  The ultimate application of Einstein's field equations is to empirically
determine the geometry of the Universe from its matter content, rather than
simply assuming the Universe can be represented by a homogeneous model on all
scales. Choosing an LTB model as the most convenient inhomogeneous model for
the early stages of development, a data reduction procedure was recently
validated using perfect test data. Here we simulate observational uncertainties
and improve the previous numerical scheme to ensure that it will be usable with
real data as soon as observational surveys are sufficiently deep and complete.
Two regions require special treatment--the origin and the maximum in the areal
radius. To minimize numerical errors near the origin, we use an LTB series
expansion to provide the initial values for integrating the differential
equations. We also use an improved method to match the numerical integration to
the series expansion that bridges the region near the maximum in the areal
radius. Because the mass enclosed within the maximum obeys a specific
relationship, we show that it is possible to correct for a fixed systematic
error in either the distance scale or the redshift-space mass density, such
that the integrated values are consistent with the data at the maximum.
