We apply the Tapered Gridded Estimator (TGE) for estimating the cosmological 21-cm power spectrum from $150 \, {\rm MHz}$ GMRT observations which corresponds to the neutral hydrogen (HI) at redshift $z = 8.28$. Here TGE is used to measure the Multi-frequency Angular Power Spectrum (MAPS) $C_{\ell}(\Delta\nu)$ first, from which we estimate the 21-cm power spectrum $P(k_{\perp},k_{\parallel})$. The data here are much too small for a detection, and the aim is to demonstrate the capabilities of the estimator. We find that the estimated power spectrum is consistent with the expected foreground and noise behaviour. This demonstrates that this estimator correctly estimates the noise bias and subtracts this out to yield an unbiased estimate of the power spectrum. More than $47\%$ of the frequency channels had to be discarded from the data owing to radio-frequency interference, however the estimated power spectrum does not show any artifacts due to missing channels. Finally, we show that it is possible to suppress the foreground contribution by tapering the sky response at large angular separations from the phase center. We combine the k modes within a rectangular region in the `EoR window' to obtain the spherically binned averaged dimensionless power spectra $\Delta^{2}(k)$ along with the statistical error $\sigma$ associated with the measured $\Delta^{2}(k)$. The lowest $k$-bin yields $\Delta^{2}(k)=(61.47)^{2}\,{\rm K}^{2}$ at $k=1.59\,\textrm{Mpc}^{-1}$, with $\sigma=(27.40)^{2} \, {\rm K}^{2}$. We obtain a $2 \, \sigma$ upper limit of $(72.66)^{2}\,\textrm{K}^{2}$ on the mean squared HI 21-cm brightness temperature fluctuations at $k=1.59\,\textrm{Mpc}^{-1}$.

中文翻译：

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使用 150 MHz GMRT 观测演示用于宇宙学 HI 21 厘米功率谱的锥形网格估计器 (TGE)

我们应用锥形网格估计器 (TGE) 来估计来自 $150 \, {\rm MHz}$ GMRT 观测值的宇宙学 21 厘米功率谱，其对应于红移 $z = 8.28 $ 处的中性氢 (HI)。这里先用TGE测量多频角功率谱（MAPS）$C_{\ell}(\Delta\nu)$，从中我们估计出21cm功率谱$P(k_{\perp}, k_{\parallel})$。这里的数据对于检测来说太小了，目的是展示估计器的能力。我们发现估计的功率谱与预期的前景和噪声行为一致。这表明该估计器正确地估计了噪声偏差并将其减去以产生功率谱的无偏差估计。由于射频干扰，超过 $47\%$ 的频率信道不得不从数据中丢弃，但是估计的功率谱没有显示由于丢失信道而导致的任何伪影。最后，我们表明可以通过在与相位中心的大角度分离处逐渐减小天空响应来抑制前景贡献。我们在“EoR 窗口”中将矩形区域内的 k 个模式组合起来，以获得球面合并的平均无量纲功率谱 $\Delta^{2}(k)$ 以及与测量 $\ 相关的统计误差 $\sigma$ Delta^{2}(k)$。最低的 $k$-bin 产生 $\Delta^{2}(k)=(61.47)^{2}\,{\rm K}^{2}$ at $k=1.59\,\textrm{Mpc} ^{-1}$，其中 $\sigma=(27.40)^{2} \, {\rm K}^{2}$。我们得到$2 \, \sigma$ 上限$(72.66)^{2}\,