CONTROL OF A COMPARATOR BY PROPAGATION
OF VARIANCE AND COVARIANCE
José Catalán
Instituto Geográfico Nacional
Espana
Commission III
Abstract
The photocoordinates measurements, as it is well known are made -
by a' comparator (stereo or mono).j)Images of the fiducial marks ur
appear on each photograph. They are defined and marked better than
images’ of“pass or control points. Weican say that the images of -
the fiducial marks, as they appear in two. sucessive photos, are -
located in the same relative positions. By comparing. the lenght
between fiducial marks in all sucessive pair of photos of the block,
we can stimate the uncertainty of a single coordinate measurement
by application of propagation lawrof variances/and covariances. -
80, it is possible a coarse control of the comparator. py using as
reference the uncertainty of a single coordinate measurement obt
ned from the usual measurements on the fiducial marks, as they a
obtained in an aerotriangulation block..A numerical example is a
SO given.
Introduction
The control of a comparator referred to in. this paper Is done by -
means.of the evaluation of the uncertainty:of a single photo-coor-
dinate measurement, by using the photo-coordinates as they are ob-
tained from the usual measuring process by a comparator. So, it -
will - be possible a Coarse control of the comparator by using ‘as -
reference the numerical value obtained.
A possible method of evaluation could be defined, as follows $1)
To.chose a set of "fixed" points along the set of photos, for -
example the four fiducial marks, 2) To express the photo- -coordi
tes of the fiducial marks referred to the photograph system wh
oficin is.the principal point. 3) TC compute both of the mean
the variance of the photocoordinates, using the numerical val
of the variance as reference.
Unfortunately, we can not assume that the images of tne four - -
fiducial marks were fixed points on.the whole block. But we
say that the images of the four fiducial marks, as they appea
two sucessive photographs, are located in the same relative p
tions, because it is possible to assume that the shrinkage fi
is the same in two sucessive photographs. So, the actual dist
petween.a pair fiducial marks is the same on the Left and the : -
right photographs. If we compute each difference of distances. .-
Obtained from each pair of left and right photographs, we would
obtain a set of deviations (so many deviations as models in the
block for each pair of fiducial marks we use). By standardizing
+his deviations we can realise that they are normally distributed,
N (0,1) for the whole block. The propagation law of variances -
and covariances allow us to link the variance of the scandardised
deviations to the variance of a single photo-coordinate for the -
