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Boletim de Ciências Geodésicas

On-line version ISSN 1982-2170

Abstract

KLEIN, Ivandro; MATSUOKA, Marcelo Tomio  and  SOUZA, Sergio Florêncio De. Theory of reliability generalised to multiple outliers: presentation, discussion and comparison with the conventional theory of reliability. Bol. Ciênc. Geod. [online]. 2011, vol.17, n.4, pp. 519-548. ISSN 1982-2170.  http://dx.doi.org/10.1590/S1982-21702011000400003.

After the adjustment of observations by the Least Squares Method (LSM), using statistical tests, it is possible to detect and identify non-random errors in the observations. The reliability theory makes use of appropriate measures to quantify the minimal detectable bias (error) in an observation, and its influence on the adjusted parameters, if not detected. The conventional reliability theory has been developed aiming at conventional testing procedures such as data snooping, which assumes that only one observation is contaminated by errors at a time. Recently, generalized measures of reliability were developed, relating to statistical tests that assumes the existence, simultaneous by, of multiple observations with errors (outliers). The goal of this paper is to present, discuss and apply the theory of reliability generalized for multiple outliers. Besides the theoretical formulation, this paper also presents experiments performed on a GPS network (Global Positioning System), where proposital errors were inserted in some observations and measures of reliability and statistical tests were calculated using the approach for multiple outliers. Comparisons with the conventional theory of reliability were also made. Finally, results were presented and discussed.

Keywords : Blunders Localization; Measures of Reliability; Multiple Outliers.

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