ADJUSTMENT OF AERIAL TRIANGULATION BY THE METHOD 
OF LEAST SQUARES 
by R. Rozrors, Geodetic Institute, Delft, Holland. 
1. Introduction. 
When trying to develop a general theory of adjusting spatial aerial triangu- 
lation by the method of least squares one meets with the difficulty that there is 
such a wide variety of triangulation methods. Their differences are essentially 
of four sorts: 
a. different processes are applied for deducing the orientation elements of each 
pair of photographs from the observed quantities (y-parallaxes and sometimes 
also x-parallaxes): empirical, numerical and graphical methods etc.; 
b. different sets of orientation elements are used: oi xi qu bzi and byi or (1f bzi — O 
or = statoscope reading if any) oi xi yia qi and byi, etc. *); 
c. scale is transferred from one model to the next in different ways: by measuring 
in the overlap the height of the nadirpoint or some other distance; 
d. terrestrial control differs in amount or kind: control points at both ends of the 
strip or also in the middle, control bases, control azimuths, etc. 
Since the largest variety seems to exist in the above category a, the author 
has endeavoured to develop a method of adjustment which is general inasmuch 
as it is applicable whatever orientation process is used. As for the other categories 
the following choice was made: 
b. orientation elements: ci xi is Gi by: (bzi = 0); 
c. scale transfer by adjusting the base length of a space model to make the height 
of the nadirpoint (or some near-by point) equal to the value, measured in the 
preceding model; 
d. control points at both ends of the strip: at each end three points at the least, 
for two of them the complete ground coordinates X, Y and Z and for the 
third the height Z. 
It is believed that for some other choice a theory of adjustment could equally 
well be developed along the lines followed in this treatise. 
Fig. 1 gives a vertical section of the strip — which is assumed to be approxi- 
mately straight — as it is flown. From each of the air stations — 1,0, 1,... n, n + 1 
the vertical is drawn. 
Fig. 2 represents the same strip as it is triangulated according to the method 
described above; after the first model has been set to ground control succeeding 
models are built, introducing machine heights of the air stations which are all equal 
(bz; — 0)”. For that the longitudinal tilt of each photograph has to be changed 
from one model to the next; these tilts are indicated by mi and pi. Fig. 2 shows 
the gaps thus produced between the models. It is evident that these gaps are caused 
by ignoring the Earth's curvature and the variation in flying height. 
The method of adjustment, developed here, closes the gaps, gives the true 
1) w = lateral tilt, x — swing, ¢ = longitudinal tilt, by and bz = base components. 
i — sequence number of the photograph. 
2) bz is kept zero with a view to avoiding the influence of certain systematic errors produced 
by the triangulation instrument.