  In this paper, we consider the problem of online asymptotic variance
estimation for particle filtering and smoothing. Current solutions for the
particle filter rely on the particle genealogy and are either unstable or hard
to tune in practice. We propose to mitigate these limitations by introducing a
new estimator of the asymptotic variance based on the so called backward
weights. The resulting estimator is weakly consistent and trades computational
cost for more stability and reduced variance. We also propose a more
computationally efficient estimator inspired by the PaRIS algorithm of Olsson &
Westerborn. As an application, particle smoothing is considered and an
estimator of the asymptotic variance of the Forward Filtering Backward
Smoothing estimator applied to additive functionals is provided.
