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In this paper, we consider the problem of online asymptotic varianceestimation for particle filtering and smoothing. Current solutions for theparticle filter rely on the particle genealogy and are either unstable or hardto tune in practice. We propose to mitigate these limitations by introducing anew estimator of the asymptotic variance based on the so called backwardweights. The resulting estimator is weakly consistent and trades computationalcost for more stability and reduced variance. We also propose a morecomputationally efficient estimator inspired by the PaRIS algorithm of Olsson &Westerborn. As an application, particle smoothing is considered and anestimator of the asymptotic variance of the Forward Filtering BackwardSmoothing estimator applied to additive functionals is provided.

Variance estimation for Sequential Monte Carlo Algorithms: a backward sampling approach