  This contribution is devoted to the comparison of various resampling
approaches that have been proposed in the literature on particle filtering. It
is first shown using simple arguments that the so-called residual and
stratified methods do yield an improvement over the basic multinomial
resampling approach. A simple counter-example showing that this property does
not hold true for systematic resampling is given. Finally, some results on the
large-sample behavior of the simple bootstrap filter algorithm are given. In
particular, a central limit theorem is established for the case where
resampling is performed using the residual approach.
