|
Showing 1 - 2 of
2 matches in All Departments
While preparing and teaching 'Introduction to Geodesy I and II' to
undergraduate students at Stuttgart University, we noticed a gap
which motivated the writing of the present book: Almost every topic
that we taught required some skills in algebra, and in particular,
computer algebra! From positioning to transformation problems
inherent in geodesy and geoinformatics, knowledge of algebra and
application of computer algebra software were required. In
preparing this book therefore, we have attempted to put together
basic concepts of abstract algebra which underpin the techniques
for solving algebraic problems. Algebraic computational algorithms
useful for solving problems which require exact solutions to
nonlinear systems of equations are presented and tested on various
problems. Though the present book focuses mainly on the two ?elds,
the concepts and techniques presented herein are nonetheless
applicable to other ?elds where algebraic computational problems
might be encountered. In Engineering for example, network
densi?cation and robotics apply resection and intersection
techniques which require algebraic solutions. Solution of nonlinear
systems of equations is an indispensable task in almost all
geosciences such as geodesy, geoinformatics, geophysics (just to
mention but a few) as well as robotics. These equations which
require exact solutions underpin the operations of ranging,
resection, intersection and other techniques that are normally
used. Examples of problems that require exact solutions include; *
three-dimensional resection problem for determining positions and
orientation of sensors, e. g. , camera, theodolites, robots,
scanners etc.
During the period April 25th to May 10th, 1984 the 3rd Course of
the International School of Advanced Geodesy entitled "Optimization
and Design of Geodetic Networks" took place in Erice. The main
subject of the course is clear from the title and consisted mainly
of that particular branch of network analysis, which results from
applying general concepts of mathematical optimization to the
design of geodetic networks. As al ways when dealing with
optimization problems, there is an a-priori choice of the risk (or
gain) function which should be minimized (or maximized) according
to the specific interest of the "designer," which might be either
of a scientific or of an economic nature or even of both. These
aspects have been reviewed in an intro ductory lecture in which the
particular needs arising in a geodetic context and their analytical
representations are examined. Subsequently the main body of the
optimization problem, which has been conven tionally divided into
zero, first, second and third order design problems, is presented.
The zero order design deals with the estimability problem, in other
words with the definition of which parameters are estimable from a
given set of observa tions. The problem results from the fact that
coordinates of points are not univocally determined from the
observations of relative quantities such as angles and distances,
whence a problem of the optimal choice of a reference system, the
so-called "datum problem" arises."
|
|