  Sequential Monte Carlo methods have been a major breakthrough in the field of
numerical signal processing for stochastic dynamical state-space systems with
partial and noisy observations. However, these methods still present certain
weaknesses. One of the most fundamental is the degeneracy of the filter due to
the impoverishment of the particles: the prediction step allows the particles
to explore the state-space and can lead to the impoverishment of the particles
if this exploration is poorly conducted or when it conflicts with the following
observation that will be used in the evaluation of the likelihood of each
particle. In this article, in order to improve this last step within the
framework of the classic bootstrap particle filter, we propose a simple
approximation of the one step fixed-lag smoother. At each time iteration, we
propose to perform additional simulations during the prediction step in order
to improve the likelihood of the selected particles.
