On the Steady-State Solutions of Fixed-Interval and Fixed-Point Smoothers

Abstract

A Necessary and sufficient condition for the existence of a steady-state solution of the covariance equation is derived both for the fixed-interval smoother and fixed-point smoother. Such condition is expressed in a concise form employing the detectability and stabilizability of the related system and a unified conclusion is reached for these two smoothers.
Finally a computing algorithm to obtain such steady-state solution is introduced and it is demonstrated that the results of the filtering solution are directly applicable.