3. ESTIMATION OF THE ACCURACY TO BE EXPECTED IN THE FINAL 
COORDINATES AND ELEV ATIONS 
3.1 Comparatively flat ground 
As demonstrated in [2] it is possible to derive theoretical expressions for the accuracy of various 
functions of the fundamental operations. The accuracy will be expressed as standard errors of the 
functions and will be founded upon the standard errors of unit weight of the measurements of the 
fundamental data of all photogrammetric work, viz. the image (model) coordinates and coordinate 
differences (parallaxes). Concerning the final coordinates and elevations of single models it is possible 
and suitable to express the accuracy to be expected as mean square values of the discrepancies in 
the check points in planimetry and elevation. The check points are regarded as conditions in which 
the discrepancies, which are caused by the errors of the fundamental operations, are determined. 
The mean square values are preferably determined mathematically from the error functions and must 
be referred to a certain area, for instance the neat model 2bd. Evidently, the number and location 
of the control points will have some influence upon the accuracy and must be taken into consideration. 
For approximately flat ground and vertical photographs the expressions for the standard errors 
of model points in planimetry and elevation are demonstrated in Appendix 1, p. 37 
are assumed concerning the number of the control points, viz. 
39. Two cases 
  
a. Two points in planimetry and three points in elevation (minimum). 
b. Five points in planimetry and elevation. 
The location of the points is demonstrated in connection with the formulas. 
From the expressions for the standard errors more concentrated expressions for the mean square 
values of the standard errors over a certain area can be determined. Such expressions can then be 
applied under various conditions concerning, for instance, the camera type, the overlap, etc. and can 
be still more concentrated. 
Here we will demonstrate such formulas as applied to the controlled tests of Sub-commissions 
IV:2 and IV:3. 
The mean square values of the discrepancies in planimetry and elevation are denoted My, M, and 
M; respectively and refer to the neat model area 2bd. Since the models after empirical orientation 
are usually not adjusted up to the requirements of the method of least squares the mean square value 
of the measured y-parallaxes in 15 model points is used as an approximate substitute for the standard 
error of unit weight of the y-parallax measurements. The general prerequisites for the application of 
the formulas are summarized below. In principle, only accidental errors are assumed in the funda- 
mental operations. 
Sub-commission 1V:2. Normal angle camera. Comparatively flat ground. Five control points in the 
corners and in the centre of the models. 
M,==1.1 Sms S 
My=1.2 Snus Ÿ 
Mz=3.88mı5 S 
S is the scale factor of the photographs. 
Sub-commission IV:3. Wide angle camera. Comparatively flat ground. Planimetry and elevation 
control points in the corners of the models. Elevation control also in the centre of the models. 
M&z:1.9 Sm15 S 
M y— 3 Sm15 S 
M,—1.8 Sm45 D 
22 
  
  
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