GJ - Privredna komora Srbije

2 2 2
QYYi QYXi QYHi 0QYYi 0QYXi 0Q
YHi
2 2 2 2 2
Σii 0 Q
0
QYXi QXXi Q
XHi
0QYXi 0QXXi 0QXHi
(7)
33 33
2 2 2
Q YHi
QXHi Q
HHi
0QYHi 0QXHi 0Q
HHi
Continuation of the SAS
2
procedure of adjustment is followed by the formation of the matrix of unit weights
1
1
P Σ in the second case when using
SAS 3
procedure the inverted covariance matrix Σ is used instead
ll
of unit weight matrix. After the unit weight matrix or the inverse covariance matrix is defined the adjustment
is in both cases followed by defining vector of absolutes terms n , normal equations coefficient matrix N ,
cofactor matrix Q , vector of unknown parameters x and residual equations v . The following equations
were used:
xx
ll
T 1
n
A Σll
f (8)
T -1
N = A ΣA
ll
(9)
1
Qxx
N (10)
x Q n (11)
xx
v Ax f (12)
By knowing the values of vectors of absolute terms x the values of adjusted coordinates can be obtained by
following equation:
Yizr Yizr Y
Xizr X0
x
X
izr
X
izr
X
(13)
H
H
izr izr H
The sum of square adjustments during the procedure
SAS 2
can be written for each coordinate as [1]:
1 1 2 2
pvv p v p v p v
(14)
Y
2 2 2
Y Y Y Y Y n Y n
1 1 2 2
pvv p v p v p v
(15)
X
2 2 2
X X X X X n X n
1 1 2 2
pvv p v p v p v
(16)
H
2 2 2
H H H H H n H n
Posteriori errors of unit weights are calculated for each of the three coordinates by usage of equations:
pvv pvv pvv
; ;
n u n u n u
Y X Z
0Y 0 X 0H
(17)
312