Particle approximation improvement of the joint smoothing distribution with on-the-fly variance estimation

Particle smoothers are widely used algorithms allowing to approximate the smoothing distribution in hidden Markov models. Existing algorithms often suffer from slow computational time or degeneracy. We propose in this paper a way to improve any of them with a linear complexity in the number of particles. When iteratively applied to the degenerated Filter-Smoother, this method leads to an algorithm which turns out to outperform existing linear particle smoothers for a fixed computational time. Moreover, the associated approximation satisfies a central limit theorem with a close-to-optimal asymptotic variance, which be easily estimated by only one run of the algorithm.