  We review and compare two different CMB dipole estimators discussed in the
literature, and assess their performances through Monte Carlo simulations. The
first method amounts to simple template regression with partial sky data, while
the second method is an optimal Wiener filter (or Gibbs sampling)
implementation. The main difference between the two methods is that the latter
approach takes into account correlations with higher-order CMB temperature
fluctuations that arise from non-orthogonal spherical harmonics on an
incomplete sky, which for recent CMB data sets (such as Planck) is the dominant
source of uncertainty. For an accepted sky fraction of 81% and an angular CMB
power spectrum corresponding to the best-fit Planck 2018 $\Lambda$CDM model, we
find that the uncertainty on the recovered dipole amplitude is about six times
smaller for the Wiener filter approach than for the template approach,
corresponding to 0.5 and 3$~\mu$K, respectively. Similar relative differences
are found for the corresponding directional parameters and other sky fractions.
We note that the Wiener filter algorithm is generally applicable to any dipole
estimation problem on an incomplete sky, as long as a statistical and
computationally tractable model is available for the unmasked higher-order
fluctuations. The methodology described in this paper forms the numerical basis
for the most recent determination of the CMB solar dipole from Planck, as
summarized by arXiv:2007.04997.
