In this paper we develop an approach to designing reduced-order multir
ate estimators. A discrete-time model that accounts for the multirate
timing sequence of measurements is presented and is shown to have peri
odically time-varying dynamics. Using discrete-time stability theory,
the optimal projection approach to fixed-order (i.e, full- and reduced
-order) estimation is generalized to obtain reduced-order periodic est
imators that account for the multirate architecture. It is shown that
the optimal reduced-order filter is characterized by means of a period
ically time-varying system of equations consisting of coupled Riccati
and Lyapunov equations. A novel homotopy algorithm, based on a Newton
correction scheme, is also presented which allows solutions to periodi
c difference Riccati equations.