(13) substituted in (12) results in 
(14) t=(BD,,)".(c-B_x°) 
# 
21) 
(14), substituted in (12) results in: 
15) AX X^, BD...) (C-BAX 
AX s (E-D, (BD,.) 'B.AX. « D,,(BD,) C 
A 217721 UE 21972) & 
Equation 15 presents the generalized S-transformation formula limited by the 
constraints under (13). 
In geodesy and photogrammetry it is common practice to consider differential 
similarity transformations and therefore C can be set to zero, hence the 
differential S-transformation is: 
b -1 
(16) AX? - (E-D4,(BD,,) B).AX 
- (S).AX 
where 
S : S-transformation matrix. 
In case the similarity transformation is not a differential one a three dimensional 
Helmert transformation can be applied in a stage of preprocessing. 
Note that the obtained least squares solution of (16) depends on the chosen 
constraints-matrix B. 
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