The parallel sum of matrices and its application in geodetic adjustments |
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Authors: | D Zhong W Welsch |
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Institution: | (1) Institute of Geodesy, Bundeswehr University Munich, D-85577 Neubiberg, Germany, DE |
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Abstract: | Summary . It is well known that for the comparison and combination of geodetic networks their heterogeneous datum definitions are
well to be considered. Various algorithms have been developed for this purpose. As an alternative concept to deal with hybrid
datum problems, the operator parallel sum of matrices is introduced in this paper. To begin with, a definition is given and some basic properties are explained. To demonstrate
the usefulness of the operator, two practical applications are given. The first deals with the estimation of parameters describing
the deformation of two networks which are to be compared to each other. The second one treats the estimation of parameters
representing the heterogeneous datum definitions of two networks which are to be merged into a hybrid network. It will be
shown that – regardless of the datum definitions of the preadjusted individual networks – the parallel sum of matrices can
be used to simplify the algorithms applied for the estimation of those parameters.
Received 15 December 1995; Accepted 24 September 1996 |
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