Another approach to reliability measures for systems with correlated observations |
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Authors: | W Prószyński |
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Institution: | (1) Present address: Engineering Geodesy and Measurement Systems, Graz University of Technology, Steyrergasse 30, 8010 Graz, Austria;(2) Department of Geomatics Engineering, University of Calgary, 2500 University Drive NW, Calgary, AB, T2N 1N4, Canada |
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Abstract: | An approach to internal reliability analysis is presented which, compared to existing approaches, offers further insight into
the system responses to observation gross errors. The proposed reliability measures are defined on the diagonal and non-diagonal
elements of the modified reliability matrix being an oblique projector. It maps the observations into the least squares residuals,
both expressed as multiples of the a priori standard deviations of the observations. The system responses to a single gross
error, such as the local, the quasi-global or the global response, are discussed and their consistency with non-correlation
case is proved. Also, the reliability criteria interpretable in terms of those responses are proposed. They enable one to
evaluate the observation systems with correlated and uncorrelated observations with respect to internal reliability. An attempt
is also made to relate the global responses to reliability numbers that are the basis for determining the magnitude of the
minimal detectable bias. Some differences of the new reliability measures in relation to existing measures are indicated.
A numerical example is provided, showing the reliability analysis for a simulated horizontal network (distances, angles and
GPS vectors), with given covariance matrix for GPS-vector components. In addition, a reliability analysis is presented for
a simple leveling network being a study case for other authors referred to in this paper. |
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