## An attempt to determine the effect of increase of observation correlations on detectability and identifi ability of a single gross error

### Witold Prószyński , Mieczysław Kwaśniak

#### Abstract

The paper presents the results of investigating the effect of increase of observation correlations on detectability and identifi ability of a single gross error, the outlier test sensitivity and also the response-based measures of internal reliability of networks. To reduce in a research a practically incomputable number of possible test options when considering all the non-diagonal elements of the correlation matrix as variables, its simplest representation was used being a matrix with all non-diagonal elements of equal values, termed uniform correlation. By raising the common correlation value incrementally, a sequence of matrix confi gurations could be obtained corresponding to the increasing level of observation correlations. For each of the measures characterizing the above mentioned features of network reliability the effect is presented in a diagram form as a function of the increasing level of observation correlations. The infl uence of observation correlations on sensitivity of the w-test for correlated observations (Förstner 1983,Teunissen 2006) is investigated in comparison with the original Baarda’s w-test designated for uncorrelated observations, to determine the character of expected sensitivity degradation of the latter when used for correlated observations. The correlation effects obtained for different reliability measures exhibit mutual consistency in a satisfactory extent. As a by-product of the analyses, a simple formula valid for any arbitrary correlation matrix is proposed for transforming the Baarda’s w-test statistics into the w-test statistics for correlated observations.Author | |||||

Journal series | Geodesy and Cartography, ISSN 2080-6736, e-ISSN 2300-2581 | ||||

Issue year | 2016 | ||||

Vol | 65 | ||||

No | 2 | ||||

Pages | 313-333 | ||||

Publication size in sheets | 1 | ||||

Keywords in English | single outlier case, correlated observations, detectability, identifi ability, outlier-test sensitivity, mean-shift model | ||||

DOI | DOI:10.1515/geocart-2016-0018 | ||||

Internal identifier | 128/2016 | ||||

Language | en angielski | ||||

Additional file |
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Score (nominal) | 13 | ||||

Score | = 13.0, 28-11-2017, ArticleFromJournal = 13.0, 28-11-2017, ArticleFromJournal | ||||

Citation count* | 1 (2018-02-17) |

* presented citation count is obtained through Internet information analysis and it is close to the number calculated by the Publish or Perish system.

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