The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part Bl. Beijing 2008 
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4. EXPERIMENTS 
This section shows the results of the georeferencing obtained by 
applying the three different sensor models. In each adjustment, 
the check points were only used as tie points, and their 
coordinates were determined in the adjustment. The same 
stochastic model was used in all cases: the a priori standard 
deviation of an image coordinate was ±0.5 pixels, and the a 
priori standard deviation of a GCP coordinate was ±0.3 m (or 
its equivalent in the case of geographic coordinates). The tables 
in this section show the root mean square (RMS) errors of the 
differences between the measured image coordinates and the 
results of back-projecting the original check points for the 
scenes (RMS X and RMS y ) for the scenes Fore and Aft. 
Furthermore, the RMS errors of object coordinate differences 
between the results of bundle adjustment and the original check 
point coordinates (RMS X , RMS Y , RMS Z ) are presented along 
with the minimum and maximum residuals in the object 
coordinates of the check points (Rx" n / Rx max , 
Ry m,n / Ry max , R z min / R z max ), and the RMS error of the standard 
error of unit weight s 0 of each adjustment. 
4.1 Results using the 3D affine model 
The georeferencing results with the 3D Affine model are 
summarized in Table 2. For this model with 9 GCPs, the RMS 
values of differences between the measured image coordinates 
and back-projected coordinates of the checkpoints were 
between 0.3 and 0.6 pixels. The corresponding RMS errors in 
object space were below 1.8 m in both planimetry and height. It 
has been shown that use of GCPs defined in UTM leads to 
better results than use of GPCs in geographic coordinates 
(Hanley et al. 2002), which was also the case with this data set. 
The results achieved for geocentric coordinates and for UTM 
are very similar, though there is a different distribution of the 
error budget to the individual components due to the different 
definitions of X, Y and Z. 
System 
Geocentric 
Geographic 
UTM 
Scene 
Fore 
Aft 
Fore 
Aft 
Fore 
Aft 
RMS X [pixel] 
0.32 
0.32 
0.54 
0.55 
0.33 
0.33 
RMSy [pixel] 
0.55 
0.41 
0.56 
0.54 
0.53 
0.42 
RMS X [m] 
1.20 
1.43 
0.80 
Rx mm /Rx max [m] 
-5.1/2.3 
-4.0/3.5 
-1.4 / 2.5 
RMSy [m] 
0.96 
1.17 
1.00 
Ry min /R Y max [m] 
-3.5/3.2 
-4.0/2.8 
-4.1 /2.4 
RMS Z [m] 
1.33 
1.81 
1.81 
R z min /R z max [m] 
-5.4/2.5 
-4.3/7.0 
-4.2/7.1 
So 
0.42 
0.53 
0.41 
Table 2. Results of georeferencing with the 3D affine model. 
4.2 Results using RPCs 
First, the accuracy of the original RPCs provided by ISRO was 
checked by back-projecting the GCPs into the images. It was 
found that there was an almost constant offset of approximately 
33 pixels in both images of the stereo pair. Whereas the offset 
was almost entirely in the flight direction in the forward looking 
image, there was both an along-track and a cross-track 
component in the backward facing image. Computing the 3D 
coordinates of the GCPs by forward intersection using the 
original RPCs, and comparing the resulting coordinates with 
those determined by GPS, resulted in RMS discrepancy values 
of 72 m in planimetry and 25 m in height. The discrepancies 
were highly systematic and applying the bias-correction was 
expected to increase the quality of the results significantly. The 
results of the forward intersection with the original RPCs are 
shown in Table 3. 
Bundle block adjustment was carried out using the three options 
of shift only, shift and drift, and affine for the bias 
compensation of the RPCs. The results achieved using 9 GCPs 
are shown in Table 4. Determining drift parameters in addition 
to the shifts results mainly in an improvement of the height 
accuracy by about 10%. Use of the affine bias correction model 
resulted in additional improvement in both the height 
component and the planimetrie accuracy. There is also an 
improvement in the image-based RMS errors. In the case of 
affine bias correction, the RMS errors of differences were 
considerably better than the pixel size in all components. 
Scene 
Fore 
Aft 
RMS X [pixel] 
0.91 
15.92 
RMSy [pixel] 
33.27 
26.80 
RMSx [m] 
2.7 
R x mm /R x max [m] 
-4.2 / -0.3 
RMSy [m] 
72.6 
Ry min /Ry max [m] 
69.3 / 74.6 
RMS Z [m] 
25.9 
R z min /R z max [m] 
-18.2/-33.0 
so 
22.46 
Table 3. Results of forward intersection with the original RPCs. 
Shift 
Shift + Drift 
Affine 
Scene 
Fore 
Aft 
Fore 
Aft 
Fore 
Aft 
RMS X [pixel] 
0.25 
0.26 
0.25 
0.26 
0.25 
0.26 
RMSy [pixel] 
0.78 
0.44 
0.74 
0.46 
0.52 
0.40 
RMS X [m] 
0.66 
0.66 
0.65 
Rx min /Rx max [m] 
-1.4/2.3 
-1.3/2.3 
-1.3 / 2.3 
RMSy [m] 
1.12 
1.16 
0.95 
Ry min /Ry max [m] 
-3.3/2.0 
-4.3 / 2.9 
-3.6/2.3 
RMS Z [m] 
2.23 
1.99 
1.67 
R z min /R z max [m] 
-6.6 / 8.2 
-4.8 / 7.5 
-4.4 / 6.8 
so 
0.59 
0.47 
0.38 
Table 4. Georeferencing results with bias corrected RPCs. 
To assess the applicability of the RPC bias correction with 
minimal ground control information, two scenarios were tested. 
Adjustment was carried out using one GCP and bias correction 
by shifts, and also using three GCPs and bias correction by 
shifts and drifts. The results are summarized in Table 5.