  This article considers the application of particle filtering to
continuous-discrete optimal filtering problems, where the system model is a
stochastic differential equation, and noisy measurements of the system are
obtained at discrete instances of time. It is shown how the Girsanov theorem
can be used for evaluating the likelihood ratios needed in importance sampling.
It is also shown how the methodology can be applied to a class of models, where
the driving noise process is lower in the dimensionality than the state and
thus the laws of state and noise are not absolutely continuous.
Rao-Blackwellization of conditionally Gaussian models and unknown static
parameter models is also considered.
