Global Positioning System Reference
In-Depth Information
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A
i
=
(
1
−
r
i
)
∇
i
(4.367)
Th
e factor
(
1
r
i
)
is called the absorption number. The larger the redundancy number,
th
e less is a blunder absorbed, i.e., the less falsification. If
r
i
−
1, the observation
is
called fully controlled, because the residual completely reflects the blunder. A
ze
ro redundancy implies uncontrolled observations in that a blunder enters into the
so
lution with its full size. Observations with small redundancy numbers might have
sm
all residuals and instill false security in the analyst. Substituting
=
∇
i
from (4.366)
ex
presses the absorption as a function of the residuals:
−
1
r
i
=−
A
i
v
i
(4.368)
r
i
Th
e residuals can be looked on as the visible parts of errors. The factor in (4.368) is
re
quired to compute the invisible part from the residuals.
[15
Lin
—
0.6
——
Nor
PgE
4.10.5 External Reliability
A
good and homogeneous internal reliability does not automatically guarantee reli-
ab
le coordinates. What are the effects of undetectable blunders on the parameters? In
de
formation analysis, where changes in parameters between adjustments of different
ep
ochs indicate existing deformations, it is particularly important that the impact of
bl
unders on the parameters be minimal. The influence of each of the marginally de-
te
ctable errors on the parameters of the adjustment or on functions of the parameters
is
called external reliability. The estimated parameters in the presence of a blunder
ar
e, for the observation equation model,
[15
N
−
1
A
T
P
(
x
=−
−
e
i
∇
i
)
(4.369)
The effect of the blunder in observation
i
is
N
−
1
A
T
Pe
i
∇
i
∇
x
=
(4.370)
Th
e shifts
x
are sometimes called local external reliability. The blunder affects all
pa
rameters. The impact of the marginally detectable blunder
∇
∇
0
i
is
N
−
1
A
T
Pe
i
∇
=
∇
0
i
x
0
i
(4.371)
Be
cause there are
n
observations, one can compute
n
vectors (4.371), showing the
im
pact of each marginal detectable blunder on the parameters. Graphical representa-
tio
ns of these effects can be very helpful in the analysis. The problem with (4.371) is
th
at the effect on the coordinates depends on the definition (minimal constraints) of
th
e coordinate system. Baarda (1968) suggested the following alternative expression:
=
∇
x
0
i
N
∇
x
0
i
2
0
i
λ
(4.372)
2
0
σ
