Removing systematics-induced 21-cm foreground residuals by
  cross-correlating filtered data
  Observations of the redshifted 21-cm signal emitted by neutral hydrogen
represent a promising probe of large-scale structure in the universe. However,
cosmological 21-cm signal is challenging to observe due to astrophysical
foregrounds which are several orders of magnitude brighter. Traditional linear
foreground removal methods can optimally remove foregrounds for a known
telescope response but are sensitive to telescope systematic errors such as
antenna gain and delay errors, leaving foreground contamination in the
recovered signal. Non-linear methods such as principal component analysis, on
the other hand, have been used successfully for foreground removal, but they
lead to signal loss that is difficult to characterize and requires careful
analysis. In this paper, we present a systematics-robust foreground removal
technique which combines both linear and non-linear methods. We first obtain
signal and foreground estimates using a linear filter. Under the assumption
that the signal estimate is contaminated by foreground residuals induced by
parameterizable systematic effects, we infer the systematics-induced
contamination by cross-correlating the initial signal and foreground estimates.
Correcting for the inferred error, we are able to subtract foreground
contamination from the linearly filtered signal up to the first order in the
amplitude of the telescope systematics. In simulations of an interferometric
21-cm survey, our algorithm removes foreground leakage induced by complex gain
errors by one to two orders of magnitude in the power spectrum. Our technique
thus eases the requirements on telescope characterization for modern and
next-generation 21-cm cosmology experiments.
