  This paper develops a probabilistic anticipation algorithm for dynamic
objects observed by an autonomous robot in an urban environment. Predictive
Gaussian mixture models are used due to their ability to probabilistically
capture continuous and discrete obstacle decisions and behaviors; the
predictive system uses the probabilistic output (state estimate and covariance)
of a tracking system, and map of the environment to compute the probability
distribution over future obstacle states for a specified anticipation horizon.
A Gaussian splitting method is proposed based on the sigma-point transform and
the nonlinear dynamics function, which enables increased accuracy as the number
of mixands grows. An approach to caching elements of this optimal splitting
method is proposed, in order to enable real-time implementation. Simulation
results and evaluations on data from the research community demonstrate that
the proposed algorithm can accurately anticipate the probability distributions
over future states of nonlinear systems.
