by the weight matrix, W, the least squares solution of 4.01 yields the 
following system of normal equations: 
(G t WG)E+G t WF = 0 ....4.04 
Formula 4.04 represents a system of equations whose size depends on the 
number of object points used in the solution. The direct solution of 
4.04 is hardly practical because of the large number of unknowns carried. 
Therefore, to reduce the size of the system, the unknowns corresponding to 
corrections to ground coordinates are eliminated. Thus, substituting 
4.02 and 4.03 into 4.04 one gets: 
D' 
+ 
D 
i 
o 
r+ 
W F = 0 
or 
(B t WB) D - (B t WC) U + B t WF = 0 
-(C^WB) D + (C t WC) D - C t WF = 0 
.... 4.05 
.... 4.06 
Eliminating the vector D from the pair of equations 4.06 we obtain: 
B t [W - (WC)(C t WC)” 1 (C t W)]BD 
- B t [W - (WC)(C t WC)“ 1 (C t W)]F 
.... 4.07 
or, more compactly, 
(B t UB)D = -B t UF 
. . . . 4.08 
where: 
U = [W - (WC) (C 1 W C)" 1 (C* W)] 
. . .. 4.09 
The solution of the system of normal equations expressed by 4.08 involves 
the inverse (B^UB)“^ which is of size 47 x 47. However, it may appear as 
an inconsistency that in the process of forming 4.08 the matrix, U, 
involves the inverse (C t WC)“-'- which may well exceed the minimum size of 47. 
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