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The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part Bl. Beijing 2008 
Dowman, 2006), thus the GCPs are divided in groups of 
1,2,3,4,5,6,9, GCPs, in order to examine and compare the 
accuracy of the models based only this issue. 
Additionally 494 tie points are measured for the UCL sensor 
model evaluation, divided in two groups of 149 and 494 
points, which are implemented in the coplanarity equation. 
6.3. RPCs model evaluation. 
In table 2 the accuracy of the ICPs are introduced based on 
the number of the GCPs (first column) when the RPCs are 
used for the orientation. 
RMSE of ICPs 
GCPs 
Distribution 
X(m) 
Y(m) 
h(m) 
0 
11.33 
114.07 
760.51 
1 
* 
14.43 
2.77 
5.38 
2 
14.99 
2.37 
4.30 
3 
* * 
2.16 
1.46 
1.74 
4 
1.64 
1.68 
1.71 
5 
1.61 
1.71 
1.87 
6 
1.72 
1.68 
1.98 
9 
* • * 
1.70 
1.65 
1.95 
Table 2. RMSE of the 25 ICPs using RPCs model. 
From the above table the following conclusions could be 
extracted: 
• The accuracy of the RPCs model where no GCPs are 
used for refinement is not very good, especially in 
height, where the RMSE is close to 800m. 
• With one GCP the accuracy is improved close to 20m. 
• With two and three GCPs the accuracy is improved 
slightly. 
• Four GCPs are enough in order to reach accuracy close 
to one pixel. 
• From 4 to 9 GCPs the RMSE is almost the same. 
6.4. UCL sensor model evaluation. 
6.4.1. Introduction. The evaluation of the UCL sensor model 
is divided in three parts as follows: 
• Evaluation of the model based on the collinearity. 
• Evaluation of the solution based on four GCPs with the 
involvement of the coplanarity. 
• Evaluation of the precision of the solution in 
combination with the coplanarity. 
6.4.2. Solution of UCL sensor model based on the 
collinearity. Based on paragraph 3 the total number 
unknown exterior parameters is 18. This means that at least 5 
GCPs are needed for the solution based only on the 
collinearity equation. In table 3 the accuracy of the ICPs are 
introduced based on the number of the GCPs (first column) 
when the UCL sensor model collinearity equations are used for 
the orientation. 
It seems that using the UCL model sufficient (subpixel) 
accuracy is achieved even in case of five GCPs. Moreover it 
gets better accuracy than the RPCs model in all cases. 
RMSE of ICPs 
GCPs 
Distrib 
ution 
X(m) 
Y(m) 
h(m) 
5 
• 
0.87 
1.02 
1.47 
6 
* * 
0.88 
0.94 
1.36 
9 
0.71 
0.83 
1.27 
Table 3. RMSE of ICPs using UCL along track Kepler model 
based on the collinearity equations and first order 
rotations and 
6.4.3. Solution based on four GCPs with the involvement 
use of coplanarity. In this paragraph the coplanarity equations 
are used in the solution providing one more equation per point 
(GCP, Tie Point) giving the opportunity to have a solution with 
4 GCPs. In table 4 the accuracy of the ICPs are introduced 
based on the number of the Tie Points used. 
It seems that using about 150 Tie points which in reality is 
information that can be extracted from the images the accuracy 
is reach the accuracy of the five GCPs solution. 
RMSE of ICPs 
GCPs 
Tie 
Points 
X(m) 
Y(m) 
h(m) 
4 
34 
1.07 
2.92 
2.45 
4 
149 
0.86 
1.09 
1.49 
Table 4. RMSE of ICPs using UCL along track Kepler model 
based on the collinearity equations and coplanarity 
equation. 
The challenge is to examine the possibility to reach an exterior 
orientation solution using less than four GCPs. 
6.4.4. Precision of the solution in combination with the 
collinearity. The reference standard deviation S 0 represents the 
precision of the adjustment. The form of the reference standard 
deviation for the unweighted case is 
S 
o 
In table 5 the reference standard deviation S a of the exterior 
orientation solution in cases of 9 and 34 (all) GCPs involved 
are introduced with different combination of Tie Points used in 
the solution through the coplanarity equation. It seems that 
using the coplanarity increases the precision of the solution 
significantly.