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Jeremiah P. Sjoberg, Richard A. Anthes, and Therese Rieckh

Abstract

The three-cornered hat (3CH) method, which was originally developed to assess the random errors of atomic clocks, is a means for estimating the error variances of three different data sets. Here we give an overview of the historical development of the 3CH and select other methods for estimating error variances that use either two or three data sets. We discuss similarities and differences between these methods and the 3CH method.

This study assesses the sensitivity of the 3CH method to the factors that limit its accuracy, including sample size, outliers, different magnitudes of errors between the data sets, biases, and unknown error correlations. Using simulated data sets for which the errors and their correlations among the data sets are known, this analysis shows the conditions under which the 3CH method provides the most and least accurate estimates. The effect of representativeness errors caused by differences in vertical resolution of data sets is investigated. These representativeness errors are generally small relative to the magnitude of the random errors in the data sets, and the impact of this source of errors can be reduced by appropriate filtering.

Open access