2.3 Analytical aerial levelling (S3) 
This step can start as soon as one model is measured. It consists of 
doing, analytically the dependent relative orientation of all the 
photos of the strip (except the first). Gross errors are searched 
for, at the adjustment of every new model connected to the segment 
of strip. The size of the errors detectable at this phase is much 
smaller then the previous ones. Errors between 3 and 100 standard 
deviations can be removed at this phase. At points commom to two 
models, even gross errors in the measurements of x photoccordinates 
can be detected and located, from the 2nd model on. 
The functional mathematical model used are the collinearity 
equations: 
m11 (X-Xo) + m12 (Y-Yo) + m13 (Z-Zo) 
x=f m31 (X-Xo) « m32 (Y-Yo) + m33 (Z-Zo) 
  
(2.3.1) 
sif m21 (X-Xo) + m22 (Y-Yo) + m23 (Z-Z0) 
yeí 3i x-Xo) « mi? (Y-YO) + m33 (2-20) 
  
Where mij are elements of the orthogonal matrix for spatial 
rotations; x, y are photocoordinates; X, Y, Z are object space 
coordinates; Xo, Yo, Zo are object space coordinates of the envolved 
perspective center and f is the camera constant. This model applied 
to photocoordinates of the fixed frame (say, left photo) is function 
of Xi, Yi, Zi only, once the exterior orientation parameters are 
hold fix. When applied to photocoordinates of the right photo, it is 
function of wa, $2, k2, Xo2, Yo2, Z02 and Xi, Yi, Zi. Constraining 
the previous and the new estimate object space coordinates, for the 
points commom to two models, to be igual [11]. 
XP^ oR 
x 1 
XU 24 (2.3.2) 
1 i 
TOES 
L 1 
will allow the algorithm to detect gross errors in. the x 
photocoordinates, at the same time that introduces the scale from 
the second model on. (for the first, it is arbitrarely established). 
Tables 2.3.1 - 2.3.4 show results of the application of the 
algorithm. 
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