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The upcoming Simons Observatory Small Aperture Telescopes aim at achieving aconstraint on the primordial tensor-to-scalar ratio $r$ at the level of$\sigma(r=0)\lesssim0.003$, observing the polarized CMB in the presence ofpartial sky coverage, cosmic variance, inhomogeneous non-white noise, andGalactic foregrounds. We present three different analysis pipelines able toconstrain $r$ given the latest available instrument performance, and comparetheir predictions on a set of sky simulations that allow us to explore a numberof Galactic foreground models and elements of instrumental noise, relevant forthe Simons Observatory. The three pipelines use different combinations ofparametric and non-parametric component separation at the map and powerspectrum levels, and employ $B$-mode purification to estimate the CMB $B$-modepower spectrum. They are tested and compared regarding their capability toanalyze a common set of simulated realistic frequency maps, and to extractconstraints on the tensor-to-scalar ratio $r$. Their performance is evaluatedin terms of bias and statistical uncertainty on this parameter. In most of thescenarios the three methodologies achieve similar performance. Nevertheless,several simulations with complex foreground signals lead to a $>2\sigma$ biason $r$ if analyzed with the default versions of these pipelines, highlightingthe need for more sophisticated pipeline components that marginalize overforeground residuals. We show two such extensions, using power-spectrum-basedand map-based methods, that are able to fully reduce the bias on $r$ below thestatistical uncertainties in all foreground models explored, at a moderate costin terms of $\sigma(r)$.

The Simons Observatory: pipeline comparison and validation for large-scale B-modes