  We present an improved framework for estimating the growth rate of
large-scale structure, using measurements of the galaxy-velocity
cross-correlation in configuration space. We consider standard estimators of
the velocity auto-correlation function, $\psi_1$ and $\psi_2$, the two-point
galaxy correlation function, $\xi_{gg}$, and introduce a new estimator of the
galaxy-velocity cross-correlation function, $\psi_3$. By including pair counts
measured from random catalogues of velocities and positions sampled from
distributions characteristic of the true data, we find that the variance in the
galaxy-velocity cross-correlation function is significantly reduced. Applying a
covariance analysis and $\chi^2$ minimisation procedure to these statistics, we
determine estimates and errors for the normalised growth rate $f\sigma_8$ and
the parameter $\beta = f/b$, where $b$ is the galaxy bias factor. We test this
framework on mock hemisphere datasets for redshift $z < 0.1$ with realistic
velocity noise constructed from the L-PICOLA simulation code, and find that we
are able to recover the fiducial value of $f\sigma_8$ from the joint
combination of $\psi_1$ + $\psi_2$ + $\psi_3$ + $\xi_{gg}$, with 15\% accuracy
from individual mocks. We also recover the fiducial $f\sigma_8$ to within
1$\sigma$ regardless of the combination of correlation statistics used. When we
consider all four statistics together we find that the statistical uncertainty
in our measurement of the growth rate is reduced by $59\%$ compared to the same
analysis only considering $\psi_2$, by $53\%$ compared to the same analysis
only considering $\psi_1$, and by $52\%$ compared to the same analysis jointly
considering $\psi_1$ and $\psi_2$.
