Objective: Coordinate Transformation by 7-parameters method
Description:
In practice, the
navigation is often necessary to express the coordinates of positions in
different coordinate systems. Therefore, each of
the navigators should be aware of the relationship between these coordinates. Equally essential is
to transform coordinates between reference systems. One method of
transformation is the transformation of 7-parameters (Fig. 1).
Fig. 1. Coordinate Transformation by 7-parameters method
Sequence of calculations:
1. Using these coordinates transform
according to B, L on X, Y, Z
|
|
where:
|
|
1. We calculate XN ,YN, ZN from
dependences:
|
|
2.
We calculate 
from dependences
|
|
gdzie:
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|
Task to perform:
Make the transformation position coordinates WGS-84 system to the ED 50:
Transformation parameters are given in the table below.
Parameters of the ellipsoid WGS-84:
|
a |
6378137 m |
|
e2 |
0,00669438 |
|
e’2 |
0,006739497 |
Parameters of ellipsoid ED 50:
|
a |
6378388 |
|
b |
6356911,95 |
|
e2 |
0,006722669 |
|
e’2 |
0,006768169 |
Fig. 2. Way of calculation
Tab. 1 Parameters of the transformation of selected frames of reference to the
WGS-84 system
|
Układ |
Krassowskiego’42 |
European 1950 |
WGS-72 |
|
ΔX [m] |
-33,4297 |
87 |
0 |
|
ΔY[m] |
146,5746 |
96 |
0 |
|
ΔZ[m] |
76,2865 |
120 |
-4,5 |
|
ex[rad] |
-1,73889*10-6 |
0 |
0 |
|
ey[rad] |
-2,56146*10-6 |
0 |
0 |
|
ez[rad] |
4,0896*10-6 |
0 |
-2,685868*10-6 |
|
k |
0,8407720*10-6 |
0 |
2,263*10-7 |
Examples:
Position in the reference system WGS 84
BWGS84=54o40’54.45” N
LWGS84=014o15’34.76’’ E
Intermidate calculationst
|
X |
3 581 691,711 |
|
Y |
910 276,364 |
|
Z |
5 180 985,172 |
|
Xnew |
3 581 778,711 |
|
Ynew |
910 372,364 |
|
Znew |
5 181 105,172 |
Final transformation
BED50 =54o40’56.64” N
LED50 =014o15’38.76” E