test strip | critical test quantity
identification no. value
F
3.9,.003 CT LT QT
GPS generated 1 173.0]366.0] 2.4
data vith 4.7
constant and 2 18.51121.0/: 2.55
linear terms
Table 1. Test quantities of the groups of
parameters. The GPS data were generated
with constant and linear errors
From the above table it is clear that the constant
and linear terms in the two strips are rejected,
i.e., they are significant, whereas the quadratic
terms are not significant. The results correctly
indicate the parameters which were expected to be
significant.
In the second experiment, the same block and same
type of adjustments were used, but the generated
GPS data contain only quadratic systematic errors.
The results of the test are given in table 2.
test strip | critical test quantity
identification no. value
F
3.,.003 CT LT QT
GPS generated 1 1.0-1678.01. 2.5
data with 4.7
quadratic term| 2 8.6 [116.0] 2.9
Table 2. Test quantities for the groups of
parameters. The data were generated vith
only quadratic errors
As we see, despite the fact that the generated GPS
data contain only quadratic errors, the linear
terms in the two strips are strongly rejected,
while the constant and quadratic terms are not
seen to be significant (the constant term is
rejected in the second strip).
The results indicates that there is a curious
interaction between linear and quadratic terms. It
appears that the linear term approximates quite
well the existing quadratic error.
To examine the influence of the GPS modelling on
the accuracy of the combined adjustment, the
previously used data sets were adjusted without
GPS, with GPS using constant and linear terms for
the GPS modelling (six parameters) and finally
vith constant, linear and quadratic terms (nine
parameters). The results are summarized in table
3. Tests 2 and 3, refer to the set of data in
which the GPS data were generated with constant
and linear errors. Tests 4 and 5 refer to the
generated GPS data with only quadratic errors.
506
absolute accuracy
Case Test | No. of (meter)
no. check
points u u u u
X y z xy
without 1 80 :1701.130[.230] . 150
GPS data
with 6 2 80 .102|.091|.095|.097
par. cor.
with 9 3 80 :175].125|].603]. 152
par. cor.
with 6 4 80 .098|.087|.094|.093
par. cor.
with 9 3 80 „179[.126].608|.155
par. cor.
Table 3. The accuracy results vith different GPS
parameters
Comparing the absolute accuracy of test 1 with
tests 2 and 4 , we see that in the latter better
absolute accuracies in planimetry and height are
obtained.
The comparison of test 1 with tests 3 and 5, in
which constant, linear and quadratic terms were
used for the GPS modelling, shows that the
planimetric absolute accuracy remains on the same
level of 15 cm, while the height accuracy
deteriorates from 23 cm to 60 cm. This indicates
that when non significant parameters (in our case
the quadratic terms) are included in the
mathematical model of the adjustment, the results
deteriorate. This showed up consistently in all
experiments with generated as well as real data.
In the experiments with the real data, the
influencing factors which were investigated were
the control configuration, where five
configurations were considered shown schematically
in figure 2, and also the GPS modelling
parameters. The blocks were adjusted with the use
of constant and linear terms, six correction
parameters, and with the use of constant linear
and quadratic terms, i.e., nine parameters per
strip.
e 9
i
| -
c =
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a = 3 1 a 5
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@ : Full control point
: Horizontal control point
»
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Figure 2. Various types of control distributions
The statistical significance of the GPS parameters
was also tested. For these experiments, the
combined adjustments were executed with the GPS
observations being modelled with constant linear
and quadratic terms. Three configurations were
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