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

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