Analytic tools for investigating the structure of network reliability measures with regard to observation correlations

Analytic tools for investigating the structure of network reliability measures with regard to... A global measure of observation correlations in a network is proposed, together with the auxiliary indices related to non-diagonal elements of the correlation matrix. Based on the above global measure, a specific representation of the correlation matrix is presented, being the result of rigorously proven theorem formulated within the present research. According to the theorem, each positive definite correlation matrix can be expressed by a scale factor and a so-called internal weight matrix. Such a representation made it possible to investigate the structure of the basic reliability measures with regard to observation correlations. Numerical examples carried out for two test networks illustrate the structure of those measures that proved to be dependent on global correlation index. Also, the levels of global correlation are proposed. It is shown that one can readily find an approximate value of the global correlation index, and hence the correlation level, for the expected values of auxiliary indices being the only knowledge about a correlation matrix of interest. The paper is an extended continuation of the previous study of authors that was confined to the elementary case termed uniform correlation. The extension covers arbitrary correlation matrices and a structure of correlation effect. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Geodesy Springer Journals

Analytic tools for investigating the structure of network reliability measures with regard to observation correlations

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Publisher
Springer Berlin Heidelberg
Copyright
Copyright © 2017 by The Author(s)
Subject
Earth Sciences; Geophysics/Geodesy; Earth Sciences, general
ISSN
0949-7714
eISSN
1432-1394
D.O.I.
10.1007/s00190-017-1064-4
Publisher site
See Article on Publisher Site

Abstract

A global measure of observation correlations in a network is proposed, together with the auxiliary indices related to non-diagonal elements of the correlation matrix. Based on the above global measure, a specific representation of the correlation matrix is presented, being the result of rigorously proven theorem formulated within the present research. According to the theorem, each positive definite correlation matrix can be expressed by a scale factor and a so-called internal weight matrix. Such a representation made it possible to investigate the structure of the basic reliability measures with regard to observation correlations. Numerical examples carried out for two test networks illustrate the structure of those measures that proved to be dependent on global correlation index. Also, the levels of global correlation are proposed. It is shown that one can readily find an approximate value of the global correlation index, and hence the correlation level, for the expected values of auxiliary indices being the only knowledge about a correlation matrix of interest. The paper is an extended continuation of the previous study of authors that was confined to the elementary case termed uniform correlation. The extension covers arbitrary correlation matrices and a structure of correlation effect.

Journal

Journal of GeodesySpringer Journals

Published: Sep 18, 2017

References

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