Title:
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Optimal design of GPS networks : operational procedures
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A method for the optimal solution for a particular aspect of
Global Positioning System (GPS) networks has been devised. This
relates to the logistics of the survey. In particular, it is the
organisation of the fieldwork that has been addressed. This
becomes especially important as the number of receivers used in
a GPS survey increases. The minimum is two but there are marked
efficiency gains by using at least one additional receiver.
The problem addressed is to determine the order in which each GPS
receiver should be moved between the points to be surveyed
bearing in mind that it is necessary that the receivers have to
be at certain points simultaneously so that the required
observations are made. Techniques within the field of Operational
Research (OR) have been used to solve this problem.
The problem has been transformed into a more complex version of
the Travelling Salesman Problem (TSP) -a classical combinatorial
problem. With this transformation achieved it was possible to
analyse the suitability of techniques within the OR field to
solve the GPS logistics problem.
A method for the optimal solution of the TSP was developed based
upon an existing branch-and-bound approach but modified to take
into account the more complex problem now being posed. This
method, however, would only work for surveys where the surveyorsstarted and ended at a survey point. To be more realistic, the
method was further enhanced to allow for a base (not a survey
point) from which the surveyors would start and end their surveys
together. This worked well, although it was restricted to surveys
that were to be completed in one working period. This method,
therefore, has been made more realistic by allowing the surveyors
to return on a number of occasions to their base, thus simulating
a survey lasting for more than one working period. The developed
algorithms have been tested on examples with correct results.
The above success is limited in that it cannot work for large
networks and so an investigation into heuristic approaches was
made. A heuristic approach does not guarantee optimality, but
usually the solution is very close to it. This line of
investigation was carried out as the guaranteed optimal solution
is only possible in applications with a few number of points and
receivers. In practice, three of four receivers may be used in
networks containing over fifty points. For such a large network,
a guaranteed optimal solution cannot be obtained in a sensible
amount of time. Modern heuristic techniques have therefore been
investigated with guidelines for their implementation to solve
the GPS logistics problem given: - simulated annealing and tabu
search seem to hold the most promise. A new approach based upon
the use of a special fractal known as a space-filling-curve was
also developed with successful results.
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