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: