being V = | — n the degrees of freedom.
Figure 2 shows the flow chart of the above explained strat-
egy.
assign the weights:
P-=
|
»| robust procedure fe à
i
l.s. adjustment
Hawkins test
on max(9?)
y
display
the results
read:
loop control key
read:
updated obs.(i)
P, = I inliers (2/3) assign the weight
Py = 0 outliers (1/3) pii
f 1
outlier detection: progressive
reassign the weights sampling
4
4
loop
control key
< 0 test > 0
null hypothesis
true
end
Fig. 2
148
4. Fields of application
Least squares methods and some other related procedures
(e.g. cluster analysis, multiple regression, variance analysis,
robust estimators) are usually appropriate for two types of
problems:
® network adjustment;
® interpolation and approximation.
In the first one, the observables are functions of point po-
sition differences, whilst in the second are functions of point
positions. These point positions (or the point position dif-
ferences) could depend on time.
Moreover the observables, depending from point positions
and time, are influenced by physical fields, according to the
data collection procedure.
Morphological factors and/or eventual kinematics param-
eters are functions of the point positions, since they are
supposed to have a similar behaviour in the neighbouring
points.
In the case of network adjustment, the geometrical model
is quite familiar. On the contrary, in the second one two
main sub-cases may occur:
€ a deterministic law for the behaviour of the phe-
nomenon under study has been previously checked, by
a variety of causes, that may be physical, geometrical,
or others;
€ no deterministic law is previously known for the phe-
nomenon behaviour.
The theory of models has a proper classification for both
sub-cases as a “grey box” model and a “black box” model,
respectively.
In the “grey box” model, the aim is the estimation of
model coefficients, followed by proper significance tests for
estimated parameters.
In the “black box” model, the main deterministic and
stochastic approaches are preferred:
€ in the first case, aside from further details, one has a
number of steps, as in the choice of an interpolation
strategy (finite elements, Fourier analysis, wavelet in-
terpolation, ...), the estimation of coefficients for the
chosen models, the variance analysis (in order to esti-
mate altogether significance of parameters and quality
of model);
® the second one employs covariance estimation, covari-
ance function modelling and collocation (linear filter-
ing and prediction ).
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B1. Vienna 1996
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