3σ-Rule for Outlier Detection from the Viewpoint of Geodetic Adjustment

Abstract

The so-called $3\sigma$-rule is a simple and widely used heuristic for outlier detection. This term is a generic term of some statistical hypothesis tests whose test statistics are known as normalized or studentized residuals. The conditions, under which this rule is statistically substantiated, were analyzed, and the extent it applies to geodetic least-squares adjustment was investigated. Then, the efficiency or nonefficiency of this method was analyzed and demonstrated on the example of repeated observations.