REDUCED-ORDER MULTIRATE ESTIMATION

In this paper we develop an approach to designing reduced-order multirate estimators. A discrete-time model that accounts for the multirate timing sequence of measurements is presented and is shown to have periodically 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 estimators that account for the multirate architecture. It is shown that the optimal reduced-order filter is characterized by means of a periodically 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 periodic difference Riccati equations.