  Planned efforts to probe the largest observable distance scales in future
cosmological surveys are motivated by a desire to detect relic correlations
left over from inflation, and the possibility of constraining novel
gravitational phenomena beyond General Relativity (GR). On such large scales,
the usual Newtonian approaches to modelling summary statistics like the power
spectrum and bispectrum are insufficient, and we must consider a fully
relativistic and gauge-independent treatment of observables such as galaxy
number counts in order to avoid subtle biases, e.g. in the determination of the
$f_{\rm NL}$ parameter. In this work, we present an initial application of an
analysis pipeline capable of accurately modelling and recovering relativistic
spectra and correlation functions. As a proof of concept, we focus on the
non-zero dipole of the redshift-space power spectrum that arises in the
cross-correlation of different mass bins of dark matter halos, using strictly
gauge-independent observable quantities evaluated on the past light cone of a
fully relativistic N-body simulation in a redshift bin $1.7 \le z \le 2.9$. We
pay particular attention to the correct estimation of power spectrum
multipoles, comparing different methods of accounting for complications such as
the survey geometry (window function) and evolution/bias effects on the past
light cone, and discuss how our results compare with previous attempts at
extracting novel GR signatures from relativistic simulations.
