  There is growing interest in using current and future gravitational-wave
interferometers to search for anisotropies in the gravitational-wave
background. One guaranteed anisotropic signal is the kinematic dipole induced
by our peculiar motion with respect to the cosmic rest frame, as measured in
other full-sky observables such as the cosmic microwave background. Our prior
knowledge of the amplitude and direction of this dipole is not explicitly
accounted for in existing searches by LIGO/Virgo/KAGRA, but could provide
crucial information to help disentangle the sources which contribute to the
gravitational-wave background. Here we develop a targeted search pipeline which
uses this prior knowledge to enable unbiased and minimum-variance inference of
the dipole magnitude. Our search generalises existing methods to allow for a
time-dependent signal model, which captures the annual modulation of the dipole
due to the Earth's orbit. We validate our pipeline on mock data, demonstrating
that neglecting this time dependence can bias the inferred dipole by as much as
$\sim10\%$. We then run our analysis on the full LIGO/Virgo O1+O2+O3 dataset,
obtaining upper limits on the dipole amplitude that are consistent with
existing anisotropic search results.
