  We address the problem of mass measurements of supersymmetric particles at
the Large Hadron Collider, using the ATLAS detector as an example. By using
Markov Chain sampling techniques to combine standard measurements of kinematic
edges in the invariant mass distributions of decay products with a measurement
of a missing $p_T$ cross-section, we show that the precision of mass
measurements at the LHC can be dramatically improved, even when we do not
assume that we have measured the kinematic endpoints precisely, or that we have
identified exactly which particles are involved in the decay chain causing the
endpoints. The generality of the technique is demonstrated in a preliminary
investigation of a non-universal SUGRA model, in which we relax the
requirements of mSUGRA by breaking the degeneracy of the GUT scale gaugino
masses. The model studied is compatible with the WMAP limits on dark matter
relic density.
