PHOTOGRAMMETRIC ENGINEERING 
3 
from the concept of central perspective, but 
other types of records, such as Radar photog 
raphy, will become increasingly important. 
In the broad field of aerial triangulation for 
geodetic control determination, additional, so- 
called “auxiliary,” data acquisition systems 
must in the future be given more considera 
tion in order to overcome the basic limitation 
of classic photogrammetric triangulation. 
This limitation is caused by the unfavorable 
laws of error propagation inherent in the geo 
metric principles which underly such pro 
cedures as strip triangulation by the formation 
of consecutive models (Folgebildanschluss) 
Electronic ranging for the determination of 
air station positions, angular orientation de 
termination with highly accurate stabilized 
platforms, relative height measurements by 
Radar, and simultaneously executed sun or 
star photography are examples of potential 
sources for additional geometric information, 
which, together with the contents of photo 
grammetric records, must be rigorously ad 
justed. A thorough adjustment demands the 
simultaneous treatment of large amounts of 
data in a statistically significant manner, and 
the ability to introduce appropriate weighting 
factors and such constraints as exist, for in 
stance, with a priori known geodetic control 
data and their associated variances. 
Accordingly, there are three major areas 
where the application of the classic analogue 
restitution process leads either to deficiencies 
or to impractical solutions. The first area is 
the general field of aerial triangulation, or 
three-dimensional, multi-station triangula 
tions, such as those performed in the new 
field of satellite photogrammetry. In this 
instance the analogue approach is at best 
impractical, for the more complex cases im 
possible, and generally not accurate enough. 
Secondly, in the evaluation of unconventional 
photography which deviates from the concept 
of central perspective, the analogue restitu 
tion equipment loses its economical sig 
nificance because of the geometric complexity 
of the data acquisition process and/or by the 
unorthodox dimensions of the data acquisi 
tion equipment. Finally, the analogue ap 
proach is unsatisfactory in all cases where, be 
cause of extreme accuracy requirements, the 
simulation of rather complex perturbations 
becomes necessary for the reconstruction 
of the data acquisition process and when no 
degradation can be tolerated during the 
process of spatial triangulation. 
The data evaluation method capable of 
solving these problems is obviously based on 
the so-called analytical approach, which 
means that the data reduction, providing the 
link between the measured raw data and the 
final triangulation result, is accomplished 
with the help of digital computations in 
accordance with a set of formulas expressing 
the mathematical model of the specific meas 
uring procedure. With the presence of re 
dundant information, as is usually required, 
the corresponding computations are per 
formed in conformity with the generalized 
principle of least squares. 
Foremost in significance in the evolution 
of this new area of photogrammetry is the 
arrival of the electronic computer. From the 
foregoing it should be self-evident that the 
basic importance of this tool is not the ability 
to perform numerical solutions for such data 
reduction procedures as are presently ex 
ecuted on the analogue type restitution 
equipment. In other words, analytical 
(numerical or computational) photogram 
metry must not be considered as a means for 
a numerical simulation of the analogue 
simulators that are presently in use for the 
reduction of photogrammetric raw data. 
The potential of the computational ap 
proach to photogrammetric triangulation in 
particular, and to three-dimensional tri 
angulation in general, must be assessed by: 
a. the possibility to design into the mathe 
matical model for the data evaluation 
process as much complexity as is con 
sistent with our knowledge about the 
physical characteristics of the various 
instrumental components and measuring 
operations which comprise a specific 
measuring procedure, and 
b. the possibility to treat, in a statistically 
rigorous manner, all data containing 
geometric information which supports 
the specific triangulation problem. The 
least squares algorithm must adjust the 
raw data not only in accordance with 
the somewhat vague theory of errors, 
but in terms of a best fit to a precon 
ceived mathematical model which de 
scribes the specific measuring pro 
cedure. The discrepancies of the fit will 
provide information about the residual 
errors (noise) and about unresolved 
systematic errors (biases) which are 
caused by deficiencies of the mathe 
matical model on which the adjustment 
was based in the first place.