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The denominator in equation (17) is obtained from subtracting the number of measurements n and the
number of unknown valuesu . The number of measurements n is the number of all measurements of a triplet
Y, X , H made during one day. Unknown values u also consist of a triplet for every made measurement.
Considering these two facts, an equation can be formed:
n u n
1
After the posteriori errors, unit of weights and cofactor matrixes of measured values are known the posteriori
standard errors for measured values Y, X , H can be defined:
(18)
QYY
0 0
Q
xx
0 QXX
0
(19)
0 0 Q
HH
Q ; Q ; Q
(20)
Y 0 YY X 0 XX H 0 HH
2
When using the
SAS 3
procedure the posteriori errors of unit weights are calculated accordingly to equation:
0
n
i1
T 1
v Σii
v
i
n
u
(21)
where
0
must be defined for measurements that were made in hourly intervals during one day. This can be
achieved by adding the values
T 1
v Σii
v of individually performed measurements.
In the
SAS 3
procedure the standard error of measured values is calculated by using the same equations (20)
as in procedure
SAS 2
.
Processing of daily measurements
It is necessary to process the measurements made in daily intervals. During the processing of data, only the
values important for accuracy comparison are extracted. For the purposes of comparison with the hourly
measurements, it was necessary to determine the input parameters such as:
• Coordinates of observation points ( Y, X , H ) ,
• A priori standard error for the triplet of coordinates
NAS
,
• A priori standard error
SAS 3
for individual coordinates defined with the help of known variance of
2
unit weight
0
and cofactor matrix.
The value of the first standard error
NAS
which is extracted from the measurements data is equal for all the
coordinates – triplet. This standard error is defined by the Coordinate Quality or the CQ parameter which is
defined as [3]:
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