  The angular power spectrum is a powerful statistic for analysing cosmological
signals imprinted in the clustering of matter. However, current galaxy and
quasar surveys cover limited portions of the sky, and are contaminated by
systematics that can mimic cosmological signatures and jeopardise the
interpretation of the measured power spectra. We provide a framework for
obtaining unbiased estimates of the angular power spectra of large-scale
structure surveys at the largest scales using quadratic estimators. The method
is tested by analysing the 600 CMASS mock catalogues constructed by Manera et
al. (2013) for the Baryon Oscillation Spectroscopic Survey (BOSS). We then
consider the Richards et al. (2009) catalogue of photometric quasars from the
Sixth Data Release (DR6) of the Sloan Digital Sky Survey (SDSS), which is known
to include significant stellar contamination and systematic uncertainties.
Focusing on the sample of ultraviolet-excess (UVX) sources, we show that the
excess clustering power present on the largest-scales can be largely mitigated
by making use of improved sky masks and projecting out the modes corresponding
to the principal systematics. In particular, we find that the sample of objects
with photometric redshift $1.3 < z_p < 2.2$ exhibits no evidence of
contamination when using our most conservative mask and mode projection. This
indicates that any residual systematics are well within the statistical
uncertainties. We conclude that, using our approach, this sample can be used
for cosmological studies.
