Steady - state K a l m a n filtering with an error b o u n d *

An estimator design problem is considered which involves both L 2 (least squares) and H ~ (worst-case frequency-domain) aspects. Specifically, the goal of the problem is to minimize an L 2 state-estimation error criterion subject to a prespecified H a constraint on the state-estimation error. The H ~ estimation-error constraint is embedded within the optimization process by replacing the covariance Lyapunov equation by a Riccati equation whose solution leads to an upper bound on the L 2 state-estimation error. The principal result is a sufficient condition for characterizing fixed-order (i.e., fulland reduced-order) estimators with bounded L 2 and H a estimation error. The sufficient condition involves a system of modified Riccati equations coupled by an oblique projection, i.e., idempotent matrix. When the H~ constraint is absent, the sufficient condition specializes to the L 2 state-estimation result given in [2].