  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
$k=1.59\,\textrm{Mpc}^{-1}$.
