a 
pa 
0 
e 
  
4. Failure with the gross error case c of arrangement D, 
where the test criterion wj = 3.15 of the x'-observation of 
point no. 2 at image 1 remained slightly under the critical 
value of c(wi4) = 3.29 
Analysing these failures it becomes evident that in 1. there is a-priori no 
chance for detection at all (zero variance problem). In 4. the situation was met, 
where the actual gross error (30um) is smaller than the minimal gross error which 
can be detected with the probability 8. - 0,8 (see Table 4). Setting vx? - - 32.4ym 
in version D the corresponding test criterion exceeds the critical value, thus 
leading to a correct rejection. 
  
The false rejection of X^ at image 3 in case Ba and of X9 at image 3 in case Bb 
is probably a result of shiftings caused by correlations. Actually the presence 
of correlations disturbs significantly the statistical foundation of the gross 
error problem, so that correlations should be subject to future studies. The 
correlations become particularly of interest in a double sense: 
- For the rejection procedure of data-snooping. The answer to the question 
whether only max (wi) or all wi which exceed the critical value should 
be rejected depends on the size of correlations. 
- For the localization of gross errors the correlations are of decisive 
importance. Consider our practical examples: In the cases Ad, Bd the 
localization of VY, is impossible since the residuals Vy (image 1) 
and Vy) (image 2) resp. Vy (image 3) and Vy? (image 4) are perfectly 
correlating. Strong correlations exist also in case Cc between the 
x'-residuals of a non-control point in all three images. Here we obtain 
for the correlation coefficients of the x'-residuals of point no.2: 
Fux [31v [0] = - 0.960 . Fux I3] vis [4] 0.956 ° vx [0] vx e [4] = - 0.960 
(image number in brackets) 
with the result that the gross error VX5 cannot be localized. 
Experiences gained so far with the data-snooping technique are very encouraging, 
expecially if its results are compared with conventional, non-statistical methods 
of gross error detection. 
From all 23 gross error cases of our examples (the 2 zero variance cases are ex- 
cluded) we obtained by conventional methods and by data-snoopina: 
lvl» 3o: 15 correct rejections, 12 incorrect rejetions 
|v|> 36: IO correct rejections, "5 incorrect rejections 
data-snooping: 19 correct rejections, 2 incorrect rejections 
So it becomes an important and promising task to do further investigations in 
this field of research to arrive lately at systems for point determination pro- 
viding for both accuracy and reliability.