  We investigate the possibility of using Gaussian process regression to smooth
data on the current past null-cone for use as the input to a relativistic
integration scheme. The algorithm we present is designed to reconstruct the
metric of spacetime within the class of spherically symmetric dust universes,
with or without a cosmological constant. Assuming that gravity is well
described by General Relativity, we demonstrate how the algorithm can be
employed to test the Copernican principle based on currently available
observations. It is shown that currently available data is not sufficient for a
conclusive result. The intrinsic noise present in realistic data presents a
challenge for our smoothing algorithm and we discuss some of its limitations as
well as possible extensions to it. We conclude by demonstrating how a direct
determination of the cosmological constant is possible using redshift drift
data.
