4 A Model for Destination and Route Prediction
The problem above can be modeled as a Markov chain reproducing the state of
a system with a random variable for the nal destination that changes through
time. A state coincides with an observation and the distribution for this variable
depends only on the distribution of the previous observations. Given a Markov
chain and a sequence of observations, it is possible to predict the resulting state
distribution [2]. Unfortunately, such approach fails in practice: (i) it predicts
only the nal destination and not the route; (ii) it is designed to work on precise
GPS data, thus it suers the problems we discussed above when used with noisy
location information. The rst problem can be faced with a model where l is a
known location and every state represents a transition from location l to l0 with
a pair (l0jl) [23]. By considering a n order Markov Model, this approach predicts
all the possible routes for the user by considering, for every transition, all the n
transitions that it has seen before. Unfortunately, Markov chains are not
exible
w.r.t. the order n (which is xed and has to be chosen at design time), so it is not
easy to nd a compromise between the right complexity and a good prediction.