199
GCP
Number
GCP
Type
Oe = on [m]
о» [m]
Residuals
in Eutm
Residuals
in Nutm
Residuals
in Hortho
1
Full GCP
20.0
4.0
-30.4
3.4
3.97
2
Full GCP
20.0
0.5
-35.9
-10.2
1.20
3
Height GCP
100.0
0.5
-33.3
21.9
0.32
4
Full GCP
5.0
2.0
1.6
2.2
-0.51
5
Full GCP
20.0
4.0
59.4
-8.1
10.79
6
Full GCP
10.0
2.0
25.1
0.6
1.59
7
Full GCP
10.0
2.0
-10.4
2.5
1.98
8
Full GCP
5.0
0.5
-11.5
-2.2
0.62
9
Height GCP
100.0
0.5
-3.8
-0.7
-0.91
10
Height GCP
60.0
0.5
-80.6
-28.5
-0.14
11
Height GCP
60.0
0.5
-59.7
21.2
0.25
12
Height GCP
60.0
0.5
-55.2
-24.1
-0.06
13
Full GCP
5.0
1.0
1.93
-0.2
2.73
14
Height GCP
100.0
4.0
-44.6
-10.7
11.41
Table 3: Residuals on the GCPs versus their input standard deviations (second set of parameters).
Compared with the first case, both bias and standard
deviation improve. The second type of parameterization of
Die seems to give better results. An explanation of this
fact is given in the following. Since we can measure only a
limited number of GCPs, we can only include in our
InSAR model a coarse description of the atmospheric
distortions. We can not compensate for all the possible
atmospheric distortions (which are highly non-linear) on
the InSAR DEMs, but only their low spatial frequency
components. In other words, we can only aim at
guarantee an accurate global geolocation of the InSAR
grid. The Die parameterization of equation (6) allows
compensating for the quadratic effects of the atmospheric
distortions but it is more sensitive to the number and
distribution of GCPs. On the contrary, the second type of
parameterization (see equation (7)) allows to compensate
for only the linear effects of the distortions but it is less
sensitive to the number and distribution of GCPs.
6. CONCLUSIONS
The interferometric procedure implemented at DIIAR -
Polytechnic of Milan for the generation of DEMs is
described. A new refinement procedure (calibration) of the
InSAR geometry based on the measure of GCPs is
proposed. It allows obtaining an accurate geolocation of
the InSAR grids through the compensation of the biases
in the sensor and SAR processing parameters, the orbit
errors and the low frequency atmospheric effects in the
interferometric phase.
Two different sets of InSAR calibration parameters are
analysed: the first one allows compensating for the
quadratic effects of the atmospheric distortions, while the
second one can only compensate for the linear effects of
such distortions. In the analysed test site, the second set
of parameters gives better results (i.e. a more accurate
global geolocation of the InSAR grid) and is less sensitive
to the number and distribution of the GCPs.
It is difficult to establish a general rule for the number and
distribution of GCPs needed for the calibration. For areas
up to 50 by 50 km (comparable with those analysed in our
test site), a set of 8-И0 GCPs, evenly distributed in the
whole scene, should assure a sufficient redundancy for
the estimation of the InSAR parameters.
It is important to underline that the calibration can only
provide the refined parameters useful to obtain a global
accurate geolocation of the InSAR grids. Most of the
distortions caused by atmosphere can not be
compensated for during the calibration. In order to
eliminate this kind of distortions, suited techniques (e.g.
based on the fusion with auxiliary height data) have to be
developed.
ACKNOWLEDGEMENTS
The authors thank Dr. Paolo Pasquali (now at Remote
Sensing Laboratories - University of Zurich) and Prof.
Claudio Prati from the Electronics and Information
Department of Polytechnic of Milan for kindly providing the
software for phase unwrapping.
APPENDIX A: LEAST SQUARES ESTIMATION OF THE
InSAR GEOMETRY PARAMETERS
The calibration of the InSAR geometry requires the
refinement of the model parameters through least squares
adjustment using ground control points. The input data for
the LS adjustment are the precise master and slave orbits
and the GCPs, i.e. points whose position in image space
(col, lin, Фи) and in object space (xp,yp,zp) is known. In the
object space the GCPs are given in the same geocentric
Cartesian system used for the orbits. To each GCP four
observations are associated: