Robust Filters for State Space Models

We consider the problem of recursive filtering in linear state-space models. The classically optimal Kalman filter (Kalman, 1960; Kalman and Bucy, 1961) is well known to be sensitive to outliers, so robustness is an issue. Several new filters have been implemented in R (R Development Core Team, 2005) within the R package robKalman (Ruckdeschel and Spangl, 2007) using the therein already available general recursive filter infrastructure. Within this framework the rLS (Ruckdeschel, 2001) and the ACM (Martin, 1979) filter have already been implemented, the latter as an equivalent realization of the filter implemented in Splus. While this ACM filter is bound to the univariate setting, based on Masreliez’s result (Masreliez, 1975) Spangl and Dutter (2008) propose a generalized ACM type filter for multivariate observations. This new filter has also been implemented in R within the robKalman package.