Summary
Criterion matrices/ideal variance — covariance matrices are constructed from continuous networks being observed by signal derivatives of first and second order. The method of constrained least- squares leads to differential equations up to fourth order, to characteristic boundary values and constraints according to the datum choice. Here only onedimensional networks on a line and on a circle are discussed. Their characteristic (modified) Green function is constructed and used for the computation of the variance — covariance function of adjusted mean signal functions. Finally numerical aspects originating fm the discrete nature of real observational series are discussed. In detail, the transformation of a criterion matrix into a network datum and its comparison with the variance — covariance matrix of an ideally configurated network is presented.
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Grafarend, E.W., Krumm, F.W. (1985). Continuous Networks I. In: Grafarend, E.W., Sansò, F. (eds) Optimization and Design of Geodetic Networks. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-70659-2_13
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DOI: https://doi.org/10.1007/978-3-642-70659-2_13
Publisher Name: Springer, Berlin, Heidelberg
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