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We present the improved visibility based Tapered Gridded Estimator (TGE) forthe power spectrum of the diffuse sky signal. The visibilities are gridded toreduce the computation, and tapered through a convolution to suppress thecontribution from the outer regions of the telescope's field of view. The TGEalso internally estimates the noise bias, and subtracts this out to give anunbiased estimate of the power spectrum. An earlier version of the 2D TGE forthe angular power spectrum $C_{\ell}$ is improved and then extended to obtainthe 3D TGE for the power spectrum $P({\bf k})$ of the 21-cm brightnesstemperature fluctuations. Analytic formulas are also presented for predictingthe variance of the binned power spectrum. The estimator and its variancepredictions are validated using simulations of $150 \, {\rm MHz}$ GMRTobservations. We find that the estimator accurately recovers the input modelfor the 1D Spherical Power Spectrum $P(k)$ and the 2D Cylindrical PowerSpectrum $P(k_\perp,k_\parallel)$, and the predicted variance is also inreasonably good agreement with the simulations.

The visibility based Tapered Gridded Estimator (TGE) for the redshifted 21-cm power spectrum