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procedure takes into account the cofactor (
SAS 3
) matrix of preliminary observations Q in addition to the a
priori variance of unit weight . In both procedures the design matrix A is formed, approximate values
of
0 0 0
2
0
Y , X , H are selected and the calculation of the vector of absolute terms f is made. The dimensions of
the design matrix A for an individual observation that was made during one day is 3 3 and is the same as
the identity matrix. The design matrix A is build only from diagonal elements that are included in the
procedure of adjustment by parameter variance:
1 0 0
A I
0 1 0
(3)
0 0 1
33 33
Approximate values used as the input data for the procedure of adjustment by parameter variance are the
smallest values obtained from the made daily observations. Values were marked withY 0
, X 0
, H 0
. The
vectors of absolute terms were calculated according to:
1 0 0 Y0 Y
Y0
Y
f A X X
0 1 0
X
X
X X
(4)
0 0 1
0
31 33 31
31
0 0
H
0 H H0
H
The two procedures used for adjustment differ when forming the variance – covariance matrix. The variance
– covariance matrix is defined as:
QYYi QYXi QYHi
2 2
Σll 0Q ll
0
QYXi QXXi Q
XHi
(5)
Q YHi
QXHi Q
HHi
The cofactor matrix of preliminary observations Q was not known for procedure
SAS 2
but when using the
procedure
SAS 3
it was available as the part of the input data. When using the procedure of adjustment
SAS 2
the correlations between measured values were not known and thus the cofactor matrix was equal to identity
matrix:
2
1 0 0
0
0 0
2 2 2
Σll
0 Q
ll
0
0 1 0
0 0
0
(6)
33 33 2
0 0 1 0 0
0
When using the procedure
SAS 3
for the adjustment where the correlations are given as a part of input data
the covariance matrix is formed as follows:
311