conditioned or even singular system (5) for certain types 
of data. 
As an example a condition equation (3) can be mentioned, 
that connects at least two unknown parameters functionally 
and the matrix product (BP;i B ) is equal to zero or ex- 
tremely small, for instance in the special case of a very 
precise observation. Another example are two functionally 
independent observation equations for different unknown 
parameters with very high stochastic correlation in the 
weight matrix P, of the observations. 
Secondly, for all other non-photogrammetric information 
two cases can be distinguished: 
- Data that do not decisively change the non-zero 
structure of the normal equation system (2) can be treated 
without special measures by the classical concept (5). 
Normally these are data that lead to connections in the 
normal equation system not exceeding the (3,3)-submatrix 
of the coordinates of one point or the (6,6)-submatrix of 
the orientation parameters or submatrices connecting these 
unknowns and additional parameters. However, this depends 
also on the modelling of the photogrammetric observations. 
Examples of this type of data are positions of control 
points with their covariance matrix having at most a 
(3,3)-diagonal structure with or without transformation 
parameters, that can be arranged in the border as addi- 
tional unknowns. This is principally the same for direct 
observations of camera positions or orientation parame- 
ters. Also object information, e.g. DTM may be mentioned 
here. 
- If the data lead to connections outside the non-zero 
structure of the existing system (2) certain measures for 
an efficient treatment should be taken into consideration: 
a) The point unknowns being affected by this information 
can be arranged behind the orientation parameters in the 
border of the system as proposed by Brown /3/, Düppe /5/, 
Larsson /9/. 
b) Another concept is to use general reordering algorithms 
to minimize the bandwidth or profile of the resulting 
system. An advantage is that these algorithms offer great 
flexibility and can be used for geodetic and photogram- 
metric problems, but they do not necessarily lead to 
optimal results. 
In both cases a) and b) the normal equation system is of 
type (5), but the sequence of the unknown parameters is 
changed. 
c) To preserve the structure of the existing system, the 
Lagrange multipliers are not eliminated. Therefore the 
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