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.