  We present BALRoGO: Bayesian Astrometric Likelihood Recovery of Galactic
Objects, a public code to measure the centers, effective radii, and bulk proper
motions of Milky Way globular clusters and Local Group dwarf spheroidals, whose
data are mixed with Milky Way field stars. Our approach presents innovative
methods such as surface density fits allowing for strong interloper
contamination and proper motion fits using a Pearson VII distribution for
interlopers, instead of classic Gaussian-mixture recipes. We also use
non-parametric approaches to represent the color-magnitude diagram of such
stellar systems based in their membership probabilities, previously derived
from surface density and proper motion fits. The robustness of our method is
verified by comparing its results with previous estimates from the literature
as well as by testing it on mock data from N-body simulations. We applied
BALRoGO to Gaia EDR3 data for over one hundred Milky Way globular clusters and
nine Local Group dwarf spheroidals, and we provide positions, effective radii,
and bulk proper motions. Finally, we make our algorithm available as an open
source software.

Astrophysics of Galaxies;Instrumentation and Methods for Astrophysics