  High-resolution Doppler-resolved spectroscopy has presented new opportunities
for studying the atmospheres of exoplanets. While the 'classical'
cross-correlation approach has proven to be efficient at finding atmospheric
species, it is unable to perform direct atmospheric retrievals. Recent work has
shown that retrievals are possible using a direct likelihood evaluation or
likelihood 'mappings'. The unique aspect of high-resolution retrievals is that
the data-processing methods required to remove the stellar and telluric lines
also distort the underlying exoplanet's signal and therefore the forward model
must be pre-processed to match this filtering. This was the key remaining
limitation in our previously published framework. This paper directly addresses
this by introducing a simple and fast model-filtering technique that can
replicate the processing performed by algorithms such as SysRem and PCA. This
enables retrievals to be performed without having to perform expensive
injection and pre-processing steps for every model. We show that we can
reliably constrain quantitative measures of the atmosphere from transmission
spectra including the temperature-pressure profile, relative abundances,
planetary velocities and rotational broadening parameters. Finally, we
demonstrate our framework using UVES transmission spectroscopy of WASP-121b. We
constrain the temperature-pressure profile and relative abundances of Fe, Cr,
and V to be $\log_{10}(\chi_{\rm Fe}/\chi_{\rm Cr})$=1.66$\pm$0.28,
$\log_{10}(\chi_{\rm Fe}/\chi_{\rm V})$=3.78$\pm$0.29 and $\log_{10}(\chi_{\rm
Fe}/\chi_{\rm Mg})$=-1.26$\pm$0.60. The relative abundances are consistent with
solar values, with the exception of Fe/Mg, where the large Mg abundance is
probably explained by the escaping atmosphere of WASP-121b that is not
accounted for in our atmospheric model.
