The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Voi. XXXVII. Part Bi. Beijing 2008
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(wideregion or hugeregion), SPOTLIGHT, allowing SAR
images with spot extension of 10x10 km 2 and spatial resolution
equal to lxl m 2 single look; STRIPMAP (HIMAGE achieving
medium resolution, wide swath imaging, with swath extension
340 km and spatial resolution of 3x3 m 2 single look;
STRIPMAP (PINGPONG), achieving medium resolution,
medium swath imaging with two radar polarization’s selectable
among HH, HV, VH and VV, a spatial resolution of 15 meters
on a swath 330 km; SCANSAR (WIDE and HUGE region),
achieving radar imaging with swath extension selectable from
lOOx 100 km 2 (WIDE REGION) to 200x 200 km 2 (HUGE
REGION), and a spatial resolution selectable from 30x30 m 2 to
100x100 m 2 .
0F X
dF,
dF x -
da i
db
dc.
dd,
B =
dFy
dFy
dFy
dFy
_ da,
dbj
dc,
ddj _
/ =
-К'
~Fy\
*=
_ a i b j c i
•U T
(/ = 1,20, j = 2,20)
Based on the least squares method, the RPC are
This paper aims to generate a RPC with an unbiased estimator ( T \ Tj
for TerraSAR-X and COSMO-SkyMed SAR imagery. yB BjX = B l (4)
2, RPC MODEL
In the RPC model, image pixel coordinates d(line, sample) are
expressed as the ratios of polynomials of ground coordinates
D(Latitude, Longitude, Height). In order to improve the
numerical stability of equations, the 2D image coordinates and
3D ground coordinates are each offset and scaled to fit the
range from -1.0 to 1.0. The RPC model between the image
coordinates d and the ground coordinates D for an image can be
presented as below (OGC, 1999),
Y _ Num L (P,L,H)
Den L (P,L,H)
Y ... Num s (P,L,H)
Den s (P ,L,H)
Where Num f p > L >H) Den L (P,L,H) NumfP,L,H) Den s (P,L,H)
are the terms of the third order polynomial of (P,L,H), Y and X
are the normalized row and column index of pixels in the image,
and P, L and H are normalized coordinate values of object
points in the ground.
Wang presents a new iteration for normal equation. The
iteration is suitable for common normal equation, morbidity
normal equations and rank-defect normal equations and its
unbiased and convergent properties have been proved (Wang et
al., 2001).
We solve the Equ(4), based on Wang’s method, as follows:
Add the x onto Equ(4):
B + E^x = B T l + x (5)
The x can be estimated:
x (k) = (B T B + E)' (B T l + * lt_l) )
According to Wang et al., (2001), the estimator is unbiased.
3. TEST DATA
In order to fit the RPC using the rigorous sensor model, we can
rewrite Equ. (1) as (Zhang, 2005),
In this study, the TerraS AR-X and COSMO-SkyMed SAR
image are used for the test.
F x = Num s (P,L,H)-X* Den s (P,L,H) = 0
F Y = Num L (P, L,H)-Y* Den L (P, L,H) = 0
The observation error equations can then be formed as,
V = Bx-1 (3)
Where,
TerraS AR-X Data
The test image of TerraS AR-X is a full scene of Beijing; basic
information about the scene is listed below.
Image Size
8104* 9042pixels
Resolution
1.6 m
Topography
Flat
imaging mode
SL
Time of Acquisition
2008/03/29/22:17:23.9
Product Type
ssc
Table 1. Basic information on the Beijing TerraS AR-X
imagery.
COSMO-SkyMed Data
The test image of COSMO-SkyMed is a full scene of Shang
hai ; basic information about the scene is listed below.