Evaluation of comparisons of absolute gravimeters using correlated quantities: reprocessing and analyses of recent comparisons

Due to the lack of a natural reference for the absolute acceleration of free fall and gravity, absolute gravimeters are compared at international comparisons, where the gravity reference is realized based on a set of precise absolute measurements and the functional model for their processing. The main estimates of comparisons, specifically, the reference values, deviations of gravimeters (biases) and associated uncertainty estimates, are obtained by the method of constrained least squares. In this paper, based on data from six comparisons, we demonstrate and discuss the importance of several aspects that significantly influence the estimated parameters, such as the type of the constraint, the weighting schemes, the correlations between measurements or outlier detection. Following the state-of-the-art key comparisons in metrology, we are applying correlations between measurements of a particular gravimeter for the first time, showing the ability to obtain appropriate uncertainty estimates, strictly applying the law of error propagation. The processing of comparisons by the method of least squares is described step by step to provide a background for analyses of absolute gravimeter comparisons in the future, reflecting all specifics of these comparisons. Estimated parameters from uniformly elaborated comparisons represent an interesting statistical data set that has been used to analyse the significance of differences between FG5, FG5X and other types of gravimeters. We believe that the described method of processing, as well as the published results, will be especially useful in the realization of the International Gravity Reference System.