There is an anisotropy in the CMB of a dipole nature, appearing 'warmer' in one direction and 'colder' in the opposite direction, consistent with a Doppler shift caused by a motion of the Earth at 368 +/- 2 km/sec in the direction of the constellation of Leo. This is based primarily on WMAP data. By taking the motion of the Earth relative to our galaxy and our galaxy relative to other nearby galaxies, the motion of the Local Group relative to the CMB is estimated at about 627 km/sec, with an uncertainty of about 22 km/sec. The motion is nearly at right angles (to the East of) the direction to the center of our galaxy, and about 30 degrees above the galactic plane.

These measurements are strictly based on the dipole anisotropy. There are also random anisotropies of various sizes but very low amplitudes, thought to be random variations in the density of the gas at the distance (about z = 17) where the CMB originates (namely, at the distance corresponding to the time when the Universe became transparent to light).

One result of this is that in using the Hubble velocity of distant galaxies to estimate their distances, we should perhaps take into account the Earth's motion relative to the CMB; but the peculiar velocities of galaxies (non-Hubble expansion motions relative to their neighbors) are typically about the same size as our motion relative to the CMB, and taking our motion into account would require spherical trigonometrical calculations corresponding to the difference in direction between our motion and the direction to the galaxy in question, as well as some way of estimating the peculiar velocity of the galaxy in question. So usually, our motion is ignored in calculating redshift-dependent distances.

Note Added June 26, 2020: Although I still see the heliocentric recessional velocity primarily in use for Hubble Flow calculations of galactic distances, the 3K CMB recessional velocity appears to be in increasing use, and as a result, as I update entries in my NGC/IC Project I am replacing all heliocentric recessional velocities with values relative to the CMB. And although, as stated above, the correction required involves a bit of tiresome trigonometry, both the LEDA and NED databases now show both the heliocentric and various other measures of recessional velocity, including the one relative to the Cosmic Microwave Background. And since that eliminates any need for even the most math-phobic to do any calculations, it's an easy fix.

The above reply provides an excellent and carefully-worded summary of current observations. An assumption, briefly mentioned, is that the observed dipole asymmetry is solely attributable to a peculiar velocity. It is a feature of the Lorentz transformation that a blackbody spectrum transforms into another of a different temperature, and therefore a dipole temperature variation is indistinguishable from one caused by a motion. This contrasts velocities based on the shifts of spectral lines, whose rest wavelengths are assumed to be invariant.

Because radiation cannot be at rest, CMB rest frame is a term used to denote a frame where CMB is perfectly isotropic, if it is homogeneous. Indeed there exists inhomogeneities of primordial origin; however one has to use their low amplitudes to filter out such anisotropy due to primordial physics beyond z=17; thus this frame is essentially co-moving with the expansion rate of the universe. This frame is good for theoretical calculations only; in practice if your instrument is stationed on the surface of the earth, or if it is a satellite based measurement, a dipole asymmetry is clearly visible in CMB, which is formed due to the motion of earth in space, with respect to co-moving frame where CMB should be isotropic.

Last year I published a research paper titled "Practical Measurement of Absolute Velocity of Earth" in Applied Physics Research Journal. Before that I did attempt to secure funds for conducting this experiment myself, but in vain. After lots of correspondence on the subject I accepted the fact that no funding agency is going to sanction funds to a retired, independent researcher, regardless of the importance of the project.

Although in principal this project does belong to Fundamental Physics domain but de facto this project is an Electronics Instrumentation project for automated precision measurement, with advanced software application. As such, in my opinion this project can be executed by interested researchers in any academic institute or research establishment.

It is surprising why the proposed project for Practical Measurement of Absolute Velocity of Earth is not being undertaken by any researcher or research establishment, even though it is technically feasible and practically doable in a few months time.

Article Practical Measurement of Absolute Velocity of Earth

The dipole in the CMB is used to quantify Earth velocity around the CMB.

The dipole is eliminated arbitrarily to obtain the pure CMB signal.

Well, there is no reason to do that. I reproduced the CMB by exciting a hyperspherical harmonic spectrum on a hyperspherical hypersurface.

CMB_SMICA is the cosmic microwave background detected by the Planck Satellite and processed such as to eliminate the dipole.

CMB_Best is the optimized Hyperspherical Harmonic Oscillations as seen from Earth Location:

𝜒= 339.46 degrees

𝜃 = 341.1 degrees

𝜙= 104.08 degrees

The argument is presented here:

https://www.quora.com/According-to-the-Hypergeometrical-Universe-Theory-HU-where-is-our-universe-within-the-hyperspherical-hypersurface/answer/Marco-Pereira-1?ch=2&srid=3aDA

The Big Pop Cosmogenesis, which explains how the Neutronium Acoustic Oscillations were produced, is presented here:

https://hypergeometricaluniverse.quora.com/Fluctuations-of-Zero-I-will-tell-you-the-Cosmogenesis-according-to-my-Hypergeometrical-Universe-theory-HU-Spoiler-al

You can see the 3D galaxy density of the Universe here:

https://qsnyc.shinyapps.io/UniverseMap/?_ga=2.240362826.896784838.1602297614-603560526.1600356343

Just dial the redshift z and you will see the predicted galaxy density.

I didn't have access to the CMB with the dipole so I couldn't add the extra term and see if it would replicate the observation.

That said, Neutronium Acoustic Oscillations (instead of Earth velocity) could explain all or part of the observed dipole.

IN other words, it is premature to attribute a velocity for Earth with respect to the CMB.

This has been done already.

https://arxiv.org/pdf/astro-ph/9609034.pdf

You are a dollar short and a day late.