  We assess the performance of the multipole expansion formalism in the case of
single-dish HI intensity mapping, including instrumental and foreground removal
effects. This formalism is used to provide MCMC forecasts for a range of HI and
cosmological parameters, including redshift space distortions and the
Alcock-Paczynski effect. We first determine the range of validity of our power
spectrum modelling by fitting to simulation data, concentrating on the
monopole, quadrupole, and hexadecapole contributions. We then show that
foreground subtraction effects can lead to severe biases in the determination
of cosmological parameters, in particular the parameters relating to the
transverse BAO rescaling, the growth rate and the HI bias ($\alpha_\perp$,
$\overline{T}_\text{HI} f\sigma_8$, and $\overline{T}_\text{HI} b_\text{HI}
\sigma_8$, respectively). We attempt to account for these biases by
constructing a 2-parameter foreground modelling prescription, and find that our
prescription leads to unbiased parameter estimation at the expense of
increasing the estimated uncertainties on cosmological parameters. In addition,
we confirm that instrumental and foreground removal effects significantly
impact the theoretical covariance matrix, and cause the covariance between
different multipoles to become non-negligible. Finally, we show the effect of
including higher-order multipoles in our analysis, and how these can be used to
investigate the presence of instrumental and systematic effects in HI intensity
mapping data.
