198
GCP
Number
GCP
Type
<je = ctn [m]
cr H [m]
Residuals
in Eutm
Residuals
in Nutm
Residuals
in Hortho
1
Full GCP
20.0
4.0
-25.6
4.3
4.44
2
Full GCP
20.0
0.5
-28.7
-8.9
0.06
3
Height GCP
100.0
0.5
-30.2
22.5
0.42
4
Full GCP
5.0
2.0
3.1
2.5
-1.03
5
Full GCP
20.0
4.0
32.0
-13.1
-1.12
6
Full GCP
10.0
2.0
28.5
1.2
0.80
7
Full GCP
10.0
2.0
-8.4
2.8
0.60
8
Full GCP
5.0
0.5
-10.3
-2.0
0.13
9
Height GCP
100.0
0.5
2.4
0.4
-0.14
10
Height GCP
60.0
0.5
-76.7
-27.9
-0.07
11
Height GCP
60.0
0.5
-58.4
-21.5
-0.19
12
Height GCP
60.0
0.5
-50.2
-23.3
-0.18
13
Full GCP
5.0
1.0
0.7
-0.4
-0.24
14
Height GCP
100.0
4.0
-56.2
-12.7
3.97
Table 2: Residuals on the GCPs versus their input standard deviations (first set of parameters).
Furthermore, in order to avoid high correlations, two more
parameters were fixed (To because very correlated with
AT and the same AT because very correlated with f D 2).
Reducing the number of parameters from 14 to 10, the
inverse of the condition number of the normal matrix
drops of four orders of magnitude.
Hence, we fixed in the adjustment the 4 parameters Ro,
foo, To and AT. For this purpose good approximate values
were needed. Two of them were estimated with the
simplified version of the InSAR calibration. For T 0 and AT,
which could not be estimated with such a calibration, the
values coming from the image auxiliary data were used.
The final estimate of the InSAR parameters was obtained
using 14 GCPs (8 full and 6 height GCPs). From the
original GCP set, 6 were removed because of their very
high residuals in the relative observations.
In Table 1, the estimated parameters with their standard
deviations are reported. Table 2 shows the residuals and
the input standard deviations associated to each GCP
coordinate. One may notice that they fit very well. As
expected, the planimetric residuals of the adjusted height
GCPs are much bigger than those of the full ones are.
With such residuals a globally accurate grid positioning of
the InSAR grid is guaranteed.
Employing the adjusted InSAR parameters, the precise
orbits and the unwrapped phases an irregular grid was
generated. This grid was interpolated in order to derive a
regular one (30 m spacing) which was compared with the
reference DEM (RMS error of about 1 m) obtaining:
Mean error (bias) = 1.5 m
Standard deviation = 19.4 m
The global (constant) bias of the grid can be considered
satisfactory, i.e. the InSAR calibration resolves quite well
the geolocation of the generated grid. The standard
deviation is quite large: this is mainly due to the large
areas affected by huge (e.g. 100 m) unwrapping-related
errors. Reducing such errors would decrease significantly
both the standard deviation and the bias.
5.3 Analysis of the Second Set of Parameters
Adopting the same set of 14 GCPs, a new InSAR
calibration was performed employing 4 parameters to
describe the interferometric constant:
D jC = d 0 + d-, • col + d 2 • lin + d 3 ■ col • lin (7)
Table 3 shows the residuals and the input standard
deviations associated to each GCP coordinate. One may
notice that these residuals are significantly bigger than
those reported in Table 2. It is not always possible to
obtain good residuals on the GCP coordinates. This
applies especially to the second set of calibration
parameters. In fact, this set can only compensate for the
linear terms of the atmospheric distortions on the
interferometric phase (see equation (7)). If non linear
distortions in the considered interferogram exist, even with
a very accurate set of GCPs big residuals may happen on
few points (those directly affected by the distortions).
However, with GCPs evenly distributed in the whole
scene, the calibration should still allow a globally accurate
positioning of the InSAR grid.
Adopting the new adjusted InSAR parameters, the precise
orbits and the unwrapped phases an irregular grid of 3D
points was generated. This grid was interpolated in order
to derive a regular one with 30 m spacing. The
interpolated grid was compared with the reference DEM
obtaining:
Mean error (bias) = 1.2 m
Standard deviation = 18.0 m
