In the following the constraints-matrix B is to be constructed. This matrix depends
on the new chosen seven-parameter S-base.
Assume the new S-base to be chosen in the terrain coordinates X. ^, Y. 4 Z4 ^
X Y Z Z
n-1' n-1' ^n-1' "n
The constraints-matrix B should make some of the elements of the new matrix
equal to zero without, however, changing the other elements of the solution
vector.
The (7xm)-matrix B then becomes:
f. iN 10'0 0000000
0100000000
0010000000
(20)
0.0.0,.10.0.00,0.0
0000100000
000000410000
Re one 000000000
The S-transformation matrix is now constructed according to (16). The (7x7)
matrix (BD*!) has to be inverted numerically.
Note that the solution S is always a different one depending on the chosen
constraints-matrix B
Denoting x for the least-squares solution using the mixed
orientation/coordinate S-base and with xc? using the new coordinate S-base the
S-transformation simply reads:
- 403 -
5
i
E
d
E
i
Dudas
—_
INED
ERE