The visibility based Tapered Gridded Estimator (TGE) for the redshifted
  21-cm power spectrum
  We present the improved visibility based Tapered Gridded Estimator (TGE) for
the power spectrum of the diffuse sky signal. The visibilities are gridded to
reduce the computation, and tapered through a convolution to suppress the
contribution from the outer regions of the telescope's field of view. The TGE
also internally estimates the noise bias, and subtracts this out to give an
unbiased estimate of the power spectrum. An earlier version of the 2D TGE for
the angular power spectrum $C_{\ell}$ is improved and then extended to obtain
the 3D TGE for the power spectrum $P({\bf k})$ of the 21-cm brightness
temperature fluctuations. Analytic formulas are also presented for predicting
the variance of the binned power spectrum. The estimator and its variance
predictions are validated using simulations of $150 \, {\rm MHz}$ GMRT
observations. We find that the estimator accurately recovers the input model
for the 1D Spherical Power Spectrum $P(k)$ and the 2D Cylindrical Power
Spectrum $P(k_\perp,k_\parallel)$, and the predicted variance is also in
reasonably good agreement with the simulations.
