  Collision prediction in a dynamic and unknown environment relies on knowledge
of how the environment is changing. Many collision prediction methods rely on
deterministic knowledge of how obstacles are moving in the environment.
However, complete deterministic knowledge of the obstacles' motion is often
unavailable. This work proposes a Gaussian process based prediction method that
replaces the assumption of deterministic knowledge of each obstacle's future
behavior with probabilistic knowledge, to allow a larger class of obstacles to
be considered. The method solely relies on position and velocity measurements
to predict collisions with dynamic obstacles. We show that the uncertainty
region for obstacle positions can be expressed in terms of a combination of
polynomials generated with Gaussian process regression. To control the growth
of uncertainty over arbitrary time horizons, a probabilistic obstacle intention
is assumed as a distribution over obstacle positions and velocities, which can
be naturally included in the Gaussian process framework. Our approach is
demonstrated in two case studies in which (i), an obstacle overtakes the agent
and (ii), an obstacle crosses the agent's path perpendicularly. In these
simulations we show that the collision can be predicted despite having limited
knowledge of the obstacle's behavior.
