  Autonomous agents rely on sensor data to construct representations of their
environment, essential for predicting future events and planning their own
actions. However, sensor measurements suffer from limited range, occlusions,
and sensor noise. These challenges become more evident in dynamic environments,
where efficiently inferring the state of the environment based on sensor
readings from different times is still an open problem. This work focuses on
inferring the state of the dynamic part of the environment, i.e., where dynamic
objects might be, based on previous observations and constraints on their
dynamics. We formalize the problem and introduce Transitional Grid Maps (TGMs),
an efficient analytical solution. TGMs are based on a set of novel assumptions
that hold in many practical scenarios. They significantly reduce the complexity
of the problem, enabling continuous prediction and updating of the entire
dynamic map based on the known static map (see Fig.1), differentiating them
from other alternatives. We compare our approach with a state-of-the-art
particle filter, obtaining more prudent predictions in occluded scenarios and
on-par results on unoccluded tracking.
