  Sequential Monte Carlo (SMC) methods are a widely used set of computational
tools for inference in non-linear non-Gaussian state-space models. We propose a
new SMC algorithm to compute the expectation of additive functionals
recursively. Essentially, it is an online or forward-only implementation of a
forward filtering backward smoothing SMC algorithm proposed in Doucet .et .al
(2000). Compared to the standard path space SMC estimator whose asymptotic
variance increases quadratically with time even under favourable mixing
assumptions, the asymptotic variance of the proposed SMC estimator only
increases linearly with time. This forward smoothing procedure allows us to
implement on-line maximum likelihood parameter estimation algorithms which do
not suffer from the particle path degeneracy problem.
