  In this paper we introduce a novel particle filter scheme for a class of
partially-observed multivariate diffusions. %continuous-time dynamic models
where the %signal is given by a multivariate diffusion process. We consider a
variety of observation schemes, including diffusion observed with error,
observation of a subset of the components of the multivariate diffusion and
arrival times of a Poisson process whose intensity is a known function of the
diffusion (Cox process). Unlike currently available methods, our particle
filters do not require approximations of the transition and/or the observation
density using time-discretisations. Instead, they build on recent methodology
for the exact simulation of the diffusion process and the unbiased estimation
of the transition density as described in \cite{besk:papa:robe:fear:2006}. %In
particular, w We introduce the Generalised Poisson Estimator, which generalises
the Poisson Estimator of \cite{besk:papa:robe:fear:2006}. %Thus, our filters
avoid the systematic biases caused by %time-discretisations and they have
significant computational %advantages over alternative continuous-time filters.
These %advantages are supported theoretically by a A central limit theorem is
given for our particle filter scheme.
