An Approach to Fixed-Point Smoothing Problems

This paper examines the possibility of deriving fixed-point smoothing algorithms through exploitation of the known solutions of a higher dimensional filtering problem. It is shown that a simple state augmentation serves to imbed the given n-dimensional smoothing problem into a 2n-dimensional filtering problem. It is further shown that computation of the smoothed estimate and the corresponding error covariance does not require implementation of the 2n-dimensional filtering equations. Some new results involving systems with or without multiple time delays and having colored observation noise have been derived in order to illustrate the versatility of the proposed technique. It is also demonstrated that the present approach leads to an easier derivation of the continuous-time fixed-point smoothing algorithm reported in the literature.