  An observer in relative motion to the Cosmic Microwave Background (CMB) rest
frame is sensitive to both aberration and Doppler effects. Both effects
introduce similar but non-identical off-diagonal couplings in the spherical
harmonic coefficients. The CMB temperature dipole may have additional
contributions from an intrinsic component, which in turn produces different
aberration and Doppler couplings. Moreover, the standard conversion from
intensity measurements into temperature also introduces spurious Doppler-like
couplings. In order to learn about the intrinsic dipole it is therefore
important to measure both aberration and Doppler couplings in an independent
manner while also removing the spurious contributions from unit conversion,
which are degenerate with the dipole. Here we present a pipeline to measure the
Doppler and aberration signal independently from each other and from the dipole
itself. We also consider realistic beaming, noise and mask effects. Our
pipeline results in independent and unbiased estimators which have
uncertainties only ~20% larger than the simple theoretical expectations. We
discuss the achievable precision in each measurement for Planck 2018, and also
forecast them for future ground-based experiments with the Simons Observatory
and CMB-S4. An alternative pipeline is presented in order to cross-check
results and improve robustness.
