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e
2
)cos
2
b
0
(2 + 7
e
2
sin
2
b
0
)
6(1
−
(
b − b
0
)
2
(
l − l
0
)
2
(1
−
e
2
sin
2
b
0
)
2
−
+O(
l
5
,b
5
)
.
l
0
)
4
cos
2
b
0
sin
2
b
0
12
−
(
l
−
A real case study is the following. For the analytic part, i.e. the determination of local to
global transformation parameters, we have chosen 60 points from the German and European GPS
reference network (DREF 91, EUREF), where global coordinates
{X,Y,Z}
given with respect
to the GRS 80 datum have been determined. The same points are equipped with o
cial local
coordinates
{x, y, z}
in the Gauss-Krueger system given with respect to the Bessel ellipsoid and
Potsdam datum. In the above Figs.
21.2
and
21.3
, we have listed these data being transformed into
ellipsoidal coordinates
{L, B, H}
and
{l,b,h}
, respectively. (Ellipsoidal longitude
l
and ellipsoidal
latitude
b
of local type (“Rauenberg”, Bessel ellipsoid-of-revolution,
a
1
=6
,
377
,
397
.
155 m.
e
2
=
0
.
006674372) versus ellipsoidal longitude
L
and ellipsoidal latitude
B
, ellipsoidal height
H
of
global type (DREF ITRF 91, GRS 80,
A
1
=6
,
378
,
137 m,
E
2
=0
.
0066943800229) of German 1st
order stations.) No heights are available in the local system. Column 10 shows the impact of the
incremental semi-major axis
δA
and squared first eccentricity
δE
2
on the pseudo-latitudes in the
partial least squares process. The estimated transformation parameters according to the partial
least squares process as described before are presented in Table
21.1
.
Table 21.1
Analysis of datum parameters of type translation, rotation, and scale. This analysis is based upon
the pseudo-observations presented in Figs.
21.2
and
21.3
1
.
0369
t
x
=
−
610
.
144 m,
α
=
−
0
.
1859
t
y
=
−
21
.
658 m,
β
=
−
t
z
=
−
421
.
401 m,
γ
=
−
1
.
2712
10
−
6
y
−
A
x
2
/
(
n −
7) (longitude)= 0
.
03117710,
s
=
−
0
.
519485
×
7) (latitude) = 0
.
02640297
y
−
A
x
2
/
(
n
−
A=
⎡
[(1
−
E
2
)
N
+
H
]sin
B
cos
L
(
N
+
H
)cos
B
[(1
−
E
2
)
N
+
H
]sin
B
sin
L
(
N
+
H
)cos
B
sin
L
(
N
+
H
)cos
B
cos
L
(
N
+
H
)cos
B
−
0
⎣
···
=
[
N
2
(
E
2
−
1)
−
MH
]sin
L
M
(
M
+
H
)
[
N
2
(1
−
E
2
)+
MH
]cos
L
M
(
M
+
H
)
sin
B
cos
L
M
+
H
sin
B
sin
L
M
+
H
cos
B
M
+
H
−
−
⎤
−
1
0
0
0
···
0
−
⎦
(21.30)
[
E
2
M
sin
2
B
+2(1
−E
2
)
N
]sin
B
cos
B
2(
M
+
H
)(1
−E
2
)
E
2
N
sin
B
cos
B
M
+
H
E
2
N
sin
B
cos
B
A
1
(
M
+
H
)
−
2
×
9
.
∈
R
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