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se elements, In multidimensional, nonhomogsneous, and as in the
cese gf terrotrianoculation, the irregulsr systems identification
gf.the cutlving'observeations.is not. an easy task. However, the
existence of outlyino elements is inciceted Dy mean error of a
pical observation G computed after the adjustment in relation
its value Gg determined a/priori before the measurement, 6 26e,
but a large value of the correction does not necessarily indica-
tes that the corresponding observation has actually a large real
error. Identification of the outlying observations using the le-
ast - squares method for an initial adjustment may be impossible
or difficult forthe realization,
The another approach to the problem rely on the change or some
modification of the general adjustment criterion, The characteri-
stic feature of the least - squares method is that it fits the es
timator. 'uniformly" to all observations, Therefore, this also
concerns the outlying observations which are not a’priori overt.
Some class of adjustment algorithms is known as the "Robust Esti=-
0 |<
+
L
>
v
mation" (Andreus 1974, Huber 1964, Krarup, Kubik and Juhl 1980,
Kubik 1982, Rey 1978, a.a.). The method is based on the applica-
tion of an iterative process modifying the least - squares prin-
ciple in- such-a yay that if in a given k-th cycle the correction
V exceeds the assumed value (the assumed limit of outlying) then
in k*-1 cycle the respective observation will get some artificia
lly lowered ueight. In this vay, none of the observations is com-
pletely excludet and the estimator, in effect, gets the desired
propertiss i.e. is a little sensible to possible deviations.
The authors have applied for the terrotriangulation netuork so
called "Principle of choise of an alternative" (Kadaj 1978,1980)
The method does not require a definition of the limit of outlying
observations and is based on a criterion defined (contrary to the
maximum likelyhood method) as follous:
2 ip — max. (1)
where: J? - denisity distribution of standardized observational
errors, v, - corrections, i = indicator of observations.
This criterion leads to the estimators being a little tender for
outlying. In practice, this means thet if all observations besi-
des the outlying ones form a uell conditioned overdetermined sys-
tem then the outlying observations included for adjustment uill
not essentially deform the results. The name of the method comes
From its probabilistic interpretation {Kedaj 1980), where, con-
trary to the maximum likelyhood principle {for the independent
observations)
ANZ) al 1 D 12.) — nex. (2)
L l x +
¢
(Zi - some occurences uith 19 (2:3 € h … Flu. ia h 20 ), the
maximum probebility for a sum of Sccurrences "Z, (sn alternative
of those occurrences) with some approximation i$ required:
/
(33
PJ z)+8 =p Pz) — max.
(65 0-an error gf the approximetion criteriom é - 0 if pccuren-
ces Z, are mutually exclusive).
