ANALYTICAL AEROTRIANGULATION : TWO-DIRECTIONAL 
TRIPLETS IN SUB-BLOCKS 
by 
Edward M. Mikhail, Ph.D.* 
Canadian Aero Service Ltd. 
Ottawa, Canada 
ABSTRACT 
A study of past and current methods of analytical aerotriangula- 
tion clearly indicates the close similarity, in basic thinking, between 
analytical treatments and instrumental techniques of triangulation. In 
this paper, the author reappraises the situation and introduces some new 
concepts and ideas that are more suitable for analytical photogrammetry. 
An equal all-around overlap, thus allowing for forming square units or sub 
blocks, instead of strips, is advocated. Two methods of sub-block triangu 
lation are presented: (1) "Sub-Block Extension," and (2) "Sub-Block Best- 
Fit." A full account is given for the second method which is composed of 
the following steps: (a) "Sub-Block Relative Orientation," (b) "Sub-Block 
Assembly," and (c) "Sub-Block Adjustment." 
Both methods presented are based on rigorous mathematical and 
statistical principles. Necessary derivations are included and are 
oriented toward systematized computational techniques suitable for elec 
tronic computers. Of considerable interest are two theoretical develop 
ments: (i) A simple, but powerful, mathematical technique for readily 
modifying an already evaluated least squares solution due to deleting some 
of the observation equations (see equations 4.30 and 4.31 in the text); 
and (ii) A novel attempt for a simultaneous three-dimensional transforma 
tion of higher degrees for the adjustment of photogrammetric strips and/or 
blocks (equation 4.41). A limited amount of test results for the latter 
development is included in the Appendix. Further investigation and tests 
may be undertaken in the future. 
* A major portion of the research presented .in this paper was carried out 
at the Surveying Department of Cornell University, Ithaca, N.Y., U.S.A., 
during the time when the author was a doctoral candidate.