  The cosmic radio dipole is an anisotropy in the number counts of radio
sources, analogous to the dipole seen in the cosmic microwave background (CMB).
Measurements of source counts of large radio surveys have shown that though the
radio dipole is generally consistent in direction with the CMB dipole, the
amplitudes are in tension. These observations present an intriguing puzzle as
to the cause of this discrepancy, with a true anisotropy breaking with the
assumptions of the cosmological principle, invalidating the most common
cosmological models that are built on these assumptions. We present a novel set
of Bayesian estimators to determine the cosmic radio dipole and compare the
results with commonly used methods on the Rapid ASKAP Continuum Survey (RACS)
and the NRAO VLA Sky Survey (NVSS) radio surveys. In addition, we adapt the
Bayesian estimators to take into account systematic effects known to affect
such large radio surveys, folding information such as the local noise floor or
array configuration directly into the parameter estimation. The enhancement of
these estimators allows us to greatly increase the amount of sources used in
the parameter estimation, yielding tighter constraints on the cosmic radio
dipole estimation than previously achieved with NVSS and RACS. We extend the
estimators further to work on multiple catalogues simultaneously, leading to a
combined parameter estimation using both NVSS and RACS. The result is a dipole
estimate that perfectly aligns with the CMB dipole in terms of direction but
with an amplitude that is three times as large, and a significance of
4.8$\sigma$. This new dipole measurement is made to an unprecedented level of
precision for radio sources, which is only matched by recent results using
infrared quasars.
