Full text: Commissions III and IV (Part 5)

problem is consequently to study the error propagation into functions 
of funetions of indirect observations. First the series of differential 
functions have to be well defined. Then the wellknown procedures for 
the study of error propagation can be applied. 
The differential relations between the coordinate errors of the ex- 
pressions (78)—(81) and the errors of the oriented image coordinates 
x'y', x"y" are demonstrated in the expressions (3) and (4). 
The differential relations between da’ dy’ dx” dy” and du’ dv’ du” dv” 
are demonstrated in the expressions (30)— (33). The corresponding 
weight- and correlation numbers are derived in the expressions (5)— (7). 
First we compute the differentials (3) and (4) except the terms db 
and for S — 1. 
Tr , , , 
For Tz. 0 Let 522.40 X rz Ko = U 
82 
, / s l / , , 9 ’ ( ) 
Yı=D Ys = —b u, => y, —h 
we find from (3) and (4) 
, € 
dx; ; rs = dx; ; ; 1,3 (83) 
” , ” 
dyjisrs = dx; ; Eis: dæ;i+rs + dy; ; r13 (84) 
dx; iiis 7 dX; iiis (85) 
a 2 1/4 5 
dy; ; 155 da i445 77 da inis + dy; i. 1,5 (86) 
^ J ) 
dx; 144 TF dx; i44 (87) 
" 34 ‚ > Q 
dy; ia da, ia 7 dz; 4 + dy; aia (88) 
; : J TI 
da i—1.1.6 dx; 1,i,6 (89) 
, n , 
di iio da; 14.6 77 dx; 1,i,6 + dy; 1,i,6 (90) 
Substituting the expressions (83)—(90) into (78)—(81) we find 
] 
: 2 : 4 , 1 Pl ; J ( 
da 0; - - 9 (da i 1.7.4 - da ii 1 1.3 I da i 1,i,6 - da ii | 1.5) (91 ) 
l 
"n , , " , 
do; 9 (dx; 1i4 — da; ji4 + dui cii 7 dx;iiis t dæ;i+rs — 
” , " , 
dy; isis T dj iis — dæ;_1i6 + YL aio dz; ; 15 + 
da; ; Lo dy; ; 1.5) (92) 
  
  
  
  
  
  
  
  
  
 
	        
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