A Tapered Gridded Estimator (TGE) for the Multi-Frequency Angular Power
  Spectrum (MAPS) and the Cosmological HI 21-cm Power Spectrum
  In this work we present a new approach to estimate the power spectrum $P({\bf
k})$ of redshifted HI 21-cm brightness temperature fluctuations. The MAPS
$C_{\ell}(\nu_a,\nu_b)$ completely quantifies the second order statistics of
the sky signal under the assumption that the signal is statistically
homogeneous and isotropic on the sky. Here we generalize an already existing
visibility based estimator for $C_{\ell}$, namely TGE, to develop an estimator
for $C_{\ell}(\nu_a,\nu_b)$. The 21-cm power spectrum is the Fourier transform
of $C_{\ell}(\Delta \nu)$ with respect to $\Delta \nu=\mid \nu_a-\nu_b \mid$,
and we use this to estimate $P({\bf k})$. Using simulations of $150 \, {\rm
MHz}$ GMRT observations, we find that this estimator is able to recover $P(k)$
with an accuracy of $5-20 \%$ over a reasonably large $k$ range even when the
data in $80 \%$ randomly chosen frequency channels is flagged.
