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We assess the performance of the multipole expansion formalism in the case ofsingle-dish HI intensity mapping, including instrumental and foreground removaleffects. This formalism is used to provide MCMC forecasts for a range of HI andcosmological parameters, including redshift space distortions and theAlcock-Paczynski effect. We first determine the range of validity of our powerspectrum modelling by fitting to simulation data, concentrating on themonopole, quadrupole, and hexadecapole contributions. We then show thatforeground subtraction effects can lead to severe biases in the determinationof cosmological parameters, in particular the parameters relating to thetransverse 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 byconstructing a 2-parameter foreground modelling prescription, and find that ourprescription leads to unbiased parameter estimation at the expense ofincreasing the estimated uncertainties on cosmological parameters. In addition,we confirm that instrumental and foreground removal effects significantlyimpact the theoretical covariance matrix, and cause the covariance betweendifferent multipoles to become non-negligible. Finally, we show the effect ofincluding higher-order multipoles in our analysis, and how these can be used toinvestigate the presence of instrumental and systematic effects in HI intensitymapping data.

Power spectrum multipole expansion for HI intensity mapping experiments: unbiased parameter estimation