On new smoothers for discrete-time linear stochastic systems with unknown disturbances

Abstract

We consider discrete-time linear stochastic systems with unknown disturbances and study two types of smoothing problems, i.e., the fixed-interval smoothing and the fixed-lag smoothing for those systems. We derive smoothing algorithms from the fixed-point smoothing algorithm proposed in the previous paper. It is shown that these algorithms reduce to the well known optimal smoothers derived from the Kalman filter when unknown inputs disappear.