solve the real problem. Here one observes from (4.7) and (4.9), that a good 
artificial approximation of the variance covariance matrix of the constrained 
coordinates is achieved by: 
  
-1 
I 0 e aH 0 f T HH 447 
1 (4.10) 
ett I | 0 c-2 "ll g I 
in which all matrices H are composed using c = 1. 
(4.10) is elaborated into: 
/ 11 12 
e M S Un 
k k 1 J 
21 -22 21. 11 12: ^ 
C iH C 2 4 1 Fi: f H 
aX ¥ Xk (4.11) 
( 11 12 
Ey S 
k k 
21 22 -22 
eH e ah + Le - S a 
L k k k 
So the artificial variance covariance matrix for a constrained block implies an 
extension of the artificial matrix of the known points to the new points X? as well 
(using the parameter value c j from the known coordinates) and in addition the 
-22 
x 
orthoganalized matrix (c 2 K c 1 H to the new points x2, 
  
X X (cel) 
k 
The extension of the matrix in case of more densification steps (for instance 
11 11 
G, itself has already a structure such as in (4.11) in stead of c 1 ), has 
been proven to be possible and results in: X 
( 11 12 13 
C iH C 1 C i" 
X X X 
21 22 -22 23 -23 
C 1 C a mic 2. C 12H C 1 *(o a! C 12H 
x x X X X x X 
31 32 32 33 -31 =33 
H H - H H - H - H 
e C 1 le à C 1° e «e. )? +48 3 2) 
X X X x x x X X x 
(4.12) 
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