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We present a comprehensive analysis of all currently available high-accuracyfrequency measurements of rotational and rovibrational transitions in thehydrogen molecular ion HD$^+$. Our analysis utilises the theoreticallycalculated hyperfine structure to extract the values of three spin-averagedtransition frequencies through a global linear least-squares adjustment thattakes into account theory-induced correlations between the differenttransitions. We subsequently use the three spin-averaged transition frequenciesas input data in a second adjustment which employs precise theoreticalexpressions for the transition frequencies, written as a function of theproton, deuteron and electron relative atomic masses, the Rydberg constant, andthe proton and deuteron charge radii. Our analysis shows that the HD$^+$ datamay significantly improve the value of the electron relative atomic mass andthe proton-electron mass ratio, in particular if combined with recenthigh-precision measurements of particle atomic masses and mass ratios obtainedfrom Penning traps.

Extraction of spin-averaged rovibrational transition frequencies in HD$^+$ for the determination of fundamental constants