It appears advantageous to have an analytical solution which is affected as 
little as possible by the number of rays involved in a specific triangulation 
case, and which in addition uses formulas already in use in the computational 
procedures previously described. Obviously, such a solution is already available 
with the observational equations (15) if only the coordinate corrections AX 
^ Y and A a, are considered as unknowns. These observational equations lead 
directly to the ‘corresponding normal equation system formed according to 
formulas (55) by introducing (AP-!AT y! as P and Bg as a null matrix. The 
necessary coefficients of the observational equations denoted by J,» 5 
K, and L and L, are given in formulas (41). 
This approach makes it necessary to compute, as a first step approximation, 
values for the coordinates of the point under consideration. This may be done 
efficiently with the use of the formulas (11), which may be written as: 
X +02Z+B =0 
x x 
  
  
  
(56) 
Y+0Z+B =0 
J y 
‚where : 
; (x-x,)A, + (y-y, 94, + cD S 
o Row = …- — 
X Q W 
a, - (x-x,)B, + (y-y,)B; + CE Loy 
Q W 
By =r (ad, , x.) 
B T" (a 2 + Y) 
The corresponding normal equation system for an n-ray solution is; 
Y Z 
n 0 “LA + [LB] 70 
n tio T = 0 ( 
2 [4] * [5,1 (57) 
+[ox] + [ap] =0 
It should be pointed out that the roots obtained from formula (57) must not 
be considered as the result of a rigorous least squares solution because there 
is no indication how nearly this approach minimizes the sum of the squares of 
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