Mobility and Uncertainty - Mobility Data - page 86

or efficiency concerns. For example, Chapter 2 describes how the position of a
mobile user may be obfuscated to protect his or her privacy either at the time the
position data are acquired or before performing an operation that could disclose
potentially harmful information to third parties. The same chapter presents
methods for the compression of trajectories, which discard nonrepresentative
positions in order to reduce the size or the digital representation of the trajectory.
Also in this case the transformation yields a result that is less similar to the
actual trajectory than the measured one. Finally, when representing a collection
of trajectories, a further level of compression makes sense: grouping similar
segments of trajectories and storing just a representative portion of each cluster
instead of all of the original segments. Once again, this is a trade-off between
accuracy and compact representation.
Uncertainty Due to Incomplete Data
Another source of uncertainty is the incompleteness of data. A typical example
is the sampling of a trajectory: we know the position of an object at given
time instants (both affected by observational errors). The positions occupied
by the object between two samples can be obtained by means of interpolation
techniques, making assumptions about the object's movement; for instance,
using linear interpolation we are assuming that the object moves from one
sample point to the next one at constant speed. Location inference is another
possibility, which is based on the use of information about the object or about
the context to restrict the possible object positions. For example, we may know
that some action performed by the moving object was only possible at given
positions, or that an object can only perform certain movements.
5.2.1 Localization Techniques and Uncertainty
The trajectory tracking methods presented in Chapter 2 , as any other method
of measurement, are affected by observational errors. These errors can directly
affect the position and time measurement (when the measure is direct), or
propagate to the computed position and time values (in the case of indirect mea-
surement). We next discuss uncertainty in the localization techniques described
in Chapter 2 , and some other ones that the interested reader may find in the
bibliographic notes section.
GPS
The computation of the GPS position is based on the computation of the dis-
tance of the receiver from a set of GPS satellites. This distance is measured
indirectly, based on the different travel time of signals from the satellites to the
receiver. Thus, an error in time measurement is propagated through the compu-
tation, and affects the accuracy of the resulting position. In practice, to obtain a