  ENDOR spectroscopy is an important tool to determine the complicated
three-dimensional structure of biomolecules and in particular enables
measurements of intramolecular distances. Usually, spectra are determined by
averaging the data matrix, which does not take into account the significant
thermal drifts that occur in the measurement process. In contrast, we present
an asymptotic analysis for the homoscedastic drift model, a pioneering
parametric model that achieves striking model fits in practice and allows both
hypothesis testing and confidence intervals for spectra. The ENDOR spectrum and
an orthogonal component are modeled as an element of complex projective space,
and formulated in the framework of generalized Fr\'echet means. To this end,
two general formulations of strong consistency for set-valued Fr\'echet means
are extended and subsequently applied to the homoscedastic drift model to prove
strong consistency. Building on this, central limit theorems for the ENDOR
spectrum are shown. Furthermore, we extend applicability by taking into account
a phase noise contribution leading to the heteroscedastic drift model. Both
drift models offer improved signal-to-noise ratio over pre-existing models.
