# A Tapered Gridded Estimator (TGE) for the Multi-Frequency Angular Power Spectrum (MAPS) and the Cosmological HI 21-cm Power Spectrum

## TL;DR

This paper introduces a new tapered gridded estimator (TGE) for accurately estimating the multi-frequency angular power spectrum and the cosmological HI 21-cm power spectrum from radio observations, even with significant data flagging.

## Contribution

The work extends an existing visibility-based estimator to handle multi-frequency data, enabling improved power spectrum estimation from HI 21-cm observations.

## Key findings

- Estimator recovers P(k) with 5-20% accuracy.
- Effective even with 80% frequency channel flagging.
- Validated using GMRT simulation data.

## Abstract

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.