International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B3. Istanbul 2004 
Table 3. APl, RMSE values achieved in UTM coordinates of the 
Ikonos data using rational equations 
  
  
  
  
  
  
  
  
  
  
  
Method GCPs ICPs Control Check 
Number | Number Points Points 
APl(m) APl(m) 
34 20 0.87 0.90 
14 Term 20 34 0.83 0.94 
7 47 0.00 4.36 
34 20 0.85 0.98 
17 Term 20 34 0.80 0.91 
7 47 = : 
34 20 0.84 0.98 
20 Term 20 3 0.76 1.22 
7 47 : = 
  
  
  
  
  
  
  
Table 4. API, RMSE values achieved in UTM coordinates of the 
Ikonos data over the Hamedan project area. 
  
  
carry out the accuracy tests of the Ikonos Geo image. The bundle 
adjustment program is very flexible and the number of exterior 
orientation parameters can be reduced from 15 to 9 as a result of 
removing the quadratic and linear terms of the polynomials which 
model the change of the conventional rotation parameters (i.e. , 
i and x) with respect to time. The results of the bundle adjustment 
when using 3 combinations of control points and check points for 
the Hamedan test field are given in Table 4. The result of 
adjustment using equation (16) are stated in tables 4 and 5. 
As can be seen in Tables 4 and 5 using equation 16 yields better 
results than using equation 15. Also, the results show increased 
improvement for 15, 12 and 9 parameters equation respectively. 
However, from the practical test, equivalent RMSE values for 
independent check points in terms of the UTM coordinate system 
for 20 GCPs and 34 ICPs are given in table 6. 
Table 6. R.m.s.e. values of the errors at the residual errors in the 
GCPs/ICPs in terms of both the WGS 1984 geocentric coordinate 
system and the UTM coordinate system on the Ikonos Geo image 
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
Table 5. AXY, residuals in WGS 1984 coordinates for the control 
and check points on the Ikonos Geo image corrected with 9, 12 
and 15 parameters and using equation 15 and with 15 parameters 
and using equation 16, over the Hamedan project area. 
  
  
  
  
  
  
  
  
  
  
  
  
  
  
Method GCPs ICPs Control Check 
Number | Number Points Points 
AXY(m) AXY (m) 
34 20 2.71 2.72 
9 20 34 2.98 2.65 
Parameters 7 47 $35 5.00 
34 20 34 20 
12 20 34 20 34 
Parameters 7 47 7 47 
34 20 2.36 2.35 
15 20 34 2.55 2.32 
Parameters 7 47 2.87 3.12 
34 20 1.01 1.31 
IS 20 34 1.15 1.10 
parameters = 47 0.97 3: 1 3 
for Geo 
image 
corrected 
  
  
  
  
  
  
  
A bundle adjustment program implementing the mathematical 
model outlined in Part 3.3.1, written by the second author in 
Borland C++ for Windows and run on a PC, has been used to 
Method GCPs ICPs Control Check corrected with 15 parameters and using equation 16, over the 
Number | Number Points Points Hamedan project area. 
APl(m) APl(m) 
34 20 0.00 3.26 Method Control Points (n=20) Check Points (n=34) 
Multiquadric [520 34 0.00 3:97 API (m) API(m) 
$ lem 7 47 0.00 6.62 
34 20 0.00 131 Orbital parameter 0.97 0.89 
Multiquadric 20 34 0.00 1.34 
emm 7 47 0.00 9.91 
34 20 0.00 132 5. CONCLUSION 
Multiquadric 20 34 0.00 1:35 : } \ 
10 Term 7 47 0.00 In this paper the accuracy potential of Ikonos Geo image was 
investigated. Rigorous models are not always available for 
34 20 0.00 1.46 satellite sensor orientation, especially for images from high 
TPS 20 34 0.00 1.36 resolution satellites such as Ikonos. Unlike the rigorous physical 
7 47 0.00 6.38 sensor model, non-rigorous models such as RFM, DLT, SDLT, 
3D affine and RBF models need no knowledge of the sensor 
model, or of orbit ephemeris and platform orientation parameters. 
Applications of these models to remotely sensed imagery acquired 
by Ikonos satellite indicate that relatively accurate geopositioning 
can be obtained through provision of ground control points. 
High resolution data increase the need for higher accuracy of data 
modelling. In order to accurately model the imaging geometry of 
high resolution flexible pointing images such as Ikonos-2, 
EROSA-1, Quickbird-2, SPOT 5 and OrbView 3, we can use 
orbital parameter model. In this paper the flexibility and 
favourable accuracy of the orbital parameter model approach has 
been demonstrated with Ikonos Geo image and the method should 
be equally useful for other high resolution satellite imaging 
systems. This investigation has shown that Ikonos Geo imagery 
has high geometric integrity. When distinct object features such as 
building corners or roads crossings are used, an accuracy of better 
than 1 m can be achieved for Ikonos Geo with orbital parameter 
model. That accuracy is within the accuracy of Ikonos Precision 
Plus product. 
Acknowledgements 
The authors would like to acknowledge the Iranian Remote 
Sensing Center (IRSC) for providing the Ikonos image, and the 
National Cartographic Center (NCC) for providing 1:1000 scale 
digital maps of the test area. 
References: 
   
  
  
  
  
  
  
   
   
   
  
  
   
   
   
    
   
    
    
   
  
   
   
   
  
    
  
   
   
    
     
   
    
  
  
   
    
  
   
   
    
  
  
   
  
   
   
   
   
   
   
   
  
  
   
       
  
   
  
    
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