Robust, reduced-order, nonstrictly proper state estimation via the optimal projection equations with guaranteed cost bounds

A state estimation design problem involving parametric plant uncertainties is considered. An estimation error bound suggested by multiplicative white-noise modeling is utilized for guaranteeing robust estimation over a specified range of parameter uncertainties. Necessary conditions that generalize the optimal projection equations for reduced-order state estimation are used to characterize the estimator that minimizes the error bound. The design equations thus effectively serve as sufficient conditions for synthesizing robust estimators. Additional features include the presence of a static estimation gain in conjunction with the dynamic (Kalman) estimator to obtain a nonstrictly proper estimator