  We tackle the problem of estimating the spatial distribution of mobile phones
from Mobile Network Operator (MNO) data, namely Call Detail Record (CDR) or
signalling data. The process of transforming MNO data to a density map requires
geolocating radio cells to determine their spatial footprint. Traditional
geolocation solutions rely on Voronoi tessellations and approximate cell
footprints by mutually disjoint regions. Recently, some pioneering work started
to consider more elaborate geolocation methods with partially overlapping
(non-disjoint) cell footprints coupled with a probabilistic model for
phone-to-cell association. Estimating the spatial density in such a
probabilistic setup is currently an open research problem and is the focus of
the present work. We start by reviewing three different estimation methods
proposed in literature and provide novel analytical insights that unveil some
key aspects of their mutual relationships and properties. Furthermore, we
develop a novel estimation approach for which a closed-form solution can be
given. Numerical results based on semi-synthetic data are presented to assess
the relative accuracy of each method. Our results indicate that the estimators
based on overlapping cells have the potential to improve spatial accuracy over
traditional approaches based on Voronoi tessellations.
