— — Cv iu V Le 
d 
n 
d 
f 
  
  
  
3.2 Rugged ground 
In the controlled experiments of Sub-commission IV:1 (Monti di Revôira) there are large elevation 
differences on the ground and the expressions mentioned for the standard errors are probably not 
applicable. Special theoretical investigations have therefore been performed concerning the error 
propagation formulas in this case. In general the same procedure was used as in reference [2]. The 
formulas refer to the actual location of the control point groups. 
The derivation of the formulas proved to be very comprehensive and cannot be demonstrated in 
detail in this connection.! 
In Appendix 1 the results of the derivations are demonstrated in Diagrams 1.1— 1.3, showing the 
distribution of the standard errors in planimetry and elevation over the model surface under the 
actual conditions concerning elevation differences, number and location of the control points and 
for the standard error of unit weight of the y-parallax measurements chosen as unity. It is assumed 
that the photographs are approximately vertical, that the errors of the fundamental operations are 
at least approximately accidental (normally distributed) and that the standard error of unit weight 
of the image (model) coordinate measurements is of the same order of magnitude as the standard 
error of unit weight of the y-parallax measurements. 
Further it is assumed that the discrepancies in conditions occurring (in particular those of the 
relative and absolute orientation) are adjusted according to the method of least squares. 
In actual test models these assumptions are more or less approximately fulfilled. There are doubtless 
systematic errors in the fundamental operations in particular Nos. 1 and 2. Further, the conditions of 
the relative and absolute orientation are in general empirically treated and certain unadjusted 
discrepancies doubtless exist, see Table 1. Therefore, instead of the standard error of unit weight 
$,,5 the mean square value of the measured residual y-parallaxes Sm,; after the relative and absolute 
orientation will be used as a substitute. This obviously means a certain approximation. 
In summary, the following expressions will be used for the prediction of the mean square values 
of the discrepancies in planimetry and elevation to be expected from the vertical photography in 
models over Monti di Revoóira: 
M,—1.5 Smys S 
My=1.5 spy; S 
M;=2.0 Smıs S 
Smy5 is the mean square value of the y-parallaxes in 15 re 
gular model points and S is the average 
scale factor of the photographs. 
DID 
3.3 The precision of the estimation of the accuracy 
When the theoretical mean square values of the discrepancies in planimetry and elevation are 
compared with corresponding practical data there will doubtless appear differences. It is obviously 
of importance to estimate the order of magnitude of those differences, which can be regarded as 
acceptable. In particular, if the expressions for the error propagation themselves are to be tested it is 
most important to determine the acceptable limits for the differences between theory and practice. 
The first prerequisite for such a test is of course that the test points on the ground shall be uniquely 
identifiable in the photographs and that the geodetic coordinates and elevations shall be completely 
reliable. 
The precision of the estimates of the accuracy will be expressed here as confidence intervals in 
accordance with statistics, see for instance reference [7 ].? 
I These derivations were performed by Mr. L. Ottoson, who will publish the complete procedure in other connection. 
? In such cases the standard error of the standard error of unit weight is sometimes used, according to the definition: 
So 
Ss — 
So 
/ 2 (n—u) 
where n—u is the degrees of freedom. This expression is here mainly used only for a demonstration of the influence 
of the number of redundant observations upon the reliability of the standard error of unit weight. 
23