  Future large scale structure surveys will measure the locations and shapes of
billions of galaxies. The precision of such catalogs will require meticulous
treatment of systematic contamination of the observed fields. We compare
several existing methods for removing such systematics from galaxy clustering
measurements. We show how all the methods, including the popular
pseudo-$C_\ell$ Mode Projection and Template Subtraction methods, can be
interpreted under a common regression framework and use this to suggest
improved estimators. We show how methods designed to mitigate systematics in
the power spectrum can be used to produce clean maps, which are necessary for
cosmological analyses beyond the power spectrum, and we extend current methods
to treat the next-order multiplicative contamination in observed maps and power
spectra. Two new mitigation methods are proposed, which incorporate desirable
features of current state-of-the-art methods while being simpler to implement.
Investigating the performance of all the methods on a common set of simulated
measurements from Year 5 of the Dark Energy Survey, we test their robustness to
various analysis cases. Our proposed methods produce improved maps and power
spectra when compared to current methods, while requiring almost no user
tuning. We end with recommendations for systematics mitigation in future
surveys, and note that the methods presented are generally applicable beyond
the galaxy distribution to any field with spatial systematics.
