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

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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.

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Data availability

Data from the comparisons of absolute gravimeters are available in the Key Comparison Database ( and cited literature. The datasets analysed in this study are available from the corresponding author on reasonable request.





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We would like to acknowledge the financial support from the project “Research related with International Gravity Reference System” funded by the Ministry of Education, Youth and Sports of the Czech Republic (MŠMT) as Grant No. LTT19008, and it is also supported by VÚGTK and ČMI. We are grateful to three anonymous reviewers for their helpful and constructive comments.

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Authors and Affiliations



V.P., H.W. and P.K. designed the research. H.W, M.V. and V.P. evaluated the data and prepared figures. V.P., H.W., R.F. and P.K. analysed the data and wrote the paper.

Corresponding author

Correspondence to Vojtech Pálinkáš.



See Tables 3, 4, 5, 6, 7, 8 and 9.

Table 3 Results of comparisons in 2009 in µGal
Table 4 Results of comparisons in 2011 in µGal
Table 5 Results of comparisons in 2013 in µGal
Table 6 Results of comparisons in 2015 in µGal
Table 7 Results of comparisons in 2017 in µGal
Table 8 Results of comparisons in 2018 in µGal
Table 9 Information on the reprocessing of comparisons based on criteria described in Sect. 2.4

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Pálinkáš, V., Wziontek, H., Vaľko, M. et al. Evaluation of comparisons of absolute gravimeters using correlated quantities: reprocessing and analyses of recent comparisons. J Geod 95, 21 (2021).

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