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