  The kinematics of satellite galaxies moving in a dark matter halo are a
direct probe of the underlying gravitational potential. Thus, the phase-space
distributions of satellites represent a powerful tool to determine the
galaxy-halo connection from observations. By stacking the signal of a large
number of satellite galaxies this potential can be unlocked even for haloes
hosting a few satellites on average. In this work, we test the impact of
various modelling assumptions on constraints derived from analysing satellite
phase-space distributions in the non-linear, 1-halo regime. We discuss their
potential to explain the discrepancy between average halo masses derived from
satellite kinematics and gravitational lensing previously reported.
Furthermore, we develop an updated, more robust analysis to extract constraints
on the galaxy-halo relation from satellite properties in spectroscopic galaxy
surveys such as the SDSS. We test the accuracy of this approach using a large
number of realistic mock catalogues. Furthermore, we find that constraints
derived from such an analysis are complementary and competitive with respect to
the commonly used galaxy clustering and galaxy-galaxy lensing observables.
