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required with such an approach. Furthermore, the approach does not pre- 
clude any filtering or smoothing of the auxiliary data that could be 
carried out before or after a preliminary block adjustment. 
1. OVERVIEW OF THE SPACE-M FORMULATION 
The mathematical formulation used in the computer program SPACE-M is.based 
on the spatial similarity relationship between a stereoscopic model and its 
terrestrial image as estimated by the method of least squares. The impli- 
cit assumptions in this approach are that compatible coordinate reference 
systems are used and that all known systematic errors have been corrected 
for in the observational information. 
For the photogrammetric system, it is customary to use a right-handed 
Cartesian coordinate system (x,y,z) with x-axis along the base (or 
parallel to it) and the z-axis positive upward. For the terrestrial system, 
it is customary in topographical mapping applications to use the Universal 
Transverse Mercator (UTM) or any similar projection for (X,Y) and heights 
above Mean Sea Level (MSL) for Z. The reasons for choosing such coordinate 
systems are discussed in [Blais, 1977 and 1979]. 
Considering the linearized spatial similarity relating the photogrammetric 
measurements (x,y,z) to their terrestrial images (X,Y,Z), one has the 
transformation equations 
x = ax +by < cz + © 
Y = ay - bx - dz + f 
Z = az + ex + dy + = 
in terms of the seven unknown parameters a, b, c, d, e, f and g per stereo- 
model. In a SPACE-M adjustment, these seven unknown parameters per stereo- 
model are estimated simultaneously and directly using all the relevant 
observational information and statistical weights using the method of least 
squares. The perspective centres are treated in exactly the same manner as 
any other photogrammetric points in the stereomodels. 
The rigorous similarity transformation of the photogrammetric stereomodel 
measurements (x,y,z) using the corresponding estimated parameters a, b, c, 
d, e, f and g per stereomodel is carried out in the following manner: 
  
  
  
  
  
  
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Z 0 0 1 0 wo Q1 ba ; 0 $1 [? g' 
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cos « = a/k 
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