Steady-state Kalman filtering with an H error bound

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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) estimators 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].

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    Citation Excerpt :

    In recent two decades, the state estimation problem has been extensively studied and has been found various applications in systems where states are unmeasurable. Kalman filtering technique, as one of the most distinguished ways to deal with the state estimation problem, has been fully studied [1,2]. However, Kalman filtering is based on the assumptions that the dynamics system under discussion is exactly known and its disturbances are stationary Gaussian noises with known statistics [3].

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Supported in part by the Air Force Office of Scientific Research under contract F49620-86-C-0002.

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