Gross error diagnostics before least squares adjustment of observations

Abstract

Existing methods for gross error diagnostics are mostly based upon the analysis of least-squares (LS) residuals after an LS adjustment has been carried out. The statistical correlations between the LS residuals, however, often make these methods ineffective. A new method is presented for the diagnosis of gross errors before an LS adjustment is performed. The method makes use of the so-called gross errors judgement equations (GEJE) derived from the linear adjustment model. In addition to carrying out gross error tests, the GEJE can be used to determine the following about a network: the maximum number of gross errors detectable in the observations; the maximum number of gross errors identifiable in the observations; and the observations in which gross errors are not detectable; the observations in which gross errors are detectable but not identifiable. Results from experimental tests show that the method is effective in analyzing the clustering properties between observations, an important factor in identifying gross errors. A comparison with some existing methods for gross error detection is also made.