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It is possible to make another serie in a different
time in order to create a second datum with the
same instrument but with another operator and
different weather conditions. The influence of the
operator and the environment is considered
"accidental" in the comparison of the two series.
Statistic theory is able to estimate instrumental
standard deviation in operative conditions, using
the addition of different series square errors.
The series number is indicated by ji.
The f value, number of the freedom grades of the
operation, that is of the indipendent measures, can
be obtained with the multiplication of the number of
the indipendent measures of every stratum with the
number of the strata:
f = V-' n j
The standard deviation s, referred to the measures
made in the different series, is determined by the
relation:
s =
This value is more or less different from de
teorethical value a in order of the mesuraments
number really made. The statistic methods make
us determine an interval so that we can think that ct
is contained with a certain probability. We can
determine that standard deviation value that
corresponds to the probability P=95% (as indicated
in DIN 18723) simply multipling the value s with a
coefficient x defined in function of f:
Each procedure used in laboratory makes
reference at this teoretical approach, with different
forms according to the measurament kind: azimut,
zenit, distances or difference of level.
3 - Optimisation tests
The aim of the optimisation tests is to verify how
the standard instrumental deviation varies in
function of the measures redundancy. When the
redundancy varies, the coefficient x, which is to be
considered a pejorative coefficient, also varies. It
increases standard deviation according with the
measures number, to consider the test
significativity. Significativity increases with the
number of indipendente measures.
From one side one tends to make a high number of
measures to give significance to the value (x
below); on the other one tends to reduce the
number of measures to reduce the time (and the
cost) for any determination (high %)■
We decided to perform some tests to verify these
values and we used WILD TC2000 teodolite. On
the traditional survey scheme, we took many
measures. On the 5 signals we made 3 series of 4
strata.
The 3 series have been carried out by 3 different
able operators, in good weather conditions (fresh
and with covered sky).
In table 1 we indicated the number of series, the
number of strata, the number of signals, the s
value, the number of free grades f (the number of
indipendent determinations), the x factor that
correspond to 95% of probability, the value
associated with the estimed population in the
limited number of tests.
It is easy to note that if we increase the measures
number we modify the value s (25% more), while
the c value changes only for 10%. When the strata
number increases we have different types of errors
that increase the dispersion of the tested values.
The evaluations of the zenital angles, tested
together with the azimut ones and described in
table 2, are instead different.
Minimum c isn’t obtained during the test with the
biggest number of freedom; that is synonym of
some outliers into measured values.
Notwithstanding this, standard deviation isn’t
substantially modified with the lower measure
number.
We considered an average value of about 14
minutes per every serie corresponding to a
complete reposition of the instrument, to a change
of operator and, if possible, to a work day. Every
stratum corresponds to 4 minutes. Every display
operation (not the old teodolites) needs about 1
minute; every point needs 2 minutes for the two
testings.
Regarding these data we can estimate the
measure time for the six examples above: 2h 56’,
2h 33', 1h 58', 1h 30', 1h 33' and 1h 2'. The relation
between time and operations is very difference
with the conditions choosed. The laboratory follows
now the fourth procedure of table 1 (that is 2 series
of 3 strata with 5 signals) for about 1 h 30' work.
4 - Conclusions
It is possible to project a reduction of the number of
measures to perform for every laboratory test on
behalf of the results above mentioned. We think
anyway it is correct not to discend more than f =10.
The real casuality of the population distribution
remains a problem.This changes a lot the results.
To avoid this problem the operators have to work
very carefully and they have to be very precise.
It’s possible to identify some outliers comparing
meausures with high accuracy reference values. A
real time check wuold be possible working into a
references polygon, known with high accuracy.
Each measure must be different from true value
less then the instrument estimated (or nominal)
standard deviation.
