It is well known that the parameters x are calculated that E
0 — o is a necessary result, where o denotes the (r,1) size
zero vector and additionally x x-min.
To obtain the matrix E from the sparse matrix A the
numerical condition A E'- 0 is considered for the compu-
tation of E. To minimize rounding errors and numerical
inaccuracies arising from the large amount of data within
the photogrammetric application iterations are carried out.
4. COMPUTATIONAL CHECKS WITHIN PROMPT
When dealing with a large amount of data, it is very impor-
tant to check the adjustment and analysis results with an
independent computation. PROMPT was designed to
provide high quality results and to insure their accuracy.
Some important numerical checks are displayed, such as
the well known ANSERMET-Check. Consider the (n,n)
size diagonal matrix of weights P (with p; > 0.0) and the
(n,n) size unit matrix I then the (n,n) size matrix (I-C)
contains the so called observations' redundancies r; on their
diagonal elements
( - C), -(r- at pA) a7 p) =7;
(4)
I
Those observations' redundancies may be taken for the
determination of the so called inner reliability parameters
and for statistical testing like the standardized or
studentized residuals.
The ANSERMET check displays the sum of the diagonal
elements (trace) of the (n,n) size matrix A (A'PA y! ATP
that has to equal the rank q of the design matrix A. Re-
member that q is an integer value. For an adjustment with
rank deficiency design matrices the numerical checks A
E'= 0 and E x = o are displayed by summing up the abso-
lute sum of the elements of the (n,r) size matrix 0 and the
(r,1) size vector o.
These numerical checks are important to control the proper
working of the computer's processor and to decide whether
to add some iterations to the computations and increase the
accuracy.
When calculating the error ellipsis for the object points the
following equation may be taken for a numerical check
sj s3vsi-4 B e.c (5)
where s denotes the standard deviation of the points' coor-
dinate and A,B,C denote the axis of the corresponding
error ellipse.
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B3. Vienna 1996
5. PERFORMANCE OF PROMPT
It is the target of PROMPT within the CDW (Close Range
Photogrammetric Workstation) of Rollei Fototechnic to
provide a most convenient and easy-to-use environment.
Using the WINDOWS platform for PC applications the
number of observations and parameters may be extended to
several thousand.
Camera data
aktiv. fest
Focal length and principal point EK LJ]
Radial symmetric distortion A1.A2 P3 L]
Radial symmetric distortion A3 F1 L]
Radial asym. and tang. dist. B1, B2 F]
Affinity C1, C2 L]
"Others
Number of Iterations
Sigmal a priori
Balancing steps
Free network
Figure. 2a: Initial PROMPT screens
Estimation method
[ Estimation Calculation of (balanced) L1-Norm method. |
ud Cancel of iteration with ESC
[ Statistics
Number of fixed points 0 Number of add. obs. a
Number of new points 107 Number of unknowns 378
Rank defic. 7 Number of photos 8
Nunber of observations 1604. Number of cameras 1
[Iteration
Max. iteration steps n 1] Act. iteration step D
Sigma 0 0.0000000 Convergency limit 1.e-005
RMS of unknowns 0.0000000
Es Programm step: Start adjustment computation.
[- Controls
Nominal actual
Ansermet dE D.0000000
Free net
A"ET [Mean value) 0.000000 0.0000000
EX 0.000000 0.0000000
Figure. 2b: Initial PROMPT screens
Graphical tools for the judgment of the results are also
integrated (ref. figure 3).
194
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