or 
23 
le 
S 
^m 
ne 
on 
as 
by 
nt 
ue 
ed 
he 
ng 
in 
er 
ue 
ng 
es 
of 
to 
an 
5) 
   
method. Barrodale and Roberts (1973) developed an modified 
simplex algorithm in which essentially only matrix A has to be 
stored in the computer. It bypasses in one step several steps 
of the conventional simplex algorithm. A great advantage of 
the'aïgorithm is that the rank of A can be less than the number 
of unknown parameters x. 
The algorithm searches that combination of observations 
(out of all observation, number of observation = n) which 
a.) is necessary for a non-redundant determination of the 
unknown parameters x 
b.) minimizes the sum of absolute residuals. 
In the ease of linear independent columns: of tA (that 
means, cif rank(A) z^ m, the number of unknown parameters x), 
exactly m of the observations are necessary for determining the 
m unknowns x. Consequently this group of observations (called 
1-NB) has residuals (v-NB) with values equal to zero. The 
remaining  n-m observations (1-B) will receive residuals (v-B), 
which are generally nonzero. The solution x represents a 
generalized median. 
The robust properties of the median value as described 
before still hold in the case of m unknown parameters. Any 
observation (or all observations) out of the group 1-B can be 
changed arbitrarily under the restriction that the signs of the 
residuals v-B do not change. The solution remains an optimal 
one and the vector x of unknown parameters will be unchanged. 
This ean be proved with. the aid -of the theory of linear 
optimization, confer Fuchs (1982). If such variations of the 
observations are interpreted as outliers, the robustness of 
adjustment using 1-norm can be easily seen. 
For smaller problems like direct linear transformation or 
absolute orientation the modified simplex algorithm is directly 
used. For error detection in the bundle adjustment itself the 
so-called -weight- iteration is ‘applied (Krarup 1980). This 
procedure is very easy to combine with the conjugate gradient 
method. By the choice of weights 
; v * const » ! 
(16) 
p 
P = const, v » const <1 resp. 
x 
Iv! 
an adjustment with minimization of the sum of absolute 
residuals can be obtained {const is" ai-relatively large 
constant). 
à. DATA STRUCTURE: 
  
The program system is designed to run on a 64 k-byte 
computer. To save important CPU memory all data are stored on 
an external device (like winchester drive  eto.). Only short 
information and data that needs very fast access are stored in 
the central memory. Due to that reason a linear linked list is 
kept in the CPU for important information and the location on