Visibility based angular power spectrum estimation in low frequency
  radio interferometric observations
  We present two estimators to quantify the angular power spectrum of the sky
signal directly from the visibilities measured in radio interferometric
observations. This is relevant for both the foregrounds and the cosmological
21-cm signal buried therein. The discussion here is restricted to the Galactic
synchrotron radiation, the most dominant foreground component after point
source removal. Our theoretical analysis is validated using simulations at 150
MHz, mainly for GMRT and also briefly for LOFAR. The Bare Estimator uses
pairwise correlations of the measured visibilities, while the Tapered Gridded
Estimator uses the visibilities after gridding in the uv plane. The former is
very precise, but computationally expensive for large data. The latter has a
lower precision, but takes less computation time which is proportional to the
data volume. The latter also allows tapering of the sky response leading to
sidelobe suppression, an useful ingredient for foreground removal. Both
estimators avoid the positive bias that arises due to the system noise. We
consider amplitude and phase errors of the gain, and the w-term as possible
sources of errors . We find that the estimated angular power spectrum is
exponentially sensitive to the variance of the phase errors but insensitive to
amplitude errors. The statistical uncertainties of the estimators are affected
by both amplitude and phase errors. The w-term does not have a significant
effect at the angular scales of our interest. We propose the Tapered Gridded
Estimator as an effective tool to observationally quantify both foregrounds and
the cosmological 21-cm signal.
