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Mapping without the sun
Zhang, Jixian

2.2 Data processing
2.2.1 Calculation ground point coordinates
In this part we calculate the target point position from the
external DEM in Cartesian coordinates. The external DEM data
with latitude (p , longitude \j/ and height h are generally defined
in geodetic coordinates. In our simulation, the external DEM
data should be firstly converted to the corresponding (P x , P y , P z )
in the Earth Center Cartesian coordinates system. The
transformation from geodetic coordinates to Cartesian
coordinates is given as(Kun Ren et al., 2003):
P x =(R + h) cos(<^) cos(y)
< P y = (R + h) cos( P z =[R(l-e 2 ) + h]sm( where P x , P , P z are coordinates of ground point P in the
Earth center Cartesian coordinate system; e = yj(a 2 +b 2 )/a 2 ,
are the numeric eccentricity; a are the semi-major axe of the
Earth; b are the semi-minor axe of the Earth;
R = a/y]1 — a 2 sin 2 (<£>) are local Earth’s radius of curvature.
2.2.2 Interpolation satellite positions
In this part we use the DEOS fortran program getorb for
obtaining the precise orbits. Firstly we obtain the precise
satellite orbits data from Delft Institute of Earth Oriented Space
Research. Then we download the precise orbits from the DEOS
ftp (ftp://dutlru2.lr.tudelft.nl/pub/orbits/), which includes the
Orbital Data Records (ODR) and the list of ODR files arclist.
The Orbital Data Records (ODR) are binary files containing the
orbital positions of a satellite as a function of time. The position
of the satellite's nominal centre-of-mass is given in the Earth
Centred Fixed coordinate system. The accuracy of the precise
orbits data provided by Delft is less than 8cm in radial direction.
Secondly we call the program getorb to interpolate the orbits
data. We know the satellite positions is a function of azimuth
time, namely rows number. The time of first state vector and
azimuth line time can be obtained from the head file of the SLC
data. So we let the time of first state vector to be the reference
time origin and the azimuth line time to be the interval time
between the rows.
Then the satellite position corresponding to the external DEM
in the Earth center Cartesian coordinates system can be
obtained. From the known positions of a target and the satellites
in the Cartesian coordinates system, the distance of the target to
each of the two satellites can be derived. Thus, the
interferogram can be simulated. The processing diagram is
shown in Fig. 2.
Fig. 2 the simulation of interferogram processing diagram
In this study case, all the SLC data presented were acquired by
the ERS-1/2 satellite system. The important ERS operating
parameters and the external DEM data parameters for our
simulation are listed in Table 1. The interferogram is simulated
according to the processing diagram shown in Fige.2. The
geolocation errors are about in a resolution cell of ERS-1/2
image, namely 3.9m in azimuth direction and 7.9m in range
direction. Here the space of pixels is 3.0 arc-second namely
about 90 meter in ground. The difference of the elevation can
change arbitrarily. The external DEM is shown in Fig. 3.