Coordinate Transformation 81
Coordinate Transformation
The generic formula used to translate and rotate from coordinate system 1 to
coordinate system 2 is as follows:
where
e
rx
=
e
x
expressed in radians, similarly for e
ry
and e
rz
.
Example: Define local datum as the WGS-72 datum
Send the following commands to the receiver:
$PASHS,UDD, 0,6378135.0, 298.26,0,0,4.5,0,0,-0.554,0.23
$PASHS,DTM,UDD
This implements the transformations listed in Table 5.2 and below.
Dx=Dy=0
Dz= 4.5 meters
m= 0.23 x 10
-6
e
x
=e
y
=0
e
z
= –2.686 x 10
-6
radians = –0.”554
in the following equation:
After issuing the $PASHS,DTM,UDD 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.
Table 5.2. Ellipsoid Parameters for WGS-72 and WGS-84
Datum
Reference
Ellipsoid
a[m] 1/f
WGS-72 WGS-72 6378135.0 298.26
WGS-84 WGS-84 6378137.0 298.257223563
x
y
z
2
Dx
Dy
Dz
1m
6–
´10+()
1 e
rz
e
ry
–
e
rz
–1e
rx
e
ry
e
rx
–1
x
y
z
1
+=
x
y
z
WGS84
0
0
4.5
10.23
6–
´10+()
12.686–
6–
´10 0
2.686
6–
´10 10
001
x
y
z
1WGS72
+=
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