  Using a perturbation technique, we derive a new approximate filtering and
smoothing methodology generalizing along different directions several existing
approaches to robust filtering based on the score and the Hessian matrix of the
observation density. The main advantages of the methodology can be summarized
as follows: (i) it relaxes the critical assumption of a Gaussian prior
distribution for the latent states underlying such approaches; (ii) can be
applied to a general class of state-space models including univariate and
multivariate location, scale and count data models; (iii) has a very simple
structure based on forward-backward recursions similar to the Kalman filter and
smoother; (iv) allows a straightforward computation of confidence bands around
the state estimates reflecting the combination of parameter and filtering
uncertainty. We show through an extensive Monte Carlo study that the mean
square loss with respect to exact simulation-based methods is small in a wide
range of scenarios. We finally illustrate empirically the application of the
methodology to the estimation of stochastic volatility and correlations in
financial time-series.
