H
P
A
|
oH Ld Nanc
dx = vector of coordinates belonging together in period I and II
to be jointly tested.
The test criterion T results in
R
ri ; 57
3m 32 (57;
with
"m T Trl 0 thon
R = (dX; -dX,,-w) (B Q, B ) (dX, -dX;,-w) : (58)
T
plo mido dips dZ pau seed gg Yao dou c
T
dX TP. rgo dYrq4 25110 o San Pins Lage). *
0
H
Q eX joint weight coefficient matrix of the point coordinates to
be tested
Mostly w = 0 has to be chosen (especially if equal approximate values are used)
Again each admissible sub-hypothesis can be tested. Here it becomes particularly
important to test for significant deformations at individual points or even at
special coordinates of individual points. After all what has been shown before
it should be an easy exercise to derive those special null-hypotheses and the
corresponding test criterions.
0n account of the purpose of deformation studies it becomes very important in
this case to apply correct confidence intervals. Hence the a-posteriori orthogo-
nalization is an indispensable demand to eliminate the disturbing effects of
high correlations.
E. Concluding remarks
The relatively small extension of the linear equations of close-range systems
often enables the application of sophisticated linear models, estimation proce-
dures and statistical techniques. This fact should be utilized more than it was
done by now to obtain best possible results with respect to accuracy and relia-
bility. Like in aerial triangulation systems the self-calibrating bundle method
can provide for significant model improvements and thus for remarkable accuracy
enhancements, if suitable and highly developed additional parameter sets are
applied, as presented in this paper with the concept of orthogonal bivariate po-
lynomials. Practical experiences with aerial triangulation systems show however,
that the functional extension of a bundle model by additional parameters must be
attended by comprehensive statistical test procedures to protect against over-
parametrization. Actually statistical methods should find more attention in close-
range applications, especially for test field analysis and in deformation measure-
ments.
A really virgin area but nevertheless a very important subject in close-range
