A Cost Orientated Approach to Geodetic Network Optimisation
by Martin Staudinger
have, among other things, the task to determine information about the
spatial position of different objects in the world. The objects are
usually divided into individual points, and these points brought in
connection to a spatial reference system. Usually, this is done by
means of a coordinate system, describing every point by one, two, or
three coordinates. In many cases, the appropriate measuring- and
calculation-method for that purpose is a geodetic network.
theory of geodetic networks connects mathematic-geometrical and
statistical concepts. Starting with a set of redundant measurements, we
get the appropriate position information as well as specifications
concerning their quality (accuracy and reliability). The method of
least squares adjustment has been well-known for now almost two hundred
Since then, surveyors always tried to establish their
measurements in the required quality but with as little cost as
possible. The method of least squares makes it possible to estimate the
quality of a geodetic network before the actual field work (a priori
adjustment). Thus, the network design can be optimised regarding
accuracy and reliability. For an optimisation of the network costs, an
appropriate cost function was missing so far.
In this thesis, we
show that it is possible to find a cost function which, at least,
indicates the cost differences between different network variants.
Among a number of simulated network variants, we can find out the one
which will presumably cause the smallest cost. The individual network
versions differ according to the type and number of geodetic
observations. Both the spatial conditions (costs for accessing the
points and travelling between them) and the actual activities, which
are undertaken by the field crew, are considered. In previous work, the
spatial positions of the points were not considered; thus all
observations of a special type (all distance observations, e.g.) were
regarded as causing the same costs and only their number was optimised.
the optimisation, we used the method of simulated annealing. Simulated
annealing is a heuristic procedure. It is suitable to solve
combinatorial optimisation problems which would otherwise not be
solvable in polynomial computation time. The algorithm produces
sub-optimal solutions and is based on an improvement of a simple local
search-algorithm: A known solution is improved by searching for a
further solution in the neighbourhood of the first one. The new
solution is accepted with a certain probability even if the new value
of the objective function (in our case: the cost of the network) is
worse than the last one. By this means it is prevented to get trapped
in a local optimal solution. The procedure was tested by some examples.
The result is that
the found cost function is able to indicate cost differences between different network versions
the cost estimation can easily be integrated in the usual network adjustment
thus, the network-design can be optimised regarding its costs.