So by definition the term "reliability" should describe the system's qualities 
for gross error detection. 
It was Baarda /2/, /3/ who developed a rather complete reliability theory. His 
approach enables the treatment of the gross error detection problem on a statis- 
d 
J 
X 
z 
tical basis. Baarda's theory may equally be applied to theoretical reliability 
studies of bundle adjustment systems as to the detection of gross errors in prac- 
tical projects. For detail information about the whole theory see /2/, /3/. In 
the following only a short extract is presented, as far as it is necessary to 
understand the practical computations presented in this paper. 
Starting from system (1) with the statistical mode] 
- e = Ax=1 P 
; (8) 
D(e) s D(1) = o 
| we get consistent, sufficient and minimum variance unbiased estimators for x and 
  
of by the least squares estimators (with redundancy r = n-u) 
| 
| A -1 
x = (APA) ATP1 = ATP] (9a) 
. T - T 
GE KARA ON) 2 WIM Te nf (9b) 
and for the residuals we obtain 
Sda zh 9S2 e T 
V E Ax-] = (I AQ, A POT s (10) 
and with 
2 ip^i T 
Oy = P AQ X (11) 
we get 
Vom = PRSE . (12) 
Regarding model (8) as null-hypothesis HC with E(c f Zn = s f , then * f H is true 
the test criterion 
0 = =r (13) 
is distributed as the central F-distribution F(r,e). Thus © is used as a global 
test criterion to test the presumed multi-dimensional normal distribution of 
| kA N(Axso Bach: 
If H isrejectedone has to set up one or more alternative hypotheses Hp. 
Since the systematic errors are widely compensated by our self-calibrating model 
we may confine ourselves on the investigation of gross errors. Then a set of p 
alternative hypotheses Ha, can be formulated as 
pr =r LLNS alternative 
Hp ll 2a Of CN ’ hypotheses (14) 
P P oc psp Cp = vector representing the 
proportions of the 
gross errors 
Yo = constant 
If Hay is accepted, then © is distributed as the noncentral F-distribution 
AUDZIS with the noncentrality parameter A, 
p