  The traditional approach to mobile phone positioning is based on the
assumption that the geographical location of a cell tower recorded in a call
details record (CDR) is a proxy for a device's location. A Voronoi tessellation
is then constructed based on the entire network of cell towers and this
tessellation is considered as a coordinate system, with the device located in a
Voronoi polygon of a cell tower that is recorded in the CDR. If Voronoi-based
positioning is correct, the uniqueness of the device trajectory is very high,
and the device can be identified based on 3-4 of its recorded locations. We
propose and investigate a probabilistic approach to device positioning that is
based on knowledge of each antennas' parameters and number of connections, as
dependent on the distance to the antenna. The critical difference between the
Voronoi-based and the real world layout is in the essential overlap of the
antennas' service areas: the device that is located in a cell tower's polygon
can be served by a more distant antenna that is chosen by the network system to
balance the network load. This overlap is too significant to be ignored.
Combining data on the distance distribution of the number of connections
available for each antenna in the network, we succeed in resolving the overlap
problem by applying Bayesian inference and construct a realistic distribution
of the device location. Probabilistic device positioning demands a full
revision of mobile phone data analysis, which we discuss with a focus on
privacy risk estimates.
