The visibility-based tapered gridded estimator (TGE) for the redshifted 21-cm power spectrum

We present an improved visibility-based tapered gridded estimator (TGE) for the power spectrum of the diffuse sky signal. The visibilities are gridded to reduce the total computation time for the calculation, 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-l is improved and then extended to obtain the 3D TGE for the power spectrum P(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-MHz Giant Metrewave Radio Telescope (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(perpendicular to), k(parallel to)), and that the predicted variance is in reasonably good agreement with the simulations.