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The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part Bl. Beijing 2008 
design matrix, to select the estimable parameters and finally to 
solve the linearized collinearity equations system in the least 
squares (LS) sense. 
SATELLITE 
POSITION 
O: right ascension of the ascending node 
i: orbit inclination 
e: satellite elevation at image centre 
a: satellite azimuth at image centre 
SENSOR 
ATTITUDE 
<|>=<|)o(t)+ao+a!t+a 2 t 2 (roll) 
0=9 o (t)+bo+b i t+b 2 t 2 (pitch) 
V=Vo(t)+c 0 +Cit+c 2 t 2 (yaw) 
VIEWING 
GEOMETRY 
d_pix: pixel size 
I 0 ,Jo,di: self-calibration parameters 
Tab 2. Full parametrization of the SISAR model 
The SISAR model was tested on Cartosat-1 images with 
different features (for the features of all images see Tab. 3). 
All the images in forward looking (FORE) have a swath of 
30km and in aft looking (AFT) have a swath 26.6km except 
Rome image that is not standard acquisition (swath 7.5km), 
since only a short part of the CCD array (3000 pixels vs. a total 
of 12000) was active. 
Image 
off-nadir 
angle (°) 
Control 
points 
AFT 
FORE 
Mausanne 
14.45 
29.10 
32 
Rome 
4.97 
26.09 
43 
Warsaw 
4.97 
26.04 
29 
Castelgandolf 
0 
12.35 
28.20 
25 
Tab 3. Data set available 
For the last images the showed results are focused on the DEM 
extraction rather than the orientation model. 
Fig 4. RMSE at check points depending upon number of 
control points, trend for Mausanne image (North, East, Height 
components) 
The RMSE of check points (CPs) residuals, computed with 
SISAR software, underlines that the accuracies are similar to 
the GSD in horizontal and about H/B (1.60) multiplied for y- 
parallax (3.7m) in vertical. The similar results are obtained by 
OrthoEngine software with worse accuracy for Mausanne 
image and better accuracy for Warsaw image with respect to 
SISAR ones (Fig. 4,5,6). 
Cartosat stereo - Roma gsd 2.50 [ml RMSE CP 
Figure 5. RMSE at check points trend for Rome image (North, 
East, Height components) 
Cartosat stereo - Warsaw gsd 2.50 |ml RMSE CP 
Figure 6. RMSE at check points trend for Warsaw image 
(North, East, Height components) 
2.2,1 RPC generation with geometric reconstruction 
The RPCs can be generated according to a terrain-independent 
scenario, using known physical sensor model, or by terrain- 
dependent scenario without using any physical sensor models 
(Tao et al., 2001b). In the last method the solution is highly 
dependent on the actual terrain relief, the distribution and the 
number of GCPs and it does not provide a sufficiently accurate 
and robust solution if the above requirements for control 
information are not satisfied. 
For the previous motivations, an innovative algorithm for the 
RPCs extraction, with a terrain independent approach, was 
implemented into the software SISAR. The basic steps of this 
algorithm are to build a 3D ground grid enveloping the terrain 
morphology of the imaged area starting from a rigorous 
orientation, and to estimate the RPCs that fit to this virtual 
space. 
At first an image discretization was made, dividing the full 
extend image space in a 2D grid. Then the points of the 2D 
image grid are used to generate the 3D ground grid: the image 
was oriented and by the knowledge of the orientation sensor 
model the collinearity equations were derived and used to 
create the 3D grid, starting from each point of the 2D grid 
image. In this respect it has to be underlined that the 2D grid is 
actually a regular grid, whereas the 3D one is not strictly 
regular, due to the image attitude. Moreover, the 3D grid points 
were generated intersecting the straight lines modelled by the 
collinearity equations with surfaces (approximately ellipsoids) 
concentric to the WGS84 ellipsoid, placed at regular elevation 
steps.