  For continuous-time linear stochastic dynamical systems driven by Wiener
processes, we consider the problem of designing ensemble filters when the
observation process is randomly time-sampled. We propose a continuous-discrete
McKean--Vlasov type diffusion process with additive Gaussian noise in
observation model, which is used to describe the evolution of the individual
particles in the ensemble. These particles are coupled through the empirical
covariance and require less computations for implementation than the optimal
ones based on solving Riccati differential equations. Using appropriate
analysis tools, we show that the empirical mean and the sample covariance of
the ensemble filter converges to the mean and covariance of the optimal filter
if the mean sampling rate of the observation process satisfies certain bounds
and as the number of particles tends to infinity.
