Particle filters for state space models with the presence of unknown static parameters

In this paper particle filters for dynamic state space models handling
unknown static parameters are discussed. The approach is based on
marginalizing the static parameters out of the posterior distribution
such that only the state vector needs to be considered. Such a
marginalization can always be applied. However, real-time applications
are only possible when the distribution of the unknown parameters given
both observations emph{and} the hidden state vector depends on some
low-dimensional sufficient statistics. Such sufficient statistics are
present in many of the commonly used state space models. Marginalizing
the static parameters avoids the problem of impoverishment which
typically occur when static parameters are included as part of the
state vector. The filters are tested on several different models, with
promising results.