The level of precision needed to detect Earth-like planets orbiting other suns motivates new developments in both instrumentation (e.g. ESPRESSO) and data analysis. The s-BART (Silva+2022) semi-Bayesian, template-matching, framework was built around the assumption that an achromatic RV-shift describes the differences between stellar spectra and a stellar model. However, as the stellar model is built from observations of the star, it leads to a mixture of information between it and the data with which it is compared to (observations), which isn't fully compatible with a Bayesian framework

To overcome such limitation, a move towards a fully probabilistic stellar model is required, capable of simultaneously extracting RVs and correcting telluric features. In this talk, we present a new methodology that leverages Gaussian Processes to generate a model of the stellar spectra whilst estimating the RV separation between observations. The model and preliminary, promising, results will be presented.