>
45
A model of superwide angle photographs was tested after analytical resititution. In this case known
regular errors were corrected for as indicated above. The results are shown in table 4.4:3.
Table 4.4:3. Super-Aviogon, c=88 mm. The Ă–land test area. Flying altitude 2600 m. Five control points in the model.
Camera
S ol5
«m
s m
«m
Rms-values of discrepancies
check points
mm in the terrain
Corresponding theoretical values according to
s ol5 an 4 conf. limits,
mm in the terrain
X
y
z
X
y
z
Super-
Aviogon 56
6.7
7.9
• 144
226
145
140< 200< 360
146< 209< 376
127< 181< 326
For the superwide angle photographs there is good agreement between the theoretical and practical
accuracy. However only one model was tested.
4.5 The Theoretical Accuracy of Photogrammetric Strip Triangulation
In previous investigations (see reference 4.5:1) the laws of error propagation have been applied to
various methods of photogrammetric triangulation, and formula systems have been derived expressing
the accuracy of the triangulation procedures to be expected for specific conditions and approximations.
The accuracy is expressed in terms of standard errors based on the standard errors of unit weight of the
fundamental operations. The regular (systematic) errors of the operations mentioned are consequently
assumed as known and corrected to the level of the irregular errors as expressed by the standard error.
In this research program new values have been determined of these basic data of fundamental operations
and, therefore, the corresponding accuracy to be expected from various triangulation procedures will be
summarized, particularly with analytical procedures. Distinction will be made between cantilever
extension and bridging between two control point groups. Wide angles cameras, vertical photography
and normal conditions are assumed.
4.51 Analytical Stereo-Radial Triangulation
Cantilever extension
The formulas for the standard error to be expected can be expressed as follows:
h I n
S-x
I/ j (14/i 2 + 21 n + 25)
Sy — So
(10n 2 + 15/1 + 107)
s 0 is the standard error of unit weight of the image coordinates,
h is the flying altitude, c is the camera constant and n is the number of models to be triangulated.
The standard error of unit weight, however, has been found to vary considerably over the image and
therefore it is desirable to derive formulas in which this variation is taken into account. Such formulas
become complicated in derivation and therefore it seems reasonable to use a mean value of the standard
error of unit weight in the formulas shown above. According to the results of practical tests in section
1.62 the mean value of s Q can be chosen as 0.01 mm. The distribution of the standard errors is shown in
fig. 4.5:1 in the Appendix.