Reduced-order multirate estimation for stable and unstable plants

An approach to designing reduced-order multirate estimators is presented. 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) estimator design 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 periodically time-varying systems of equations consisting of coupled Riccati/Lyapunov equations corresponding to each subinterval of the period