47
4.54 Confidence Limits of the Standard Errors
Because the determination of the standard error of unit weight cannot be exact the standard
errors of the model coordinates will have a corresponding uncertainty increased by the influence of the
approximations used to derive tractable formulas. The confidence limits of the theoretically derived
standard errors provide a means of judging the significance of the differences between these standard
errors and the root mean square values of true discrepancies in geodetic, errorless check points.
For such a determination of the confidence limits the degrees of freedom and the level of significance
must be given. The assumption is made here that the standard errors of unit weight are estimated from
y-parallax measurements in 9 model points, i.e., there are 4 degrees of freedom and the significance level
of 5 per cent is chosen.
According to ordinary statistical principles the confidence limits of the standard errors will be 0,6s—
2.9s.
The confidence limits of individual discrepancies between photogrammetric and geodetic (check)
coordinates are, according to the i-distribution, 4 degrees of freedom and the 5 per cent confidence level,
4- 2.8s where s is the standard error of the photogrammetric coordinate in question.
Reference 4.5:1. Hallert, B.: Investigations into the Accuracy of \arious Methods of Photogrammetric
Triangulation. Transactions of the Royal Institute of Technology Stockholm, Sweden
Nr 162 1960.
5. SUMMARY AND CONCLUSIONS
The purpose of these investigations has been to develop methods for testing the fundamental opera
tions of photogrammetry and to apply the methods to actual problems.
All photogrammetry is founded upon the image coordinates of the photographs, and therefore parti
cular attention has been paid to investigations of the sources of error of such coordinates. The flatness
defects of the image seem to be of considerable importance and have been examined in different ways.
Further, the stability of emulsions and the emulsion base has been investigated, and the weight distri
bution of image coordinates in films and glass diapositives has been tested in practice. Photographs
from aerial cameras have been calibrated and tested in the laboratory and the field using the method
of least squares, and the properties of residual image coordinate errors have been tested with statistical
methods. New procedures and formulas for the determination of the accuracy of the elements of the
interior orientation have been developed. A great number of photographs from non-topographic cameras
and X-ray instruments have been tested and calibrated.
A number of restitution instruments including stereocomparators, A7—A8 autographs and stereo-
planigraphs have been tested and regular errors have been distinguished as well as possible from the
irregular errors, which have been statistically estimated as standard errors of unit weight.
The operations of relative and absolute orientation have been tested from different points of view and,
in particular, distinction has been made between the precision and the accuracy of the fundamental
measurements. Standard errors of unit weight of empirical and analytical relative orientation have been
determined.
Finally the accuracy to be expected in the final results of the photogrammetric procedure has been
determined with respect to the accuracy of the fundamental operations. Analytical photogrammetry
applied to aerial photographs according to new, simple formula systems has been tested concerning the
theoretical accuracy.
In conclusion:
The main sources of errors of the photogrammetric procedure are to be found in the image coordinates
of the basic photographs. There are many possible causes of these errors which should be much more
carefully investigated than has yet been done. The shrinkage of the emulsion and emulsion base seems
to be the most important source of error in ordinary photogrammetric work, and the introduction of
new film base material is highly desired. Flatness defects of the image plane are of considerable impor-
