The optimal reduced-order estimator for systems with singular measurement noise

The optimal reduced-order estimator is completely characterized by necessary conditions, resulting from the optimal projection equations. The solution consists of one Riccati equation and two Lyapunov equations coupled by two projections. Explicit expressions for all of the estimator parameters are given. The relation between the reduced-order singular estimator and the full-order optimal singular estimator (which is of reduced order itself) is investigated. It is shown that under certain conditions the optimal estimator is recovered from the reduced-order estimator