{"title":"Steady-state kalman filtering with an H∞ error bound","authors":"D. Bernstein, W. Haddad","doi":"10.1109/ACC.1989.4173324","DOIUrl":null,"url":null,"abstract":"An estimator design problem is considered which involves both L<sub>2</sub> (least squares) and H<sub>∞</sub> (worst-case frequency-domain) aspects. Specifically, the goal of the problem is to minimize an L<sub>2</sub> state-estimation error criterion subject to a prespecified H<sub>∞</sub> constraint on the state-estimation error. The H<sub>∞</sub> 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<sub>2</sub> state-estimation error. The principal result is a sufficient condition for characterizing fixed-order (i.e., full- and reduced-order) estimator with bounded L<sub>2</sub> and H<sub>∞</sub> estimation error. The sufficient condition involves a system of modified Riccati equations coupled by an oblique projection, i.e., idempotent matrix. When the H<sub>∞</sub> constraint is absent, the sufficient condition specializes to the L<sub>2</sub> state-estimation result given in [2]. The full version of this paper can be found in [10].","PeriodicalId":383719,"journal":{"name":"1989 American Control Conference","volume":"16 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1989-06-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"107","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"1989 American Control Conference","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/ACC.1989.4173324","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 107
Abstract
An estimator design problem is considered which involves both L2 (least squares) and H∞ (worst-case frequency-domain) aspects. Specifically, the goal of the problem is to minimize an L2 state-estimation error criterion subject to a prespecified H∞ 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 L2 state-estimation error. The principal result is a sufficient condition for characterizing fixed-order (i.e., full- and reduced-order) estimator with bounded L2 and H∞ 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 L2 state-estimation result given in [2]. The full version of this paper can be found in [10].