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

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 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 occurs when static parameters are included as part of the state vector. The filters are tested on several different models, with promising results.