-point space intersection is conducted for the 30 independent check points, leading to the accuracy results in Table 2. It is made clear that a single-valued variable squint angle is more suitable than a constant zero squint. The root-mean-square errors also indicate that a tentative second-order polynomial modeling (5) of the squint parameter has the highest accuracy level, in terms of the planimetric point positioning with the airborne Chaochou SAR-image.
Table 1. Iterative optimal determination of significant orientation parameters for the Chaochou SAR-image
| |
Stage-1
| Stage-2
| Stage-3
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Parameter set:
(besides t and M)
a0,..., a3
b0,..., b3
c0, ..., c3
|
a0,..., a3
b0,..., b3
c0, c1, c3
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a0, a1, a3
b0,..., b3
c0, c1, c3
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|
Parameter having
a maximum
F-test statistic
| c2
| a2
| -
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Minimum criteria:
Vp
AIC
|
0.38
98
630
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0.26
67
575
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0.29
75
592
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| Optimization
| No
| Yes
| No
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5. Summary
The SAR-image range/Doppler equations are introduced so as to recognize the geometric squint parameter. Before
Table 2. Planimetric point accuracy in relation to the squint, t, parameter modeling
| |
Root-mean-square errors |
| X/Easting (m) |
Y/Northing (m) |
| t (= 0.0 deg) |
± 6.2 |
± 7.1 |
| t as a variable ( = -0.38 deg ) |
± 5.4 |
± 6.1 |
t modeled by using a
2nd-order polynomial:
T0 = -0.053 deg
T1= 3.26×10-3 deg/pixel
T2= 2.44×10-6 deg/pixel2 |
± 4.8 |
± 5.3 |
embarking on a polynomial modeling of the squint angle, a least-squares estimation algorithm and a parametric significance testing methodology are briefly given. They serve as a sufficient processing tool in order to obtain an optimal set of radar's orientation parameters. In studying the space resection/intersection of the airborne SAR Chaochou image, a second-order polynomial description of the squint parameter yields an improved Easting coordinate accuracy of ± 4.8 m and an improved Northing accuracy of ± 5.3 m.
Based on the positive experimental outcome, some future SAR-image processing schemes are itemized here: (1) automated setting of a polynomial expansion order for the squint angle; (2) possibility of a first-order range-dependent modeling of the pixel-spacing parameter; (3) application of the proposed methodology to spaceborne Earth resources SAR imagery.
Acknowledgments
The writers are indebted to the Council of Agriculture for sponsoring the 1993 GlobeSAR campaign. Thanks also go to Mr. C.-T. Wang of the NSC Satellite Remote Sensing Laboratory for pre-processing the SAR image.
References
- Curlander, J.C., Kwok, R., Pang, S.S., 1987. A post-processing system for automated rectification and registration of spaceborne SAR imagery. International Journal of Remote Sensing, 8(4), pp.621-638.
- Dowman, I., 1992. The geometry of SAR images for geocoding and stereo applications. International Journal of Remote Sensing, 13(9), pp.1609-1617.
- Gelautz, M., Frick, H., Raggam, J., Burgstaller, J., Leberl, F., 1998. SAR image simulation and analysis of alpine terrain. ISPRS Journal of Photogrammetry and Remote Sensing, 53(1), pp.17-38.
- INTERA, 1994. GlobeSAR CV-580 campaign to Taiwan 1993 final report. Intera Information Technologies Ltd., Ontario, Canada, 56p.
- Koch, K.R., 1999. Parameter Estimation and Hypothesis Testing in Linear Models. Springer-Verlag, Berlin.
- Leberl, F., 1976. Imaging radar applications to mapping and charting. Photogrammetria, 32, pp.75-100.
- Leberl, F., 1979. Accuracy analysis of stereo side-looking radar. Photogrammetric Engineering and Remote Sensing, 45(8), pp.1083-1096.
- Lee, C., Theiss, H.J., Bethel, J.S., Mikhail, E.M., 2000. Rigorous mathematical modeling of airborne pushbroom imaging systems. Photogrammetric Engineering and Remote Sensing, 66(4), pp.385-392.
- Leick, A., 1995. GPS Satellite Surveying. John Wiley & Sons, Inc., New York.
- Mikhail, E.M., 1976. Observations and Least Squares. University Press of America, Lanham, Maryland.
- Tannous, I., Pikeroen, B., 1994. Parametric modeling of spaceborne SAR image geometry. Application: SEASAT/SPOT image registration. Photogrammetric Engineering and Remote Sensing, 60(6), pp.755-766.
- Toutin, Th., Gray, L., 2000. State-of-the-art of elevation extraction from satellite SAR data. ISPRS Journal of Photogrammetry and remote Sensing, 55(1), pp.13-33.
- Wu, J., Lin, D.-C., 2000. Radargrammetric parameter evaluation of an airborne SAR image. Photogrammetric Engineering and Remote Sensing, 66(1), pp. 41-47.
- Zhong, D., 1997. Robust estimation and optimal selection of polynomial parameters for the interpolation of GPS geoid heights. Journal of Geodesy, 71(9), pp.552-561.
Figure 3. Airborne Chaochou SAR-image (C-band, HH-polarization, ten-look) in slant-range projection, on 30 October, 1993; 30 control points shown by (?), and 30 check points by (-); terrain heights varying between 4.0 m and 84.0 m
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