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Particle smoothers are widely used algorithms allowing to approximate thesmoothing distribution in hidden Markov models. Existing algorithms oftensuffer from slow computational time or degeneracy. We propose in this paper away to improve any of them with a linear complexity in the number of particles.When iteratively applied to the degenerated Filter-Smoother, this method leadsto an algorithm which turns out to outperform existing linear particlesmoothers for a fixed computational time. Moreover, the associatedapproximation satisfies a central limit theorem with a close-to-optimalasymptotic variance, which be easily estimated by only one run of thealgorithm.

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