The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part Bl. Beijing 2008 
265 
a b £ d £ / g h 1 
X 
1.0319 
-1.7718 
-1.3051 
-9.1167 
17.3118 
10.5423 
2.4225 
2.1977 
-0.6297 
y 
0.0083 
0.5383 
-0.3401 
-26.9256 
51.1289 
31.1360 
-0.2547 
0.5727 
-1.8598 
z 
0.0139 
-0.7741 
0.4298 
36.3311 
-68.9891 
-42.0122 
0.4050 
0.9602 
2.5094 
Table 2. Error propagation coefficients for Tibet Zhang area 
From table 1 and 2, we can see that in Tibet Zhang area the 
mean normal height value is up to 4827m, in where around 
10608m, 2764m and 4634m positioning error would be caused 
in x, y and z direction respectively if the normal height were 
not adopted. So the earth model must be corrected using the 
known DEM. Fortunately, the NASA Shuttle Radar 
Topographic Mission (SRTM) has provided DEM for over 
80% of the globe and the vertical error of the DEM is reported 
to be less than 16m. When the SRTM DEM in Tibet Zhang 
area is used, the error caused by elevation can reduce to 35m, 
9m and 15m. The Doppler center frequency error is the second 
error resource to be considered, which will be produced when 
the Doppler center frequency true value is not equal to zero 
that is assumed in SAR imaging. Taking the test data in Tibet 
Zhang area as example, its Doppler center frequency true value 
is -113.55Hz. If the true value were not adopted, around 71.5m, 
211.1m and 284.9m positioning error would be caused in x, y 
and z direction, respectively. Fortunately, the true Doppler 
center frequency can be estimated by the Doppler frequency 
center and Doppler frequency variation rate parameters which 
can be obtained from the SAR auxiliary data. When the true 
Doppler center frequency is adopted the Doppler center 
frequency nonzero error can be ignored. 
Once the earth model error and the Doppler center frequency 
nonzero error have been corrected, the satellite orbit parameter 
(positions and velocities in x, y and z direction) errors become 
the most dominant. Table 3 shows the typical orbit and 
atmospheric delay errors in pixel location with the ERS-2 C- 
band SAR. Since the orbit is very nearly a straight line during 
one second, the high precision XYZ velocity ( XYZ vol ) can be 
approximated as follows 
XYZ t (t) = XYZ (t + 0.5 sec) - XYZ (t - 0.5 sec) (7) 
So the uncertainty of the XYZ velocity can be given by 
times the uncertainty of the XYZ position. 
The calculations in table 3 are based on the nominal system 
parameters of the ERS-2 and assume the error of the mean 
normal high is zero and the true value of Doppler center 
frequency is used. 
Typical TZ SAR image NJ SAR image TW SAR image 
error 
(36.299°, 91.105°) 
/7v Au Av 
(32.097°, 119.511°) 
/7y do dz 
(24.031°, 120.509°) 
//y dv. dz 
— t 
-v t 
— t 
— ( 
-v t 
—t 
t 
V t 
—t 
dx 
A f, 
0 6 
0 0 
0 0 
1 1 
Q_4 
0_2 
1-4 
Q-S 
Q41 
ClA s 
d y s 
5.2 
9.3 
2.8 
4.0 
6.5 
1.1 
3.6 
6.5 
2.1 
3.4 
dz s 
8.2 
10.7 
2.8 
3.5 
7.3 
7.1 
4.1 
5.3 
5.9 
5.4 
dv x 
0.9 
8.0 
23.7 
31.9 
5.6 
40.6 
60.7 
1.9 
34.3 
68.4 
dv y 
7.4 
127.9 
377.6 
509.6 
33.0 
241.4 
360.8 
11.6 
205.8 
410.4 
dv z 
11.5 
121.6 
359.2 
484.6 
41.1 
300.9 
449.8 
9.8 
173.9 
346.7 
dR 
2.8 
6.8 
0.7 
1.1 
6.4 
2.8 
1.2 
6.3 
3.0 
1.3 
Total 
177 
522 
704 
54 
388 
580 
19 
272 
542 
Table 3. Typical error sources in the ERS-2 SAR images and their effect on positioning in x, y and z direction (unit: meter) 
From Tab.3 it can be found that the maximum positioning 
errors are caused by the satellite velocity uncertainties whose 
maximum reach 703.95m, 579.81m and 541.58m in three sites 
in the z direction, respectively. It almost equals to the total 
errors in that direction, so reducing the orbit errors is critical to 
the accurate positioning using R-D model. If the other errors 
are ignored, the required absolute accuracy of orbit 
determination should be in the order of 19cm to achieve a 
positioning accuracy of around 25 m predicted by Curlander 
(Curlander, 1982) using the R-D model. So the precise orbit, 
which can be provided for free by many organizations, must be 
used. The error caused by atmospheric delay is the smallest 
among all of these errors and its maximum error is only 6.8m 
in three groups of test. But in Taiwan test site the atmospheric 
delay error accounts for 33% of the total error in x direction. 
So it may become remarkable in low latitude area. Moreover, 
comparing the results of Tibet Zhang autonomous region, 
Nanjing city and Taiwan province it can be found that the 
positioning errors using R-D model are nonlinear. They 
decrease gradually with decreasing latitude as well as 
increasing longitude. At last, it should be noted that the max. z 
direction error is 704 meter, but it is permitted in the technical