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After issuing the $PASHS,DTM,USR command, the receiver internally transforms positions from
the reference datum (WGS-84) to the user-defined datum. In standard text books, however, the
datum transformations are given from local datums to WGS-84. To simplify entering the
transformation parameters, the translation, rotation, and scale parameters are defined from the local
datum to WGS-84.
The generic formula used to translate and rotate from coordinate system 1 to
coordinate system 2 is as follows:
where
Example: Define local datum as the WGS-72 datum
$PASHS,UDD, 0,6378135.0, 298.26,0,0,4.5,0,0,-0.554,0.23
$PASHS,DTM,USR
This implements the transformations listed in Table 4.7 and below.
WGS-72
WGS-84
∆x=∆y=0
ε
x
in the following equation:
x
y
z
WGS84
Advanced Operation
∆x
x
(
∆y
=
+
1
y
∆z
z
2
ε
ε
=
expressed in radians, similarly for
rx
x
Table 4.7: Ellipsoid Parameters for WGS-72 and WGS-84
Datum
Reference Ellipsoid
WGS-72
WGS-84
∆z= 4.5 meters
ε
=ε
=0
= –2.686 x 10
y
z
0
(
×10
=
+
1
+
0.23
0
4.5
ε
ε
1
–
rz
ry
6 –
×10
)
ε
ε
+
m
–
1
rz
rx
ε
ε
–
1
ry
rx
ε
and
ry
a[m]
6378135.0
298.26
6378137.0
298.257223563
-6
m= 0.23 x 10
-6
radians = –0. 554
×10
1
–
2.686
6 –
)
6 –
×10
2.686
1
0
0
x
y
z
1
ε
.
rz
1/f
6 –
0
x
y
0
z
1
1WGS72
41
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