  Amongst the most popular explanations for dark energy are modified theories
of gravity. The galaxy overdensity and peculiar velocity fields help us to
constrain the growth rate of structure and distinguish different models of
gravity. We introduce an improved method for constraining the growth rate of
structure with the galaxy overdensity and peculiar velocity fields. This method
reduces the modelling systematic error by accounting for the wide-angle effect
and the zero-point calibration uncertainty during the modelling process. We
also speed up the posterior sampling by around 30 times by first calculating
the likelihood at a small number of fiducial points and then interpolating the
likelihood values during MCMC sampling. We test the new method on mocks and we
find it is able to recover the fiducial growth rate of structure. We applied
our new method to the SDSS PV catalogue, which is the largest single peculiar
velocity catalogue to date. Our constraint on the growth rate of structure is
\(f\sigma_8 = 0.405_{-0.071}^{+0.076}\) (stat) \(\pm 0.009\) (sys) at the
effective redshift of 0.073. Our constraint is consistent with a Planck 2018
cosmological model, \(f\sigma_8 = 0.448\), within one standard deviation. Our
improved methodology will enable similar analysis on future data, with even
larger sample sizes and covering larger angular areas on the sky.
