nated satelli- 
ystem, which 
and Geode - 
system it is 
record. 
irget in terms 
un as an illu- 
I and Echo 
of a world- 
First, the 
disturbing 
patial direc- 
rical strength 
dellite should 
lg from unfa- 
possible 
Lise varia - 
plan for a 
102 sides. 
, a nominal 
sr practical 
meed by 
ons, the 
jor world 
neighbor - 
shed in 
in jud - 
angulation. 
are inter- 
s Cata - 
910) a 
advan - 
errors, 
at the 
the who- 
* contai- 
than the 
racy as 
on of star 
ng south- 
mean 
faint, 
epart from 
geometric 
by 1975 
these two systems will have deviated from each other by as much as 0. "9 in right ascension 
at-60° declination. Precision geodetic satellite triangulation depends on the removal of such 
discrepancies, emphasizing the need for intensive series of fundamental astronomical obser - 
vational programs [10]. 
Entirely in accordance with any other photogrammetric triangulation procedure, the 
collinearity condition is the basic element of measurement in stellar triangulation. In other 
words, any system of stellar triangulation can be conceived as a multitude of individual rays, 
where the direction of each of these rays is determined from a corresponding photogramme - 
trie record. 
Therefore, it is first of interest to study the accuracy with which such a direction can 
be obtained, in order to follow ultimately with the problem of determining the accuracy of the 
final triangulation as the result of propagating the errors of the individual rays into the confi 
guration of the spatial triangulation. 
The problem of how accurately an individual ray can be interpolated into the star back 
ground can be studied by considering two independent error-sources : 
a - The accuracy with which the spatial orientation of the photogrammetric record can be 
established from the star photography, and 
b - the accuracy with which the image of the satellite can be measured. 
The accuracy of the determination of the orientation of the photogrammetric record is 
obtained from the inverse matrix of the normal equation system associated with the analytical 
treatment of the single photogrammetric camera. Experience has shown that, despite previous 
ly established camera calibrations, it is necessary to incorporate, in addition to the six geome 
trical parameters (three rotations and three translations), three to seven parameters, depen - 
ding on the quality of the photogrammetric camera, describing the distortion characteristics 
of the specific photogrammetric record at the moment of exposure. In addition, it is obviously 
necessary to provide means for correcting both the plate measurements and the star catalog 
values in accordance with assigned weighting factors. 
The following diagram shows the number of stars which must be measured on an 18x18 
cm photography, obtained with f = 300 mm, as a function of the number of parameters carried 
in the solution, in order to obtain a certain overall orientation accuracy. It is important to note 
that not only the absolute number of parameters, but also the need for additional star imagery 
increases with the size of the area of the photogrammetric record used for the recording of the 
satellite information. If, for example, 2/3 of the record is to be used for recording satellite 
images, and 9 parameters are considered necessary for describing the mathematical model of 
the photogrammetric camera, it is necessary to measure 15 0 approximately evenly distributed 
star images in order to obtain a minimum orientation accuracy of t 0. 5 seconds of arc, if the 
mean error of unit weight for a single coordinate measurement is + 3 microns. 
The coordinate measuring process obviously is one of the key operations during the da 
ta evaluation. The problem begins with the need for a calibration standard in the form of a cali 
brated grid with which the comparator calibration can be performed. Quite a few papers have 
been published in the past few years which are concerned, in part, v/ith the measuring of plate 
coordinates for precision photogrammetric triangulation. In these publications it has become 
customary to claim a coordinate measuring accuracy of better than one micron. It is of inte - 
rest to consider such statements in light of the fact that at present the national institutes for ca 
libration - to name a few, the Bureau of Standards in the U. S. A. ; the Physikalische Technis - 
che Bundesanstalt in Braunschweig, Germany ; the Eidgenössische Amt für Mass und Gewicht 
in Bern, Switzerland ; - do not accept the task of calibrating a line grid of 200 x 200 mm to an 
accuracy of 1 1 H- . As a matter of fact, these institutes apparently have to apply their full ca - 
pabilities in order to calibrate the positions of a sequence of lines on a 200 mm glass scale to 
an accuracy of t 0. 5 p. . 
It was necessary, therefore, to develop a special measuring procedure in order to ob 
tain the coordinates of a selected number of grid intersections (25 points arranged in a 5 cm 
- 45 -