Full text: Commissions III and IV (Part 5)

  
    
   
  
   
   
     
    
  
   
  
    
   
  
   
  
The normal equation system as shown in (35) is typical in its arrangement for 
any photogrammetric triangulation problem. The number of points recorded at 
any one station and the number of stations involved in a specific measuring 
program will obviously influence the overall size of this matrix system but 
will not change its basic character, A study of the corresponding matrix 
(see Fig. 4) shows that we have along the diagonal, a sequence of fully 
separated symmetrically arranged square submatrices, The fact that the two 
types of submatrices which appear vary in size is less significant than the 
fact that in each submatrix of the first group, By (AP! AT)" Bx , the 
spatial coordinates of only one specific object point (in a general case up. to 
3) are present, while in each submatrix of the second group Bl (AP~'AT yl Bo, 
only the orientation elements of one specific camera station (in a general case 
wp to 9), appear. The By (AP AT)! Bg and the BL (Ap^! AT y^! By 
submatrices express the fact that a specific point was photographed from certain 
camera stations, | 
Viewing our system of normal equations with respect to the method of 
partitioning as described in this report with formulas (22) through (50), a 
Suitable point for partitioning is obviously that point on the diagonal, which 
separates the parameters associated with the model, from the parameters con- 
nected with the camera orientations, as indicated by the dotted lines in 
formula (35). According to formula (27), we may write: 
{85 tae" Y e, - [a5 (rA Y e, [e tne wr e] [estan Y Be] - 
(eL ae"! -[BS cae A e [etae Me] [pta nr ])a 0 
or, with reference to (32): 
r r 
à (CoBo); Ao = (695, (37)
	        
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