parameters to be carried as fixed or free 
unknowns. The shift and drift parameters 
are employed to model biases in the 
exterior orientation parameters t in 
instances where absolute constraints are 
imposed (via P¢) through the provision of 
prior estimates for the position and 
attitude of the sensor. 
A standard fold-in solution approach 
involving an elimination of the object 
point coordinates x is employed in the 
solution of the  least-squares normal 
equation system generated from Eqs. 3. 
The unknown orientation elements t are 
first obtained as follows: 
S 
T 
t 
t=[S+P—(PC, PC)Q FL 4) 
where 
tata 
T pi lo 
[Es +P CI PC | 
o ^e ta or 
Cp, ee PO. E 
T T 
Le[C 3 BL ~ (BC, pes / ) 
Q 
B z(B'BB& p); 
$2 Y s, Sj- AT RA) -ATRB)EGI RA); 
1 
C- Y G. C, - Bb -(A RB, BGP DE P1); 
T 
With 3 x 3 back substitution the solution 
for the XYZ coordinates of each ground 
point j is obtained as 
Il 
BI(B"PI+P,1,),-(B"BA)] j=12,-n. 65) 
with the associated covariance matrix 
being determined by the expression 
C 
., =B+B(B'RA),G(A'RB);B] j=12;-n. (6) 
Finally, the systematic error terms ta 
and tp are determined, if included. In 
their analysis of MOMS-02/D2 ground point 
determination, Kornus et al (1995) 
identified a significant: timing offset 
between the Space Shuttle navigation data 
and the image recording times. (This 
amounted to 0.48 seconds or several 
kilometres. In recognition of 
uncertainties regarding the quality of 
the navigation data, an examination of 
the effectiveness of imposing exterior 
orientation constraints coupled with 
shift" and  drift' parameters  was'?not 
thoroughly pursued for the present 
investigation. In the few bundle 
adjustments conducted which included a 
priori weights Pr and the parameters ta 
210 
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B3. Vienna 1996 
and tp, it was concluded that the shift 
and‘ drift’ terms had little ‘impact on 
accuracy for the Australian Testfield 
data. 
4. INSIGHTS FROM 2-D TRANSFORMATION 
From the standpoint of evaluating the 
accuracy ..of DIM extraction, the flat 
terrain of the Australian Testfield was a 
disadvantage. From a ground point 
determination perspective, however, it 
was advantageous in one respect, namely 
that 2-D image-to-ground transformation 
had the potential of providing an insight 
into the quality of the photogrammetric 
data. A series of affine, and second- and 
third-order polynomial transformations 
were made between the GPS ground control 
and the measured image coordinates 
(Melbourne set) in each of the three 
channels. The aim of this exercise was to 
reveal gross errors in the image 
mensuration stage and to provide an 
indication of the appropriate order to be 
adopted for the Lagrange polynomials. 
Transformations covering the full 110 km 
long testfield were first carried out, 
and this was followed by a second stage 
which considered 2-D transformations in 
four ‘localised’ areas, each of 
approximately 25 km in length. The 
resulting RMS values of XY ground point 
residuals from the transformations are 
listed in Table 1. In the table it can be 
seen that, as expected, localised 
transformations yielded smaller residuals 
than those for the full testfield, except 
at the eastern end of the area (Set 4) 
which was a region of poorer control 
point. quality. The following... points 
regarding the results in Table 1 are 
noteworthy in the context of this 
investigation: 
e. There. is essentially) no idistinction 
between the results for the 4.5m HR 
and 13.5m lower-resolution (LR) 
channels. This may be attributable to 
either poor ground control point 
identification or the lower quality of 
the nadir-looking imagery. 
e There is generally a notable 
improvement in the second-order 
transformation as compared to the 
first-order model, but a more modest 
improvement when proceeding from a 
second-order to a third-order model, 
especially in the smaller areas (Sets 
1-4). The implication here is that a 
Lagrange polynomial of second- or 
third-order might be most appropriate 
for the subsequent interpolation of 
exterior orientation parameters in the 
bundle adjustment. 
e The second- and third-order models 
yield a  planimetric ground „point 
accuracy at the 9m level (0.7 pixels 
in the LR imagery) over the full 110 
T Ann 
      
     
  
   
  
   
  
  
   
   
  
  
    
   
   
  
   
   
   
    
  
   
    
     
    
   
    
   
     
     
    
    
  
   
   
   
  
  
    
     
   
    
  
    
      
      
     
   
  
   
   
    
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